Contents

The question

If you ask who is authorized to prepare a value opinion in a particular country, you will get a list of categories: persons recognized by law, a regulator, a professional organization, or the market as qualified to carry out the valuation, along with the types of value they may give and for whom. Asking the same question about a second country yields a different kind of list, not merely different details. In the United States, the ladder is divided by the value and complexity of the property into Licensed, Certified Residential, and Certified General, with higher rungs left to private designations. In Germany, the division is based on purpose: an unprotected base title, a certification layer, a sworn public appointment for court use, and a separate statutory committee holding transaction data. In India, classification is by asset class; in Russia, by “direction.” Brazil does not restrict people: the engineering degree is the gate for engineering valuations under NBR 14653 (Associação Brasileira de Normas Técnicas 2019), though CNAI-registered real estate brokers issue market-value opinions under a COFECI resolution, a practice the engineering council contested in court (Conselho Federal de Corretores de Imóveis 2007); grading under the standard applies to the work. Japan has a single qualification, set at a high level through an examination, that applies in all cases.

This is not six arrangements of a single ladder; rather, it is six ontologies. Attempting to place them within one hierarchical structure would misrepresent five of them. The article therefore carries out two tasks: it maintains their distinctness, records each jurisdiction’s own ontology as stated, and adds annotations to each native class referencing a common ontology with a small number of facets. This way, comparisons are based on annotations, not names. The approach is faceted classification as used in library science (Ranganathan 1967). Each class is a point in several dimensions, and when comparing, one dimension is kept constant while others are examined.

The list presented is the Journal’s coverage of 134 jurisdictions, recorded using standards from the appendix to this issue’s article comparing international valuation standards (Craytor 2026). The term “jurisdiction” is used operationally to mean a separate valuation-regulatory system. It does not correspond one-to-one with sovereign states: Quebec is listed separately from Canada as it alone has a statutory order; Puerto Rico is separate from the United States because it functions as a separate licensing authority despite federal criteria; Dubai and Abu Dhabi are listed separately as each licenses its own valuers; and the Cayman Islands with Bermuda, and the OECS states, are each listed as a single entry: the OECS states because they share a currency union and a bank supervisor, the Cayman Islands and Bermuda because they share the same unregulated, RICS-led pattern (RICS is the Royal Institution of Chartered Surveyors). In quantitative sections, the observational unit is called a regime for this reason. The appendix provides, for each jurisdiction, the applicable standard and its legal status, whether a license or register acts as a gate to practice, all checked against primary sources. The current article also includes classes, facets, and entry paths. It examines what is required to reach the top of the profession in each country and how countries group when only that factor is considered.

Native ontologies and one reference ontology

In the case of the eight reference countries—the United States, Germany, France, the United Kingdom, Japan, Brazil, Spain and Italy—the list provides all the native classes in full, including the statutory tiers, the registers, the court lists, the certifications, the private designations, the public offices, and the open title in which the law offers no protection. For the other 126 jurisdictions, the record only gives the highest class applicable to commercial and residential work, as well as the main regulated or market-recognized classes identified in the research pass of Section 7; a complete listing will be carried out in the next stage of the work. This is by design a stage-one ontology of the apex class—the class that manages the profession in each jurisdiction—and the figures and tables should be read as describing that class and its entry path, not the whole ladder beneath it. We retain the native names and arrange the classes in a hierarchical structure based on a parent-child relationship (so that, for example, the MAI (Member of the Appraisal Institute) presupposes the Certified General). Table 1 shows the schema and Figure 1 displays the structure. The public offices—such as assessors, the French Direction de l’immobilier de l’État, the British Valuation Office Agency and the German Gutachterausschuss—are included since in a number of countries they are the class that has the regulated function, and a reader who is only interested in private practitioners can exclude them by means of one characteristic.

The apex class is chosen by one rule. It is the class that, in practice, controls commercial, institutional and court work and the reproduction of competence in the profession: not the highest statutory title where that title is empty of such work, and not a private designation unless it is the effective gate to it. Four kinds of exception are marked in the roster. Where the legal apex and the managing apex are different classes—the American Certified General and the MAI; the German sworn expert and the valuer certified for lending by HypZert (the German certifier of mortgage-lending valuers)—both are recorded, the roster carries an apex split facet, and the primary row—the one that enters the tables and the distance matrix—is the managing apex in every such regime, not only the American one. Where the apex is a firm rather than a person—the Spanish sociedad de tasación, the Pakistani and Bangladeshi bank panels—the row records the firm’s gate and the person who signs within it. Where no legal apex exists and a professional body’s registration is the whole gate—the United Kingdom, the Netherlands, the Nordic authorizations—the row is marked market-only. And where the apex is a public office, it is kept in the same scheme. The rule is stated so that it can be applied by someone other than the author; the roster’s apex_note column records, for each regime, which class it selected and why.

The reference ontology annotates each class with the facets of Section 3. Comparison then yields three relations, and only these:

• Equivalent: two native classes carry the same effective level, the same asset and purpose scope, and the same enforcement source. A RICS Registered Valuer and a taxateur on the NRVT (Nederlands Register Vastgoed Taxateurs, the Dutch valuers’ register) are equivalent.

• Analogous: the same function under a different constitution or enforcement. The American Certified General appraiser who holds the MAI and the German öffentlich bestellter und vereidigter Sachverständiger are analogous: both are the effective gate to litigation and institutional work; one is a private designation enforced as a matter of practice by lenders, agencies and courts, which weigh it as a credential; the other a chamber appointment under § 36 of the Trade Regulation Act. Most of what is useful in the comparison is of this kind.

• No counterpart: a facet value one jurisdiction fills and another leaves empty. Japan and France have no restricted residential appraiser class; the United States has no court tier in law; Brazil grades no persons.

Because the relations are computed from the annotations rather than declared class to class, adding a regime never requires revisiting the mappings of the others. That is what makes the full roster tractable.

The facets

Scope level and status, read twice

The central facets describe what a class holder may sign. They are not one ladder. The first is an ordinal scope level:

The remaining two are status facets, existing independently of the scope level and of one another: regulated-purpose—this involves being admitted to a supervised register for lending, taxation, expropriation, insolvency, or fund valuation; and court or sworn—this means being listed, sworn in, or appointed as an expert with a legal status different from that of an ordinary witness. A sworn court expert is not a higher category than a lending-register valuer, nor is the lending-register valuer a higher category than a sworn court expert; they are instead separate branches. The Spanish signatory for a sociedad de tasación has regulated-purpose status but not court status; the German öffentlich bestellter und vereidigter Sachverständiger has court status and, in the case of lending, requires the additional qualification under the BelWertV (Mortgage Lending Value Regulation); the Japanese appraiser has both of these on a single credential. The data file still labels the two status facets L3 (regulated purpose) and L4 (court or sworn), a holdover from an earlier draft that treated all five as one ladder. Nevertheless, no order is claimed between L2 and the two status facets or between the status facets themselves. What is stated is only a partial order: each status requires at least L2.

Each class exhibits these aspects twice. The de jure annotation records the level at which the law permits the holder to sign. In contrast, the de facto annotation is the level to which the market actually admits the holder, together with the body that enforces this requirement: statute, a court, a financial regulator, lender panels, institutional clients, a professional body, or no one at all. The distinction is not a mere refinement; it is where the comparison takes place. The MAI contributes nothing legally to the Certified General license, yet it serves as the effective gateway to high-value commercial, institutional, eminent-domain, and litigation work. The German HypZert certification is a private qualification and the usual way lenders meet the Mortgage Lending Value Regulation (BelWertV), which presumes the competence of valuers appointed or certified by a state or accredited body (§ 6). The British MRICS (Member of the RICS) has little legal significance (a few statutes name RICS membership, such as the Charities Act 2011, s. 119(3)) but is, in practice, highly important: it confers no statutory power to sign and, at the same time, is widely treated as the gateway to institutional assignments. Comparisons between different systems are therefore based on the de facto annotation, and the de jure annotation is retained since the fact that the effective gateway is set out in a statute, in a regulator’s rule, or only in client practice is itself a classifying feature.

