@prefix amt: . @prefix rdf: . @prefix rdfs: . @prefix owl: . @prefix xsd: . @prefix skos: . @prefix dct: . @prefix fw: . # ============================================================================= # Academic Meta Tool (AMT) Ontology # Version: Leonard Edition (extended) # ============================================================================= # # This ontology formalises the AMT vocabulary including all classes, properties, # axiom structures and fuzzy logic operators. It is designed to be self- # describing: any tool that wants to consume or produce AMT-compliant data can # rely on this file alone, without needing to read implementation source code. # # The original AMT ontology defined only the class hierarchy; this version adds: # - formal property definitions with domain/range # - n-ary role chain axioms (in addition to the legacy 2-ary form) # - fuzzy logic operators with mathematical formulae # - reasoning rule descriptions for each axiom type # # ============================================================================= a owl:Ontology ; dct:title "Academic Meta Tool Ontology"@en ; rdfs:label "AMT"@en ; dct:description "Vocabulary and reasoning rules for fuzzy semantic networks."@en ; owl:versionInfo "Leonard Edition (extended)"@en ; dct:creator "Florian Thiery", "Martin Unold" ; dct:created "2018-01-19"^^xsd:date ; dct:license ; dct:source ; rdfs:seeAlso . # ============================================================================= # 1. Core classes # ============================================================================= amt:Concept a rdfs:Class ; rdfs:subClassOf rdfs:Class ; rdfs:label "Concept"@en ; rdfs:comment "A class of entities in the modelled domain (e.g. Person, Place)."@en . amt:Role a rdfs:Class ; rdfs:subClassOf rdf:Property ; rdfs:label "Role"@en ; rdfs:comment "A typed relation between Concepts (e.g. connectedWith, partOf)."@en . amt:Axiom a rdfs:Class ; rdfs:subClassOf rdfs:Class ; rdfs:label "Axiom"@en ; rdfs:comment "Abstract base class for all AMT axioms."@en . amt:InferenceAxiom a rdfs:Class ; rdfs:subClassOf amt:Axiom ; rdfs:label "Inference Axiom"@en ; rdfs:comment "Axiom that derives new edges from existing ones."@en . amt:IntegrityAxiom a rdfs:Class ; rdfs:subClassOf amt:Axiom ; rdfs:label "Integrity Axiom"@en ; rdfs:comment "Axiom that constrains which edge configurations are valid."@en . amt:RoleChainAxiom a rdfs:Class ; rdfs:subClassOf amt:InferenceAxiom ; rdfs:label "Role Chain Axiom"@en ; rdfs:comment "Asserts that a chain of roles implies a consequent role; supports both legacy 2-ary form (antecedent1/antecedent2) and n-ary form (antecedents as RDF list)."@en ; skos:note "Reasoning rule: if edges (a -r1-> b) and (b -r2-> c) exist with weights w1 and w2, infer (a -consequent-> c) with weight = logic(w1, w2). Generalises to n antecedents." . amt:InverseAxiom a rdfs:Class ; rdfs:subClassOf amt:InferenceAxiom ; rdfs:label "Inverse Axiom"@en ; rdfs:comment "Asserts that two roles are inverses of each other."@en ; skos:note "Reasoning rule: if edge (a -antecedent-> b) exists with weight w, infer (b -inverse-> a) with weight w." . amt:SubsumptionAxiom a rdfs:Class ; rdfs:subClassOf amt:InferenceAxiom ; rdfs:label "Subsumption Axiom"@en ; rdfs:comment "Asserts that one role is finer than another: every edge carrying the sub-role also carries the super-role, at no lower weight. A statement about roles, not about any pair of nodes."@en ; skos:note "Two readings. Entailment: if edge (a -subRole-> b) exists with weight w, infer (a -superRole-> b) with weight w. Redundancy elimination: if both (a -subRole-> b, w1) and (a -superRole-> b, w2) exist with w1 >= w2, the super-role edge is implied and may be suppressed. An implementation must offer entailment as its default and elimination as an option, because a consumer that does not know the role hierarchy needs every edge spelled out." . amt:DisjointAxiom a rdfs:Class ; rdfs:subClassOf amt:IntegrityAxiom ; rdfs:label "Disjoint Axiom"@en ; rdfs:comment "Asserts that two roles cannot simultaneously hold between the same pair of nodes."