Constitution, specialty, generality

Three further facet groups complete the scheme. Constitution records how a class exists: statutory tier, register, court list, certification, private designation, public office, open title, firm license, or—Brazil’s case—an assignment grade that attaches to the report rather than the person. It also records the axis on which the jurisdiction cuts its ladder (value, asset, purpose, private seniority, none, or the assignment) and whether a court tier exists at all.

Specialty is a separate axis because practitioners specialize along four lines: by asset (office, hotel, vineyard, aircraft, plant), by interest (a fractional-interest specialist may value any asset class; leased fee, easement, and air-rights work are specialties similarly), by purpose (right of way, federal acquisition under the Yellow Book (the Uniform Appraisal Standards for Federal Land Acquisitions), litigation, relocation, conservation easements), and by abstract categories like going-concern allocation and partial-interest discounts. Each specialty is recorded with its formality: statutory license class, private credential, or reputation only. In the United States, specialties form the ladder’s real upper structure, and almost none is in license law; in India and Russia specialty is the primary legal axis, and in the Netherlands it is the primary axis of the professional register (the NRVT chambers).

Generality—whether a practitioner does many kinds of work or one—is a characteristic of persons, not of classes, and the record cannot hold its distribution. What it records is which way the regime pushes: whether the license is per asset class (forced-specialist), covers everything (permitted-generalist), or the market is too small to specialize (generalist-by-necessity); where specialization happens (in the license, the firm, or the individual); and who polices competence for an assignment—the appraiser under a competency rule such as USPAP’s (The Appraisal Foundation 2024), the license class, or the licensed firm, as in a Spanish sociedad de tasación.

Two facets at the level of the jurisdiction

Two facts about the surrounding system predict much of the rest. Collateral demand records whether mortgage lending generates a per-loan appraisal by an independent appraiser. Where it does, an L1 tier for high-volume residential lending work tends to exist, and the practitioner count is high; where lending is underwritten largely on the borrower’s income and a guarantee, as in France, or on the public land-price system, as in Japan, the appraiser class begins at L2 and is small. Data regime records whether transaction prices are public. Collateral demand is, on the evidence of Section 5, closely associated with the size of a profession; the data regime is recorded but not yet analyzed. The two facets are the reason a French or Japanese practitioner count is not comparable with an American one without them.

Entry criteria

To compare the requirements needed to attain the highest level in the profession, we must break the gate down into its components. Each class has a structured entry record which includes an education gate, recorded as a category—either none, coursework hours, any bachelor’s degree, a particular degree, or a master’s—rather than as a score, so that a five-year engineering degree is not treated as if it were the result of an examination; an exam, with the rigor index ranging from 0 to 12 as given in Table 2, which is left blank if there is no such exam; supervised experience; a demonstration (in the form of a report, a portfolio, or a submitted Gutachten); an appointment (this consisting of an oath, a listing, or a decision by a chamber or court); and the number of years it takes to reach that level, which is accumulated along the parent chain. A marker indicating the highest class in each jurisdiction for commercial work and for residential work allows the path to be traced and the totals added up. It is in this way that the American total—the state’s ladder together with the Institute’s—can be compared with the German total (a degree, several years of practice, an examination before the chamber’s expert committee, public appointment, and an oath).

The rubric is a rubric, and its limit should be stated. A five percent pass rate among anyone who sits and a sixty-five percent pass rate among degree-holders who have completed three hundred hours of coursework are not the same selectivity. The education gate is kept beside the score rather than folded into it for that reason; the two are read together.

Table 3 gives the entry path for the eight regimes whose native ontologies are fully recorded, which serve as the reference points for the rest of the roster.

Three things stand out before adding the rest of the roster. The United States is the only regime where the effective top requires passing two independent systems, the state’s and a private body’s, and the only one where a bachelor’s degree in any field satisfies the education criterion. Japan and Brazil are extremes on opposite sides: Japan has no education requirement and a two-stage exam that fewer than one in fifteen candidates completes; Brazil requires a five-year degree and no valuation exam—both produce a single top class valuing a house and a refinery alike. Practitioners per capita split the eight into two groups by a factor of three: about twenty per 100,000 where lending demands a per-loan appraisal, and five to seven where it is moderate or absent. The collateral-demand facet predicts the count.

The roster: what the annotations show

Appendix 8.1 sets out the entry path for every jurisdiction in the roster. Its license and status columns are the facts verified for the standards appendix; its education, examination, years, and count columns were first entered from the author’s knowledge and then checked, in the research pass described in Section 7, against the regulator’s own statement, and every row carries a confidence grade. When the 134 rows are read across, the annotations support four statements.

The education gate is a specific degree almost everywhere.

Of the 115 regimes whose education requirement is known, 96 call for a degree in a named field—engineering, architecture, surveying, real estate, economics—or for a named accredited program. Any bachelor’s degree is accepted in only three: the United States, under the Appraiser Qualifications Board’s 2026 criteria (Appraiser Qualifications Board 2026a) (an exposure draft of 2026 proposes removing the degree requirement altogether (Appraiser Qualifications Board 2026b)); Canada outside Quebec; and Puerto Rico. Two regimes impose no educational requirement whatsoever and rely on the examination alone as the gate, namely Japan and South Korea. Four require a master’s degree, either in practice or for the highest level: France, Luxembourg, Poland, and Estonia. Ten make a course or a diploma, rather than a degree, the gate—Switzerland’s federal Fachausweis, the Nordic valuer programs, Hungary’s vocational qualification, and the diplomas issued by the regulators themselves in Dubai, Bahrain, Kuwait and Jordan. Twenty-eight regimes require a degree but no valuation examination at all; these are the engineering-discipline and bank-register countries, most of Latin America, and the Iberian Peninsula, and in their case selectivity rests entirely on the degree.

Examination rigor peaks in East Asia.

On the index, Japan scores 11, South Korea and Taiwan 10, followed by the American MAI comprehensive examination and the German chamber examination at 9; Austria, Slovenia, China and Israel at 8; and Poland, Czechia, Slovakia and Vietnam at 7. The American state examination scores 1. Taiwan is the most selective regime on both dimensions at the same time: it follows the Japanese examination model—the Examination Yuan’s essay examination covering property law, land law, real-estate economics, investment analysis and appraisal theory, with a pass rate that has usually remained below fifteen percent—and in addition it requires a related degree to sit the examination and two years of supervised practice before the practicing license is granted. Japan applies no degree-based eligibility filter before the examination; Taiwan does. For a question about whom a profession recruits, that is the difference between “anyone may try” and “only graduates may try.”

The regime types by count.

When each jurisdiction is assigned to the type implied by its effective gate and its source of enforcement (Table 4), the result is as follows: fifty state-constituted regimes with a prescribed method (twenty-two of them with a state examination and twenty-eight with a register on a degree); twenty-four chartered or professional-body regimes, the inheritance of the Commonwealth; twenty-four bank-supervisor registers, in which the panel of a financial regulator or of a bank association is the only gate; fourteen open-title regimes with body authorization, the French and Nordic pattern; seven engineering-discipline regimes; five state-administered regimes with no private profession; eight jurisdictions in which no valuer class could be found at all; and two of the American type, the United States and Puerto Rico (which share the AQB conduct license, not the private managing class above it). On this count, the American model is the rarest regime type in the roster: two regimes, against five for “state valuers only.”

Practitioner density is associated with collateral demand.

Wherever both quantities are known, the number of practitioners per 100,000 of population runs at about twenty where residential lending requires a per-loan appraisal as a matter of routine—the United States, the United Kingdom, Spain, Poland, Romania, the Netherlands, Australia—and at under eight where it is moderate or absent—Germany (moderate), France, Japan, Sweden, Taiwan, and nearly the whole of Africa and Asia. This association appears in the roster, not in a demonstrated function; the pattern is consistent with the hypothesis that demand for per-loan collateral appraisal, rather than the mode of regulation, governs the size of the profession. The hypothesis can be tested once practitioner counts have been filled in for the remainder of the roster.

Clusters and the map

The hand-assigned types A–G are a proposed classification, and the clustering in this section is not a test of it. The types were assigned on two facets—what constitutes the profession and who enforces the effective gate—so a distance matrix that includes the enforcement facet recovers the typology partly by construction. The question the clustering can answer is a narrower one: when only the entry recipe to the apex class is encoded, do the recipes fall into families, and are those families the ones the types predict? Each regime with at least two known entry facets—108 of the 126 regimes with a valuer class (the eight type-X jurisdictions have none)—was therefore encoded on five conceptual facets: the education gate (ordinal, five categories); the examination (the rigor index, and separately whether an examination exists); years to the top; the logarithm of practitioners per capita; and collateral demand. The enforcement indicators are excluded from the primary encoding and kept as a secondary one. A Gower distance (Gower 1971) (a measure of how different two regimes are, which can combine yes/no, ranked and numeric facets) was computed between every pair, with missing facets skipped pairwise; the weights are normalized per conceptual facet, one unit each, the examination’s unit split 0.75 to the index and 0.25 to its presence. Every pair also records \(n_{ij}\), the number of jointly observed variables: at least 4 of the 6 encoded variables for every pair and 5 at the median. We submitted the distance matrix to average-linkage hierarchical clustering and to two-dimensional metric multidimensional scaling (Kruskal and Wish 1978) (a placement of the regimes on a plane that keeps their distances as nearly as possible), and left out 18 regimes with fewer than two known facets because they would have clustered together on missingness alone. The hierarchy is cut at \(k = 7\) for direct comparison with the seven hand-assigned types; the cut is comparative, not data-optimized. Silhouette width measures how much closer each regime is to its own cluster than to the next; 1 is perfect. Cophenetic correlation measures how faithfully the tree keeps the original distances. Mean silhouette width is 0.43 at \(k = 2\), 0.49 at \(k = 5\) and 0.55 at \(k = 9\)–\(10\), and the cophenetic correlation is 0.74; but the \(k = 2\) cut merely isolates Japan and South Korea from everyone else, and the two families described below first separate at \(k = 5\), so the \(k = 7\) presentation adds only the small course-or-diploma and state-examination outlier groups to a structure that is already present at five. The per-regime file records the clusters at \(k = 4\) to \(8\).

Figure 2 shows the hand-assigned types with the roster as leaves. Figure 3 is the map; Figure 4 the hierarchy cut at seven, with membership in Table 5; and Table 6 the sensitivity of the principal groupings to restricting the run to H-confidence regimes and to near-complete cases.

Read against the hand-assigned types, the seven empirical clusters (Table 5) sort the entry recipes, not the types. The Adjusted Rand Index measures agreement between two groupings beyond chance; 0 is chance, 1 is identical. The Adjusted Rand Index between the types and the cut is 0.14 (Table 7), which is to say the clustering does not recover the typology; with the enforcement indicators added back it rises only to 0.27, and only under average linkage. What the recipes do fall into is the following. Cluster 1 is Japan and South Korea: no education gate and the two most rigorous examinations. Cluster 2 (thirteen regimes) is the degree-without-examination family—France, Belgium, Luxembourg, Sweden, the Southern Cone, Brazil, Portugal, Senegal—in which selectivity lies wholly in the degree and collateral demand is low. Clusters 3 and 4 (eleven regimes together) are the course-or-diploma gates: the Nordic and Gulf diplomas, Hungary, the Bahamas and Barbados, Switzerland—and Puerto Rico, whose any-bachelor’s gate and low-rigor state examination place it there. Cluster 6 is Belarus, China and Taiwan: a rigorous state examination, very few practitioners, no collateral demand.

The two large clusters are the finding, and it is not the one the types predicted. Cluster 5 (forty regimes) and cluster 7 (thirty-nine) are both centered on a specific degree, an examination and about four to five years; they differ in collateral demand (a mean of 2.0 on the three-point scale against 1.0), in examination rigor (4.1 against 5.4) and in practitioner density (about ten per 100,000 against five). Cluster 5 is the mortgage-market family: the Anglosphere—Canada, Australia, New Zealand, the United Kingdom, Ireland, Hong Kong, Malaysia—beside the Latin American and Gulf registers, India, Israel, Turkey, and the United States. Cluster 7 is the state-examination family with lower collateral demand: Germany, Austria, the post-Soviet certificates, the Balkans, Italy, Iran, Indonesia, the Philippines and much of Africa. Each of them mixes type A and type B regimes (13 and 13 in cluster 5; 26 and 9 in cluster 7), and in none of the three runs of Table 6 does more than half of the A and B regimes fall in one cluster (49, 48 and 43 percent; Table 6). On the entry recipe alone, then, the line between a ministry register and a chartered body is invisible, and the line that is visible runs between regimes whose lending system requires a per-loan appraisal as a matter of routine and regimes whose does not. It should be said plainly which facets draw that line: collateral demand and practitioner density move, examination rigor moves a little, and the education gate (2.98 against 3.03 on the five-point scale) and years (4.3 against 5.0) barely move at all. The split is a market-structure cut that the entry recipe carries, more than an entry-criteria cut in its own right, and it is subject to the same qualification as the density hypothesis of Section 5. It is a statement about the recipes, not about the legal or political systems, and it should be read as one.

The United States is not alone on these facets. In the primary encoding it sits in cluster 5 with Canada, the United Kingdom and Ireland as its nearest regimes (Gower distances 0.09, 0.12 and 0.13), and it shares a cluster with all three at every \(k\) from 2 to 10, and with Canada through \(k = 12\). Table 7 shows what produced the singleton reported in an earlier draft of this article: the United States separates from every other regime only when the enforcement indicators are in the matrix and the American apex is coded as Certified General plus MAI, and only under average linkage. Coded as the license-only Certified General, it joins the course-or-diploma clusters beside Puerto Rico (distance 0.04). The converse check is also in the robustness file. The roster’s primary row is the managing apex for every split regime; for Germany that is the chamber appointment, which controls court and institutional work, and the split is with the lending apex, the HypZert-certified valuer. Recoding Germany’s row to that lending apex (rigor index 5, four to six years; the second Germany line of Table 3) moves Germany’s nearest neighbors to Kazakhstan, Italy and Croatia and leaves the United States’ cluster unchanged at every \(k\). The American position is therefore a fact about one facet, not about the cluster space: the class the statute puts at the top and the class that manages the upper market are different classes. That split—recorded in the roster as apex split—is shared by fifteen other regimes (Germany for lending, Puerto Rico, France, Italy, Canada, Australia, India, Singapore, Hong Kong, Bahrain, Denmark, Hungary, Belgium, Luxembourg, Morocco), and a further seventeen have no legal apex at all. What is unusual in the United States, and in Puerto Rico, which shares its license and examination, is that the managing apex is a private designation, conferred by a body with no footing in licensing law, resting on the lowest-rigor state examination in the roster; that is visible in Table 3 without any clustering. Federal law recognizes such designations only in general terms: for the appraisal of a charitable gift, a qualified appraiser may be one who “has earned an appraisal designation from a recognized professional appraiser organization” (26 U.S.C. § 170(f)(11)(E)(ii)(I)) (United States Code 2026).

Two groupings the hand assignment expected do not survive, and are recorded as such. Japan, South Korea, and Taiwan split in every run: Taiwan’s degree gate and tiny practitioner count carry it to cluster 6. And the engineering-order pair Brazil–Costa Rica, and the Iberian pair Spain–Portugal, split in every run in which both appear, because on the entry recipe Brazil and Portugal have no examination while Costa Rica and Spain sit in the high-collateral register family.