@en ; skos:note "Consistency check: violated if both (a -role1-> b) and (a -role2-> b) exist." . amt:SelfDisjointAxiom a rdfs:Class ; rdfs:subClassOf amt:IntegrityAxiom ; rdfs:label "Self-Disjoint Axiom"@en ; rdfs:comment "Asserts that a role cannot hold between a node and itself."@en ; skos:note "Consistency check: violated if any edge (a -role-> a) exists." . # ============================================================================= # 2. Properties for Concepts and Roles # ============================================================================= amt:placeholder a rdf:Property ; rdfs:label "placeholder"@en ; rdfs:comment "Hint for the expected label format of instances of a Concept."@en ; rdfs:domain amt:Concept ; rdfs:range rdfs:Literal . amt:instanceOf a rdf:Property ; rdfs:label "instance of"@en ; rdfs:comment "Links an individual node to its Concept."@en ; rdfs:range amt:Concept . # ============================================================================= # 3. Properties for RoleChainAxiom # ============================================================================= amt:antecedent1 a rdf:Property ; rdfs:label "antecedent 1"@en ; rdfs:comment "First role in a 2-step role chain (legacy form). Use amt:antecedents for chains of length n != 2."@en ; rdfs:domain amt:RoleChainAxiom ; rdfs:range amt:Role . amt:antecedent2 a rdf:Property ; rdfs:label "antecedent 2"@en ; rdfs:comment "Second role in a 2-step role chain (legacy form)."@en ; rdfs:domain amt:RoleChainAxiom ; rdfs:range amt:Role . amt:antecedents a rdf:Property ; rdfs:label "antecedents"@en ; rdfs:comment "Ordered RDF list of n roles forming the chain. Generalises antecedent1/antecedent2 to arbitrary chain length."@en ; rdfs:domain amt:RoleChainAxiom ; rdfs:range rdf:List . amt:consequent a rdf:Property ; rdfs:label "consequent"@en ; rdfs:comment "Role inferred between the first and last node of the chain."@en ; rdfs:domain amt:RoleChainAxiom ; rdfs:range amt:Role . amt:logic a rdf:Property ; rdfs:label "logic"@en ; rdfs:comment "Fuzzy logic operator used to combine weights along the inference chain."@en ; rdfs:domain amt:InferenceAxiom ; rdfs:range amt:Logic . amt:logicParameter a rdf:Property ; rdfs:label "logic parameter"@en ; rdfs:comment "Numeric parameter for parametrised logics (e.g. gamma for Hamacher product)."@en ; rdfs:domain amt:InferenceAxiom ; rdfs:range xsd:decimal . # ============================================================================= # 4. Properties for InverseAxiom # ============================================================================= amt:antecedent a rdf:Property ; rdfs:label "antecedent"@en ; rdfs:comment "Role whose inverse is being declared."@en ; rdfs:domain amt:InverseAxiom ; rdfs:range amt:Role . amt:inverse a rdf:Property ; rdfs:label "inverse"@en ; rdfs:comment "Inverse role of the antecedent."@en ; rdfs:domain amt:InverseAxiom ; rdfs:range amt:Role . # ============================================================================= # 4b. Properties for SubsumptionAxiom # ============================================================================= amt:subRole a rdf:Property ; rdfs:label "sub-role"@en ; rdfs:comment "The finer role. Every edge carrying it also carries the super-role."@en ; rdfs:domain amt:SubsumptionAxiom ; rdfs:range amt:Role . amt:superRole a rdf:Property ; rdfs:label "super-role"@en ; rdfs:comment "The coarser role, implied by the sub-role at no lower weight."@en ; rdfs:domain amt:SubsumptionAxiom ; rdfs:range amt:Role . # ============================================================================= # 5. Properties for DisjointAxiom and SelfDisjointAxiom # ============================================================================= amt:role1 a rdf:Property ; rdfs:label "role 1"@en ; rdfs:comment "First role in a disjointness assertion."@en ; rdfs:domain amt:DisjointAxiom ; rdfs:range amt:Role . amt:role2 a rdf:Property ; rdfs:label "role 2"@en ; rdfs:comment "Second role in a disjointness assertion."@en ; rdfs:domain amt:DisjointAxiom ; rdfs:range amt:Role . amt:role a rdf:Property ; rdfs:label "role"@en ; rdfs:comment "Role declared as self-disjoint (irreflexive)."@en ; rdfs:domain amt:SelfDisjointAxiom ; rdfs:range amt:Role . # ============================================================================= # 6. Properties for Quadruples (weighted edges) # ============================================================================= amt:weight a rdf:Property ; rdfs:label "weight"@en ; rdfs:comment "Fuzzy truth value in the closed interval [0, 1] attached to a quadruple."@en ; rdfs:range xsd:decimal . # ============================================================================= # 7. Logic class and operators # ============================================================================= amt:Logic a rdfs:Class ; rdfs:subClassOf rdfs:Class ; rdfs:label "Logic"@en ; rdfs:comment "A fuzzy logic operator used to combine weights in inference chains."@en . amt:formula a rdf:Property ; rdfs:label "formula"@en ; rdfs:comment "Mathematical formula of the operator in plain notation (variables x, y for binary; x_1..x_n for n-ary)."@en ; rdfs:domain amt:Logic ; rdfs:range xsd:string . amt:arity a rdf:Property ; rdfs:label "arity"@en ; rdfs:comment "Either 'binary' (associative, can be applied pairwise) or 'n-ary' (must receive the full weight list at once)."@en ; rdfs:domain amt:Logic ; rdfs:range xsd:string . amt:isParametrised a rdf:Property ; rdfs:label "is parametrised"@en ; rdfs:comment "True if the operator requires an additional numeric parameter (provided via amt:logicParameter on the axiom)."@en ; rdfs:domain amt:Logic ; rdfs:range xsd:boolean . amt:recommendedFor a rdf:Property ; rdfs:label "recommended for"@en ; rdfs:comment "Free-text hint about typical use cases of the operator."@en ; rdfs:domain amt:Logic ; rdfs:range xsd:string . # --- Operator instances ------------------------------------------------------ # Each operator is also an fw:PropagationMethod of the FW ontology # (http://w3id.org/fw_ontology/), so that a derived statement can name it as # its fw:hasMethod. fw:implementedBy points to the code at the tag of release # 0.6.0 (amt/logic.py), which does not change with later commits. amt:GoedelLogic a amt:Logic, fw:PropagationMethod ; fw:implementedBy ; rdfs:label "Gödel logic"@en ; rdfs:comment "Bottleneck semantics: the chain is as strong as its weakest link. Path length is ignored."@en ; amt:formula "min(x, y)" ; amt:arity "binary" ; amt:isParametrised false ; amt:recommendedFor "Curated mappings; chains where path length should not penalise the result. Good default for n=2 and n=3." . amt:ProductLogic a amt:Logic, fw:PropagationMethod ; fw:implementedBy ; rdfs:label "Product logic"@en ; rdfs:comment "Probabilistic conjunction: weights multiply along the chain. Penalises path length exponentially."@en ; amt:formula "x * y" ; amt:arity "binary" ; amt:isParametrised false ; amt:recommendedFor "Independent-evidence semantics. Best for n=2; can be too aggressive for chains with n >= 4." . amt:LukasiewiczLogic a amt:Logic, fw:PropagationMethod ; fw:implementedBy ; rdfs:label "Łukasiewicz logic"@en ; rdfs:comment "Bounded sum: max(x + y - 1, 0). Hard cutoff that collapses long chains to 0."@en ; amt:formula "max(x + y - 1, 0)" ; amt:arity "binary" ; amt:isParametrised false ; amt:recommendedFor "Strict reasoning at n=2. Practically unusable for n >= 4 because the result almost always becomes 0." . amt:EinsteinProduct a amt:Logic, fw:PropagationMethod ; fw:implementedBy ; rdfs:label "Einstein product"@en ; rdfs:comment "Soft multiplication, lying between Gödel and Product. Stricter than Gödel, gentler than Product."@en ; amt:formula "(x * y) / (2 - (x + y - x * y))" ; amt:arity "binary" ; amt:isParametrised false ; amt:recommendedFor "Automatically generated mappings of medium confidence. Good middle ground for n=3 and n=4." . amt:GeometricMean a amt:Logic, fw:PropagationMethod ; fw:implementedBy ; rdfs:label "Geometric mean"@en ; rdfs:comment "Aggregation operator: n-th root of the product. Path-length neutral; expresses average link quality."