What the data cannot yet say

The license and status facts underlying the roster were verified against primary sources by ten regional research passes recorded in the standards appendix. The columns this article adds—education gate, examination format and pass rate, years, practitioner count—were first set from the author’s knowledge and then checked in a research pass on 25 September 2026. This pass obtained, for 91 of the 134 jurisdictions, the regulator’s, board’s, chamber’s, or statute’s own statement of entry criteria; sources are recorded row by row in the Journal’s repository. The pass corrected the education gate in eleven regimes (from degree to course or diploma in Switzerland, Denmark, Dubai, Bahrain, Kuwait, Jordan, Barbados, among others), removed a supposed examination in five (Sweden, Portugal, Jordan, Ecuador, Venezuela), added one in three (Guatemala, El Salvador, Malta), and moved Guyana from a private register to a public office. Afterward, the roster is graded H for 99 jurisdictions, M for 31, and L for 4. What remains unverified is narrower and named: published pass rates for Israel, Poland, Vietnam, Turkey, India, and China (the last from a secondary source); grade-by-grade criteria of Sri Lanka’s institute; Peruvian, Belarusian, and Armenian entry rules, whose pages could not be read; and practitioner counts, blank for about half the roster either because no countable class exists—in an engineering-gate regime “appraiser” is not a class anyone counts—or because the regulator publishes a register without a total. The map in Figure 3 is thus a map of a checked table; its Kruskal Stress-1 of 0.180 on 108 points means it preserves the gross structure and not the fine distances, and the conclusions rest on the distance matrix, not the plane.

Two design decisions remain open and are recorded rather than settled. Public offices are kept in the same ontology as private practitioners because in several regimes they carry regulated-purpose or court status; readers who disagree can filter them by the kind facet. Specialties are listed in full only for the United States, where the author can vouch for them; for other regimes, only specialties formally recognized by law or credential are recorded.

The next steps are the ones the pass left: the published pass rates and the unread entry rules named above, and the promotion of the 126 summary rows to full native-ontology blocks, region by region.

Data and reproducibility

The data are three files in the Journal’s repository, directory docs/appraiser-regimes: ontology.yaml (the native ontologies of the eight reference regimes and the facet schema), roster-paths.tsv (one row per regime: the effective top class, education gate, rigor index, years, practitioners per 100,000, collateral demand, enforcement source, hand-assigned type, confidence, and the date of verification), and research-log.tsv (the source register of Appendix 8.2, also published online as Supplementary Table S1: one line per fetch, with the finding and the addresses). The license and status columns come from the standards appendix (Craytor 2026), verified against primary sources on 12 September 2026; we checked the entry-path columns on 25 September 2026. The scripts are analyze.py (encoding, Gower distance with the weights stated in Section 6, average-linkage clustering with SciPy, metric MDS with scikit-learn at seed 0, eight initializations and 600 iterations, Kruskal Stress-1 computed from the fitted configuration, the three sensitivity runs, and every figure of Section 6), ontology-tree.py and ontology-schema.py (Figures 2 and 1), and make-tables.py (every table). Versions: Python 3.14.4, NumPy 2.5.3, SciPy 1.18.1, scikit-learn 1.9.1, Matplotlib 3.11.2, adjustText 1.4.0. Running the four scripts from the data regenerates every figure and table in this article; the numbers quoted in the prose are listed at the head of the article source as the ones to re-derive after any change to the data.

Conclusion

The comparative record does not support treating national appraiser systems as versions of a single licensing ladder. Regimes divide valuation authority along different axes—property scope, asset class, regulated purpose, professional status, the assignment itself—and the effective gate may be imposed by statute, regulator, professional body, lender, court or client practice. This article keeps each regime’s ontology as the regime states it and compares only the annotations: the scope level and status, who enforces them, how the class is constituted, and what it takes to enter. When the entry recipe alone is encoded and weighted evenly, two large families emerge that cut across the types—a mortgage-market family and a state-examination family—and the line between a ministry register and a chartered body, which is a line about who signs the certificate, is not visible on what it takes to earn it.

The United States is not a type of its own on the entry recipe; it belongs with the Anglosphere and the other regimes whose lending systems demand a per-loan appraisal. Its peculiarity lies in one facet. The legal apex—a general license on a degree in any subject and an examination of low rigor—and the managing apex—the Appraisal Institute’s designations, enforced by lenders, agencies, institutional clients and courts, which weigh it as a credential—are different classes, and the second has no footing in licensing law. Other regimes split the apex too—between a chamber and a lender’s certifier, between a court list and a charter, and, in Canada, Australia and Hong Kong, between a statute and a professional body. The American case is the extreme of that last kind rather than a kind of its own: it and Puerto Rico, which shares its license and examination, alone combine a managing class with no footing in licensing law and a statutory examination beneath it that is the least rigorous in the roster. Whether that arrangement selects for the profession the country needs is a question the annotations pose and cannot answer.

The companion program (who-may-sign)

The method of Sections 3–6 is stated a second time below, as a Prolog program, so that it can be queried and contradicted rather than only read. The program is called who-may-sign, the name it will carry when it is moved to a repository of its own; for this issue it is published with the article. It has three parts. The file printed here, who_may_sign.pl, holds the rules: the closed vocabularies of the scheme; the reading of the source ladder as a scope level with two independent status facets, de jure and de facto; the apex rule of Section 2; the three relations equivalent, analogous and no counterpart; the regime types of Table 4, including the threshold that separates A1 from A2; the facet-normalized Gower distance of Section 6, recomputed from the roster; and every quantified claim the prose makes, each written as a quantified_claim/2 fact beside the computed/2 rule that derives it from the data. Two further files are generated from the data by make-facts.py and are not printed: roster_facts.pl, the 134 rows of Appendix 8.1 as facts, and reference_facts.pl, the sixty native classes of the eight reference regimes. check/0 succeeds only if every vocabulary is closed, every row is well formed, the reference ontology nowhere contradicts the roster’s apex-split facet, every type whose enforcer does not fit its definition is annotated as an exception, and every printed number agrees with its recomputation; claims_report/0 prints the claims beside the recomputed values. The three American distances of Section 6 are recomputed in Prolog to the two decimals printed there.

Trealla is the Journal’s Prolog; compatibility with SWI-Prolog and Scryer Prolog is maintained as a requirement, so the program is plain ISO Prolog with no construct peculiar to any one system. Six test suites of 257 tests (tests/) pass under all three; run-tests.sh runs them. The program, its fact files, the generator and the tests are published online as Supplementary File S2.

% SPDX-License-Identifier: AGPL-3.0-or-later
% Copyright (C) 2026 William Bert Craytor. Published by The Valuation Engineer
% Journal (Pacific Vista Net). This program is free software: you can
% redistribute it and/or modify it under the terms of the GNU Affero General
% Public License as published by the Free Software Foundation, either version 3
% of the License, or (at your option) any later version. It is distributed
% WITHOUT ANY WARRANTY, without even the implied warranty of MERCHANTABILITY or
% FITNESS FOR A PARTICULAR PURPOSE; see the COPYING file beside it or
% <https://www.gnu.org/licenses/agpl-3.0.html>.

/* who_may_sign.pl -- who-may-sign: the ontology of apex signing authority,
   in Prolog.

   PROJECT NAME.  "who-may-sign" is the name this program will carry when it
   moves to its own repository. The three files travel together:

     who_may_sign.pl      this file: the reference ontology, the apex rule,
                          the three cross-regime relations, the regime types,
                          the Gower distance on the entry recipe, and every
                          quantified claim the article prints, recomputed.
     roster_facts.pl      GENERATED: the 134 regimes, one row each.
     reference_facts.pl   GENERATED: the native ontologies of the eight
                          reference regimes (60 classes).

   Written for Vol. 1, Issue 2 of The Valuation Engineer, Comparative Practice
   department, item M1: "Who May Sign a Value Opinion: An Ontology of Apex
   Signing Authority in 134 Jurisdictions". The article's method is that no
   regime's classes are renamed to fit another's; each native class is
   ANNOTATED against one reference ontology of facets, and comparison is made
   on the annotations only. This file states that method as rules, so that
   the relations the article draws can be queried, and its numbers recomputed.