@en ; amt:formula "(x_1 * x_2 * ... * x_n)^(1/n)" ; amt:arity "n-ary" ; amt:isParametrised false ; amt:recommendedFor "Comparing inferences across different chain lengths. Recommended default for n >= 4. Note: not a t-norm in the strict sense." . amt:HamacherProduct a amt:Logic, fw:PropagationMethod ; fw:implementedBy ; rdfs:label "Hamacher product"@en ; rdfs:comment "Parametrised t-norm family. Sensitivity to path length is controlled by a gamma parameter."@en ; amt:formula "(x * y) / (gamma + (1 - gamma) * (x + y - x * y))" ; amt:arity "binary" ; amt:isParametrised true ; amt:recommendedFor "Research applications where path-length sensitivity should be tuned empirically. gamma = 1 equals Product; gamma < 1 stricter; gamma > 1 softer." . # ============================================================================= # 8. Reasoning rules (informal but machine-readable description) # ============================================================================= # # These are not OWL/RDFS axioms (RDFS cannot express arithmetic). They are # annotations that document what an AMT-compliant reasoner must do, so that # implementations in other languages can be derived from this file. # # ============================================================================= amt:ReasoningRule a rdfs:Class ; rdfs:label "Reasoning Rule"@en ; rdfs:comment "Informal but normative description of an inference or consistency rule."@en . amt:appliesTo a rdf:Property ; rdfs:label "applies to"@en ; rdfs:domain amt:ReasoningRule ; rdfs:range rdfs:Class . amt:precondition a rdf:Property ; rdfs:label "precondition"@en ; rdfs:domain amt:ReasoningRule ; rdfs:range xsd:string . amt:effect a rdf:Property ; rdfs:label "effect"@en ; rdfs:domain amt:ReasoningRule ; rdfs:range xsd:string . amt:RoleChainRule a amt:ReasoningRule ; rdfs:label "Role Chain Inference Rule"@en ; amt:appliesTo amt:RoleChainAxiom ; amt:precondition "There exists a sequence of edges e_1, ..., e_n such that e_i has role antecedents[i] and the target of e_i equals the source of e_{i+1}." ; amt:effect "Add a new edge from source of e_1 to target of e_n with role = consequent and weight = logic(weight(e_1), ..., weight(e_n)). Mark the edge as inferred. Iterate to fixpoint." . amt:InverseRule a amt:ReasoningRule ; rdfs:label "Inverse Inference Rule"@en ; amt:appliesTo amt:InverseAxiom ; amt:precondition "There exists an edge (a -antecedent-> b) with weight w." ; amt:effect "Add an edge (b -inverse-> a) with weight w. Mark the edge as inferred. Iterate to fixpoint." . amt:SubsumptionRule a amt:ReasoningRule ; rdfs:label "Subsumption Inference Rule"@en ; amt:appliesTo amt:SubsumptionAxiom ; amt:precondition "There exists an edge (a -subRole-> b) with weight w." ; amt:effect "Default (entailment) mode: add an edge (a -superRole-> b) with weight w. Mark the edge as inferred. Iterate to fixpoint. Minimal mode: apply no entailment, and after the fixpoint suppress every inferred edge (a -superRole-> b, w2) for which an edge (a -subRole-> b, w1) with w1 >= w2 exists. Never suppress an asserted edge; when w1 < w2 keep both, because a coarse relation derived along a strong path can be worth more than a fine relation derived along a weak one." . amt:DisjointRule a amt:ReasoningRule ; rdfs:label "Disjoint Consistency Rule"@en ; amt:appliesTo amt:DisjointAxiom ; amt:precondition "There exist edges (a -role1-> b) and (a -role2-> b) with weights > 0." ; amt:effect "Report a consistency violation. Both edges contradict the disjointness assertion." . amt:SelfDisjointRule a amt:ReasoningRule ; rdfs:label "Self-Disjoint Consistency Rule"@en ; amt:appliesTo amt:SelfDisjointAxiom ; amt:precondition "There exists an edge (a -role-> a) with weight > 0." ; amt:effect "Report a consistency violation. The role is asserted to be irreflexive." .