   Entry points:

     scope_level(?Class, ?L)           l0 | l1 | l2, de jure
     regulated_purpose(?Class)         status facet, de jure
     court_sworn(?Class)               status facet, de jure
     effective_scope(?Class, ?L)       the same three, read de facto
     effective_regulated_purpose(?Class)
     effective_court_sworn(?Class)
     effective_enforcers(?Class, ?Set) who imposes the de facto requirement
     legal_apex(?Regime, ?Class)       the statute's top class
     managing_apex(?Regime, ?Class)    the class that in practice manages the
                                       upper market (the ARTICLE'S apex rule)
     split_witnessed(?Regime)          the two differ in the reference ontology
     equivalent(?C1, ?C2)              the three relations of Section 2
     analogous(?C1, ?C2)
     no_counterpart(?Regime, ?Facet)
     regime_type(?Regime, ?Type)       a1 a2 b c d e f g x, from the hand type
     distance(?I, ?J, -D)              facet-normalized Gower, entry recipe only
     nearest(+J, +K, -Pairs)           the K nearest regimes, D-Regime pairs
     quantified_claim(?Id, ?Value)     what the article prints
     computed(?Id, -Value)             what the data give
     check                             every audit; true iff the program is clean
     claims_report                            print each claim beside its recomputation

   Plain ISO Prolog throughout. Trealla is the Journal's Prolog; SWI-Prolog and
   Scryer Prolog must pass the same tests (tests/, run-tests.sh). No modules,
   no format/2, no double-quoted strings, no library(lists) names: the few
   list helpers this file needs are defined at the end under their own names.

   Consult order:  roster_facts.pl, reference_facts.pl, who_may_sign.pl.       */

:- dynamic(range_cache/2).

/* ====================================================================== */
/* 1. CLOSED VOCABULARIES                                                 */
/* ====================================================================== */

/* Every fact value must be one of these. open_vocabulary/2 names any that is
   not, and check/0 fails on it. `unknown` is a value, not an absence: it says
   the research pass did not establish the facet.                              */

education_gate(none).  education_gate(coursework).  education_gate(any_bachelors).
education_gate(specific_degree).  education_gate(masters).  education_gate(unknown).

collateral_demand_value(high).  collateral_demand_value(med).
collateral_demand_value(low).   collateral_demand_value(unknown).

enforcer_token(statute).  enforcer_token(court).  enforcer_token(financial_regulator).
enforcer_token(lender_panels).  enforcer_token(institutional_clients).
enforcer_token(professional_body).  enforcer_token(state).  enforcer_token(none).
enforcer_token(government_agencies).  enforcer_token(counsel).

type_letter(a).  type_letter(b).  type_letter(c).  type_letter(d).
type_letter(e).  type_letter(f).  type_letter(g).  type_letter(x).

apex_split_value(none).  apex_split_value(split).  apex_split_value(market_only).
apex_split_value(unclear).  apex_split_value(unknown).

confidence_grade(h).  confidence_grade(m).  confidence_grade(l).

class_kind(statutory_tier).  class_kind(register).  class_kind(court_list).
class_kind(certification).  class_kind(designation).  class_kind(public_office).
class_kind(open_title).  class_kind(firm_licence).  class_kind(employment_role).
class_kind(assignment_grade).

ladder_level(l0).  ladder_level(l1).  ladder_level(l2).  ladder_level(l3).
ladder_level(l4).  ladder_level(unknown).

open_vocabulary(education(J, E))  :- education(J, E), \+ education_gate(E).
open_vocabulary(collateral(J, C)) :- collateral(J, C), \+ collateral_demand_value(C).
open_vocabulary(enforcer(J, T))   :- enforcer(J, T), \+ enforcer_token(T).
open_vocabulary(hand_type(J, T))  :- hand_type(J, T, _), \+ type_letter(T).
open_vocabulary(apex_split(J, S)) :- apex_split(J, S), \+ apex_split_value(S).
open_vocabulary(confidence(J, G)) :- confidence(J, G), \+ confidence_grade(G).
open_vocabulary(exam(J, E))       :- exam(J, E), \+ number(E), E \== none, E \== unknown.
open_vocabulary(class_kind(C, K)) :- class(C, _, _, K, _), \+ class_kind(K).
open_vocabulary(level(C, L))      :- class(C, _, _, _, L), \+ ladder_level(L).
open_vocabulary(class_enforcer(C, T)) :- class_enforcer(C, T), \+ enforcer_token(T).

/* Each regime carries each row facet exactly once. */
row_facet(education).  row_facet(exam).  row_facet(years).  row_facet(per_100k).
row_facet(collateral).  row_facet(hand_type).  row_facet(confidence).
row_facet(apex_split).  row_facet(verified).

facet_count(J, education, N)  :- tally(education(J, _), N).
facet_count(J, exam, N)       :- tally(exam(J, _), N).
facet_count(J, years, N)      :- tally(years(J, _, _), N).
facet_count(J, per_100k, N)   :- tally(per_100k(J, _), N).
facet_count(J, collateral, N) :- tally(collateral(J, _), N).
facet_count(J, hand_type, N)  :- tally(hand_type(J, _, _), N).
facet_count(J, confidence, N) :- tally(confidence(J, _), N).
facet_count(J, apex_split, N) :- tally(apex_split(J, _), N).
facet_count(J, verified, N)   :- tally(verified(J, _), N).

malformed_row(J, F) :- regime(J, _, _), row_facet(F), facet_count(J, F, N), N =\= 1.

dangling_parent(C, P) :- parent(C, P), \+ class(P, _, _, _, _).
parent_across_regimes(C, P) :- parent(C, P), class(C, R1, _, _, _), class(P, R2, _, _, _), R1 \== R2.
duplicate_class(C) :- class(C, _, _, _, _), tally(class(C, _, _, _, _), N), N > 1.

/* ====================================================================== */
/* 2. THE REFERENCE ONTOLOGY                                              */
/* ====================================================================== */

/* The source data carry a five-step ladder L0..L4. The article reads it as
   an ordinal SCOPE LEVEL (l0 trainee, l1 restricted, l2 general) and two
   STATUS facets that exist independently of it and of each other:
   regulated-purpose (the old L3) and court-or-sworn (the old L4). A sworn
   expert is not above a lending-register valuer; they are different branches. */

level_scope(l0, l0).  level_scope(l1, l1).  level_scope(l2, l2).
level_scope(l3, l2).  level_scope(l4, l2).

scope_level(C, S)      :- class(C, _, _, _, L), level_scope(L, S).
regulated_purpose(C)   :- class(C, _, _, _, l3).
court_sworn(C)         :- class(C, _, _, _, l4).

/* Read twice: de jure is what the law lets the holder sign; de facto is the
   level the market admits the holder to. Where the annotation carries no de
   facto level, the two coincide. The two STATUS facets are legal statuses --
   admission to a supervised register, a sworn or listed standing -- and the
   market cannot confer them; what it can do is admit a class to the WORK of
   that tier. An annotation of "L4-equivalent" on a private designation
   therefore raises the class's effective level on the ladder (and so makes it
   ANALOGOUS to a court list elsewhere) without making it court-sworn.        */

effective_level(C, L) :-                 % decided with L unbound, then unified:
    ( de_facto_level(C, L0) -> true      % a bound L must not skip the de facto clause
    ; class(C, _, _, _, L0) ),
    L = L0.

effective_scope(C, S)          :- effective_level(C, L), level_scope(L, S).
effective_regulated_purpose(C) :- regulated_purpose(C).
effective_court_sworn(C)       :- court_sworn(C).

market_equivalent(C, regulated_purpose) :- de_facto_level(C, l3), \+ regulated_purpose(C).
market_equivalent(C, court_sworn)       :- de_facto_level(C, l4), \+ court_sworn(C).

/* Who imposes the effective gate. An annotated class names its enforcers;
   an unannotated one is enforced by whoever constitutes it (constituted_by/2,
   Table 3's column: the state, the profession, the client, or no one).      */

default_enforcer(C, E) :-                % likewise decided before E is unified
    ( class(C, _, _, court_list, _)  -> E0 = court
    ; constituted_by(C, state)       -> E0 = statute
    ; constituted_by(C, profession)  -> E0 = professional_body
    ; constituted_by(C, client)      -> E0 = lender_panels
    ; constituted_by(C, none)        -> E0 = none ),
    E = E0.

effective_enforcers(C, Set) :-
    ( class_enforcer(C, _) -> findall(E, class_enforcer(C, E), Es), sort(Es, Set0)
    ; default_enforcer(C, E), Set0 = [E] ),
    Set = Set0.

/* A class that signs a price opinion and not an appraisal (a broker's
   estimate, a bank's internal formula) is in the ontology because the regime
   has it, but it is not an appraiser class and never a counterpart to one.  */

appraiser_class(C) :- class(C, _, _, _, _), \+ price_opinion_only(C).

level_rank(l0, 0).  level_rank(l1, 1).  level_rank(l2, 2).  level_rank(l3, 3).  level_rank(l4, 4).

/* ====================================================================== */
/* 3. THE APEX RULE                                                       */
/* ====================================================================== */

/* Section 2 of the article: the apex is the class that, in practice,
   controls commercial, institutional and court work and the reproduction of
   competence -- not the highest statutory title where that title is empty
   of such work, and not a private designation unless it is the effective
   gate to it. In the reference ontology the candidates are the classes
   marked top_for/2 (the class that manages each market). The MANAGING apex
   is the candidate with the highest effective level. A LEGAL apex is any
   state-constituted appraiser class of general scope that is a professional
   class and not a public office: the classes the statute places at the top.
   There may be several (a ministry register and a court list are not ranked
   against each other: the status facets are branches, not rungs). The apex
   is SPLIT when the managing apex is not one of them, and the regime is
   MARKET-ONLY when there is none.                                            */

apex_candidate(R, C) :- class(C, R, _, _, _), \+ \+ top_for(C, _).

state_constituted(C) :- constituted_by(C, state).

legal_apex(R, C) :-
    ref_regime(R), class(C, R, _, K, _), K \== public_office,
    appraiser_class(C), state_constituted(C), scope_level(C, l2).

managing_apex(R, C) :-
    ref_regime(R), apex_candidate(R, C), effective_level(C, L), level_rank(L, N),
    \+ ( apex_candidate(R, C2), C2 \== C, effective_level(C2, L2), level_rank(L2, N2), N2 > N ).

split_witnessed(R)       :- managing_apex(R, M), legal_apex(R, _), \+ legal_apex(R, M).
market_only_witnessed(R) :- managing_apex(R, _), \+ legal_apex(R, _).

ancestor(C, P) :- parent(C, P).
ancestor(C, A) :- parent(C, P), ancestor(P, A).

/* The roster's apex_split facet and the reference ontology must agree in the
   direction the reference ontology can speak to. It marks only the managing
   class of each market, so it witnesses a split only where a de facto
   annotation raises a class above its legal parent (the United States); the
   German, French and Italian splits of the roster rest on classes the
   ontology holds but does not rank against each other, and are not
   contradicted. A witnessed split must be on the row, and a witnessed
   market-only regime must be marked market-only.                            */
split_disagreement(R) :- split_witnessed(R), \+ apex_split(R, split).
split_disagreement(R) :- market_only_witnessed(R), \+ apex_split(R, market_only).

/* ====================================================================== */
/* 4. THE THREE RELATIONS                                                 */
/* ====================================================================== */

/* Only these three relations are drawn between regimes, and only on the
   annotations, never on the names.                                          */

/* EQUIVALENT: the same effective level, the same de jure scope and status,
   the same enforcers. ANALOGOUS: the same effective level -- the same job in
   the regime's division of work -- under a different constitution, a
   different status or a different enforcer. The MAI and the German o.b.u.v.
   are analogous: both are the gate to the upper market, one as a chamber's
   sworn list, the other as a private designation lenders and courts expect. */

status(C, Scope, Reg, Court) :-
    scope_level(C, Scope),
    ( regulated_purpose(C) -> Reg = yes ; Reg = no ),
    ( court_sworn(C) -> Court = yes ; Court = no ).

equivalent(C1, C2) :-
    appraiser_class(C1), appraiser_class(C2),
    class(C1, R1, _, _, _), class(C2, R2, _, _, _), R1 \== R2,
    effective_level(C1, L), effective_level(C2, L),
    status(C1, S, Reg, Court), status(C2, S, Reg, Court),
    effective_enforcers(C1, E), effective_enforcers(C2, E).

analogous(C1, C2) :-
    appraiser_class(C1), appraiser_class(C2),
    class(C1, R1, _, K1, _), class(C2, R2, _, K2, _), R1 \== R2,
    effective_level(C1, L), effective_level(C2, L), L \== unknown,
    status(C1, S1, Reg1, Court1), status(C2, S2, Reg2, Court2),
    effective_enforcers(C1, E1), effective_enforcers(C2, E2),
    ( ( K1 \== K2 ; E1 \== E2 ; S1-Reg1-Court1 \== S2-Reg2-Court2 ) -> true ),
    \+ equivalent(C1, C2).

no_counterpart(R, scope_level(S)) :-
    ref_regime(R), level_scope(_, S),
    \+ ( appraiser_class(C), class(C, R, _, _, _), effective_scope(C, S) ).
no_counterpart(R, regulated_purpose) :-
    ref_regime(R), \+ ( class(C, R, _, _, _), effective_regulated_purpose(C) ).
no_counterpart(R, court_sworn) :-
    ref_regime(R), \+ ( class(C, R, _, _, _), effective_court_sworn(C) ).

/* ====================================================================== */
/* 5. THE REGIME TYPES                                                    */
/* ====================================================================== */

/* Table 3 of the article. The types are hand-assigned on the annotations;
   the roster carries the letter. A1 and A2 are the two halves of type A: the
   article counts a state EXAMINATION as the gate where the rigor index is
   6 or more (a real examination, not a course assessment), and a register
   on a degree otherwise. That threshold reproduces the printed 22 / 28.    */

type_definition(a1, state,      'prescribed method; a state examination as the gate (rigor index >= 6)').
type_definition(a2, state,      'prescribed method; a ministry or regulator register on a degree').
type_definition(b,  profession, 'a chartered or professional body: accredited degree, body assessment, market-enforced registration').
type_definition(c,  profession, 'an engineering or architecture order: the professional degree and registration are the gate').
type_definition(d,  client,     'a bank-supervisor or bank-association register or panel is the only gate').
type_definition(e,  profession, 'no license and no protected title; a charter or body authorization').
type_definition(f,  state,      'state valuers; no private profession').
type_definition(g,  state,      'a statutory conduct license cut by value tier under the AQB criteria (Title XI, at lenders\' instance), no method prescribed').
type_definition(x,  none,       'no valuer class found').

a1_threshold(6).

rigor(J, R) :- exam(J, E), ( number(E) -> R = E ; R = 0 ).

regime_type(J, T) :- hand_type(J, T0, _), refine_type(J, T0, T1), T = T1.

refine_type(J, a, a1) :- rigor(J, R), a1_threshold(T), R >= T, !.
refine_type(_, a, a2) :- !.
refine_type(_, T, T).

/* Which enforcer tokens a type's gate is compatible with. The audit
   gate_inconsistent/1 lists every regime whose row names none of them; the
   four the roster contains are annotated as type_gate_exception/2 with the
   reason, and check/0 fails on any unannotated one.                          */

type_gate(a1, statute).  type_gate(a1, state).  type_gate(a1, court).  type_gate(a1, financial_regulator).
type_gate(a2, statute).  type_gate(a2, state).  type_gate(a2, court).  type_gate(a2, financial_regulator).
type_gate(b, professional_body).  type_gate(b, lender_panels).  type_gate(b, statute).  type_gate(b, institutional_clients).
type_gate(c, statute).  type_gate(c, professional_body).  type_gate(c, court).
type_gate(d, lender_panels).  type_gate(d, financial_regulator).  type_gate(d, statute).
type_gate(e, none).  type_gate(e, professional_body).  type_gate(e, institutional_clients).
type_gate(e, lender_panels).  type_gate(e, court).  type_gate(e, statute).  type_gate(e, financial_regulator).
type_gate(f, state).  type_gate(f, statute).
type_gate(g, statute).  type_gate(g, lender_panels).

gate_inconsistent(J) :-
    regime_type(J, T), T \== x,
    \+ ( enforcer(J, E), type_gate(T, E) ).

type_gate_exception(estonia,    'a professional body operates the register inside a statutory qualification framework; the framework is the state\'s, the examination the body\'s').
type_gate_exception(argentina,  'provincial engineering colleges constitute the profession; the Tribunal de Tasaciones de la Nacion (TTN) enforces for state work').
type_gate_exception(costa_rica, 'the financial regulator (SUGEF) is the only enforcer over a CFIA engineering register').
type_gate_exception(oecs_states, 'no enforcer found; the row is graded on the bank panels of the OECS states, whose statement was not read').

unannotated_gate_inconsistency(J) :- gate_inconsistent(J), \+ type_gate_exception(J, _).
stale_gate_exception(J)           :- type_gate_exception(J, _), \+ gate_inconsistent(J).

/* ====================================================================== */
/* 6. THE DISTANCE                                                        */
/* ====================================================================== */

/* analyze.py's primary encoding, reproduced: the entry recipe only, six
   variables in five facets, weights normalized per facet, Gower distance
   (range-scaled absolute difference for numeric variables, mismatch for the
   binary one), averaged over the variables both regimes have. Regimes with
   fewer than two known entry facets, and the eight type-X rows, are not
   analyzed, so that they do not cluster on missingness.                    */

edu_code(none, 0).  edu_code(coursework, 1).  edu_code(any_bachelors, 2).
edu_code(specific_degree, 3).  edu_code(masters, 4).
coll_code(low, 0).  coll_code(med, 1).  coll_code(high, 2).

known_entry(J, education) :- education(J, E), E \== unknown.
known_entry(J, exam)      :- exam(J, E), number(E).
known_entry(J, years)     :- years(J, Lo, _), number(Lo).
known_entry(J, per_100k)  :- per_100k(J, N), number(N).

known_count(J, N) :- tally(known_entry(J, _), N).

analyzed(J) :- hand_type(J, T, _), T \== x, known_count(J, N), N >= 2.

var_value(J, education, V)    :- education(J, E), edu_code(E, V).
var_value(J, exam, V)         :- rigor(J, V).
var_value(J, exam_present, V) :- rigor(J, R), ( R > 0 -> V = 1 ; V = 0 ).
var_value(J, years, V)        :- years(J, Lo, _), number(Lo), V = Lo.
var_value(J, per_100k, V)     :- per_100k(J, N), number(N), V is log(1 + N).
var_value(J, collateral, V)   :- collateral(J, C), coll_code(C, V).

numeric_var(education).  numeric_var(exam).  numeric_var(years).
numeric_var(per_100k).   numeric_var(collateral).
binary_var(exam_present).

weight(education, 1.0).  weight(exam, 0.75).  weight(exam_present, 0.25).
weight(years, 1.0).      weight(per_100k, 1.0).  weight(collateral, 1.0).

var_range(Var, R) :- range_cache(Var, R), !.
var_range(Var, R) :-
    numeric_var(Var),
    findall(V, ( analyzed(J), var_value(J, Var, V) ), Vs),
    max_of(Vs, Max), min_of(Vs, Min), R0 is Max - Min,
    ( R0 =:= 0 -> R = 1 ; R = R0 ),
    assertz(range_cache(Var, R)).

var_diff(Var, A, B, D) :- numeric_var(Var), var_range(Var, R), D is abs(A - B) / R.
var_diff(Var, A, B, D) :- binary_var(Var), D is abs(A - B).

distance(I, J, D) :-
    analyzed(I), analyzed(J),
    findall(W-Dv, ( weight(Var, W), var_value(I, Var, A), var_value(J, Var, B),
                    var_diff(Var, A, B, Dv) ), Pairs),
    ( Pairs == [] -> D = 1.0
    ; weighted_mean(Pairs, D) ).

shared_variables(I, J, N) :-
    tally(( weight(Var, _), var_value(I, Var, _), var_value(J, Var, _) ), N).

nearest(J, K, Nearest) :-
    findall(D-X, ( analyzed(X), X \== J, distance(J, X, D) ), Pairs),
    keysort(Pairs, Sorted), take(K, Sorted, Nearest).

nearest_names(J, K, Names) :- nearest(J, K, Pairs), strip_keys(Pairs, Names).

cluster_size(K, N) :- tally(cluster(_, K), N).

cluster_mean(K, Var, M) :-
    findall(V, ( cluster(J, K), var_value(J, Var, V) ), Vs),
    Vs \== [], sum_of(Vs, S), list_length(Vs, N), M is S / N.

same_cluster(I, J) :- cluster(I, K), cluster(J, K).

/* ====================================================================== */
/* 7. THE CLAIMS                                                          */
/* ====================================================================== */

/* Every quantified comparative claim the article prints, and how the data
   give it. check/0 fails if any recomputation disagrees. Lists are compared
   sorted; reals to the precision the prose uses.                            */

quantified_claim(regimes, 134).
quantified_claim(reference_regimes, 8).
quantified_claim(reference_classes, 60).

% Section 5: the education gate
quantified_claim(education_known, 115).
quantified_claim(education(specific_degree), 96).
quantified_claim(education(any_bachelors), 3).
quantified_claim(education(none), 2).
quantified_claim(education(masters), 4).
quantified_claim(education(coursework), 10).
quantified_claim(regimes_with(education(any_bachelors)), [canada, puerto_rico, united_states]).
quantified_claim(regimes_with(education(none)), [japan, south_korea]).
quantified_claim(regimes_with(education(masters)), [estonia, france, luxembourg, poland]).
quantified_claim(degree_and_no_exam, 28).

% Section 5: the rigor index
quantified_claim(max_rigor, 11).
quantified_claim(regimes_with(rigor(11)), [japan]).
quantified_claim(regimes_with(rigor(10)), [south_korea, taiwan]).
quantified_claim(regimes_with(rigor(9)), [germany, united_states]).
quantified_claim(regimes_with(rigor(8)), [austria, china, israel, slovenia]).
quantified_claim(regimes_with(rigor(7)), [czechia, poland, slovakia, vietnam]).
quantified_claim(private_rigorous_exam, [united_states]).   % rigor >= 9 and no statute behind it

% Section 5: the types
quantified_claim(type_count(a), 50).  quantified_claim(type_count(a1), 22).
quantified_claim(type_count(a2), 28).  quantified_claim(type_count(b), 24).
quantified_claim(type_count(c), 7).   quantified_claim(type_count(d), 24).
quantified_claim(type_count(e), 14).  quantified_claim(type_count(f), 5).
quantified_claim(type_count(g), 2).   quantified_claim(type_count(x), 8).
quantified_claim(regimes_with(type(g)), [puerto_rico, united_states]).

% Section 5 / abstract: the apex split facet
quantified_claim(apex_split(none), 89).   quantified_claim(apex_split(split), 16).
quantified_claim(apex_split(market_only), 17).  quantified_claim(apex_split(unclear), 4).
quantified_claim(other_split_regimes, 15).      % "fifteen other regimes split the apex"

% Section 6: the map
quantified_claim(analyzed, 108).
quantified_claim(left_out, 18).
quantified_claim(cluster_size(1), 2).   quantified_claim(cluster_size(2), 13).
quantified_claim(cluster_size(3), 7).   quantified_claim(cluster_size(4), 4).
quantified_claim(cluster_size(5), 40).  quantified_claim(cluster_size(6), 3).
quantified_claim(cluster_size(7), 39).
quantified_claim(cluster_mean(5, collateral), 2.0).
quantified_claim(cluster_mean(5, exam), 4.1).
quantified_claim(cluster_mean(7, collateral), 1.0).
quantified_claim(cluster_mean(7, exam), 5.4).
quantified_claim(cluster_of(united_states), 5).
quantified_claim(same_cluster(united_states, canada), yes).
quantified_claim(nearest(united_states), [canada, united_kingdom, ireland]).
quantified_claim(distance(united_states, canada), 0.09).
quantified_claim(distance(united_states, united_kingdom), 0.12).
quantified_claim(distance(united_states, ireland), 0.13).
quantified_claim(shared_variables_min, 4).
quantified_claim(shared_variables_max, 6).

% Section 7: the record
quantified_claim(verified_rows, 91).
quantified_claim(confidence(h), 99).  quantified_claim(confidence(m), 31).  quantified_claim(confidence(l), 4).

% Section 2 / Figure 2: what the reference ontology says
quantified_claim(no_counterpart(united_states, court_sworn), yes).
quantified_claim(no_counterpart(japan, scope_level(l1)), yes).
quantified_claim(split_witnessed(united_states), yes).
quantified_claim(market_only_witnessed(united_kingdom), yes).
quantified_claim(managing_apex(united_states), us_mai).
quantified_claim(legal_apex(united_states), [us_cert_gen]).
quantified_claim(legal_apex(france), [fr_evaluateur_opc, fr_expert_judiciaire]).   % the AMF fund-valuer register and the court list
quantified_claim(split_witnessed(france), yes).
quantified_claim(legal_apex(united_kingdom), []).
quantified_claim(analogous(us_mai, de_oebuv), yes).
quantified_claim(equivalent(us_mai, de_oebuv), no).

/* ---- recomputation --------------------------------------------------- */

computed(regimes, N)            :- tally(regime(_, _, _), N).
computed(reference_regimes, N)  :- tally(ref_regime(_), N).
computed(reference_classes, N)  :- tally(class(_, _, _, _, _), N).

computed(education_known, N)    :- tally(( education(_, E), E \== unknown ), N).
computed(education(G), N)       :- education_gate(G), tally(education(_, G), N).
computed(regimes_with(education(G)), L) :- findall(J, education(J, G), L0), sort(L0, L).
computed(degree_and_no_exam, N) :- tally(( education(J, specific_degree), rigor(J, 0) ), N).

computed(max_rigor, M)          :- findall(R, rigor(_, R), Rs), max_of(Rs, M).
computed(regimes_with(rigor(R)), L) :- findall(J, rigor(J, R), L0), sort(L0, L).
computed(private_rigorous_exam, L) :-
    findall(J, ( rigor(J, R), R >= 9, \+ enforcer(J, statute), \+ enforcer(J, state) ), L0), sort(L0, L).

computed(type_count(a), N)      :- tally(hand_type(_, a, _), N).
computed(type_count(T), N)      :- T \== a, type_definition(T, _, _), tally(regime_type(_, T), N).
computed(regimes_with(type(T)), L) :- findall(J, regime_type(J, T), L0), sort(L0, L).

computed(apex_split(S), N)      :- apex_split_value(S), tally(apex_split(_, S), N).
computed(other_split_regimes, N) :- tally(( apex_split(J, split), J \== united_states ), N).

computed(analyzed, N)           :- tally(analyzed(_), N).
computed(left_out, N)           :- tally(( hand_type(J, T, _), T \== x, \+ analyzed(J) ), N).
computed(cluster_size(K), N)    :- cluster_size(K, N).
computed(cluster_mean(K, V), M) :- cluster_mean(K, V, M0), M is round(M0 * 10) / 10.
computed(cluster_of(J), K)      :- cluster(J, K).
computed(same_cluster(I, J), A) :- ( same_cluster(I, J) -> A = yes ; A = no ).
computed(nearest(J), L)         :- nearest_names(J, 3, L).
computed(distance(I, J), D)     :- distance(I, J, D0), D is round(D0 * 100) / 100.
computed(shared_variables_min, N) :-
    findall(S, ( analyzed(I), analyzed(J), I @< J, shared_variables(I, J, S) ), Ss), min_of(Ss, N).
computed(shared_variables_max, N) :-
    findall(S, ( analyzed(I), analyzed(J), I @< J, shared_variables(I, J, S) ), Ss), max_of(Ss, N).

computed(verified_rows, N)      :- tally(( verified(_, D), D \== none ), N).
computed(confidence(G), N)      :- confidence_grade(G), tally(confidence(_, G), N).

computed(no_counterpart(R, F), A) :- ( no_counterpart(R, F) -> A = yes ; A = no ).
computed(split_witnessed(R), A)   :- ( split_witnessed(R) -> A = yes ; A = no ).
computed(market_only_witnessed(R), A) :- ( market_only_witnessed(R) -> A = yes ; A = no ).
computed(analogous(C1, C2), A)    :- ( analogous(C1, C2) -> A = yes ; A = no ).
computed(equivalent(C1, C2), A)   :- ( equivalent(C1, C2) -> A = yes ; A = no ).
computed(managing_apex(R), C)     :- managing_apex(R, C).
computed(legal_apex(R), L)        :- findall(C, legal_apex(R, C), L0), sort(L0, L).

/* A claim agrees with its recomputation when the two are identical, or both
   numbers within half a unit of the last printed digit.                      */

claim_disagrees(Id, Printed, Found) :-
    quantified_claim(Id, Printed),
    ( computed(Id, Found) -> true ; Found = no_recomputation ),
    \+ agrees(Printed, Found).

agrees(P, F) :- P == F, !.
agrees(P, F) :- number(P), number(F), abs(P - F) < 0.051, !.
agrees(P, F) :- number(P), number(F), integer(P), abs(P - F) < 0.5.

/* ====================================================================== */
/* 8. CHECK AND REPORT                                                    */
/* ====================================================================== */

check :-
    \+ open_vocabulary(_),
    \+ malformed_row(_, _),
    \+ dangling_parent(_, _),
    \+ parent_across_regimes(_, _),
    \+ duplicate_class(_),
    \+ split_disagreement(_),
    \+ unannotated_gate_inconsistency(_),
    \+ stale_gate_exception(_),
    \+ claim_disagrees(_, _, _).

claims_report :-
    ( quantified_claim(Id, P),
      ( computed(Id, F) -> true ; F = no_recomputation ),
      ( agrees(P, F) -> Mark = '   ' ; Mark = ' !!' ),
      write(Mark), write(' '), write(Id), write('  printed '), write(P),
      write('  found '), write(F), nl, fail
    ; true ),
    ( claim_disagrees(_, _, _) -> write('DISAGREEMENTS ABOVE'), nl ; write('all claims agree'), nl ).

/* ====================================================================== */
/* 9. LIST HELPERS (own names, so no library is assumed)                  */
/* ====================================================================== */

tally(Goal, N) :- findall(x, Goal, Xs), list_length(Xs, N).   % not count/2: the harness owns that name

list_length([], 0).                        % length/2 is a library predicate in Scryer, not a builtin
list_length([_ | Xs], N) :- list_length(Xs, N0), N is N0 + 1.

max_of([X | Xs], M) :- max_of_(Xs, X, M).
max_of_([], M, M).
max_of_([X | Xs], A, M) :- ( X > A -> max_of_(Xs, X, M) ; max_of_(Xs, A, M) ).

min_of([X | Xs], M) :- min_of_(Xs, X, M).
min_of_([], M, M).
min_of_([X | Xs], A, M) :- ( X < A -> min_of_(Xs, X, M) ; min_of_(Xs, A, M) ).

sum_of([], 0).
sum_of([X | Xs], S) :- sum_of(Xs, S0), S is S0 + X.

weighted_mean(Pairs, M) :- wsum(Pairs, 0, 0, SW, SWD), M is SWD / SW.
wsum([], SW, SWD, SW, SWD).
wsum([W-D | Ps], AW, AWD, SW, SWD) :- AW1 is AW + W, AWD1 is AWD + W * D, wsum(Ps, AW1, AWD1, SW, SWD).

take(0, _, []) :- !.
take(_, [], []) :- !.
take(N, [X | Xs], [X | Ys]) :- N1 is N - 1, take(N1, Xs, Ys).

strip_keys([], []).
strip_keys([_-V | Ps], [V | Vs]) :- strip_keys(Ps, Vs).

[title=References]

References