Academic Meta Tool Vocabulary

Axiom

Abstract base class for all AMT axioms.

Subclass of

rdfs:Class

Inference Axiom

Axiom that derives new edges from existing ones.

Subclass of

amt:Axiom

Inverse Axiom

Asserts that two roles are inverses of each other.

Note. Reasoning rule: if edge (a -antecedent-> b) exists with weight w, infer (b -inverse-> a) with weight w.

Subclass of

amt:InferenceAxiom

Role Chain Axiom

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).

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.

Subclass of

amt:InferenceAxiom

Subsumption Axiomadded since 2018

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.

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.

Subclass of

amt:InferenceAxiom

Integrity Axiom

Axiom that constrains which edge configurations are valid.

Subclass of

amt:Axiom

Disjoint Axiom

Asserts that two roles cannot simultaneously hold between the same pair of nodes.

Note. Consistency check: violated if both (a -role1-> b) and (a -role2-> b) exist.

Subclass of

amt:IntegrityAxiom

Self-Disjoint Axiom

Asserts that a role cannot hold between a node and itself.

Note. Consistency check: violated if any edge (a -role-> a) exists.

Subclass of

amt:IntegrityAxiom

Concept

A class of entities in the modelled domain (e.g. Person, Place).

Subclass of

rdfs:Class

Logic

A fuzzy logic operator used to combine weights in inference chains.

Subclass of

rdfs:Class

Reasoning Ruleadded since 2018

Informal but normative description of an inference or consistency rule.

Role

A typed relation between Concepts (e.g. connectedWith, partOf).

Subclass of

rdf:Property

logic

Fuzzy logic operator used to combine weights along the inference chain.

Domain

amt:InferenceAxiom

Range

amt:Logic

logic parameteradded since 2018

Numeric parameter for parametrised logics (e.g. gamma for Hamacher product).

Domain

amt:InferenceAxiom

Range

xsd:decimal

antecedent

Role whose inverse is being declared.

Domain

amt:InverseAxiom

Range

amt:Role

inverse

Inverse role of the antecedent.

Domain

amt:InverseAxiom

Range

amt:Role

antecedent 1

First role in a 2-step role chain (legacy form). Use amt:antecedents for chains of length n != 2.

Domain

amt:RoleChainAxiom

Range

amt:Role

antecedent 2

Second role in a 2-step role chain (legacy form).

Domain

amt:RoleChainAxiom

Range

amt:Role

antecedentsadded since 2018

Ordered RDF list of n roles forming the chain. Generalises antecedent1/antecedent2 to arbitrary chain length.

Domain

amt:RoleChainAxiom

Range

rdf:List

consequent

Role inferred between the first and last node of the chain.

Domain

amt:RoleChainAxiom

Range

amt:Role

sub-roleadded since 2018

The finer role. Every edge carrying it also carries the super-role.

Domain

amt:SubsumptionAxiom

Range

amt:Role

super-roleadded since 2018

The coarser role, implied by the sub-role at no lower weight.

Domain

amt:SubsumptionAxiom

Range

amt:Role

role 1

First role in a disjointness assertion.

Domain

amt:DisjointAxiom

Range

amt:Role

role 2

Second role in a disjointness assertion.

Domain

amt:DisjointAxiom

Range

amt:Role

role

Role declared as self-disjoint (irreflexive).

Domain

amt:SelfDisjointAxiom

Range

amt:Role

placeholder

Hint for the expected label format of instances of a Concept.

Domain

amt:Concept

Range

rdfs:Literal

arityadded since 2018

Either 'binary' (associative, can be applied pairwise) or 'n-ary' (must receive the full weight list at once).

Domain

amt:Logic

Range

xsd:string

formulaadded since 2018

Mathematical formula of the operator in plain notation (variables x, y for binary; x_1..x_n for n-ary).

Domain

amt:Logic

Range

xsd:string

is parametrisedadded since 2018

True if the operator requires an additional numeric parameter (provided via amt:logicParameter on the axiom).

Domain

amt:Logic

Range

xsd:boolean

recommended foradded since 2018

Free-text hint about typical use cases of the operator.

Domain

amt:Logic

Range

xsd:string

applies toadded since 2018

Domain

amt:ReasoningRule

Range

rdfs:Class

effectadded since 2018

Domain

amt:ReasoningRule

Range

xsd:string

preconditionadded since 2018

Domain

amt:ReasoningRule

Range

xsd:string

instance of

Links an individual node to its Concept.

Range

amt:Concept

weight

Fuzzy truth value in the closed interval [0, 1] attached to a quadruple.

Range

xsd:decimal

Disjoint Consistency Ruleadded since 2018

Applies to

amt:DisjointAxiom

Precondition

There exist edges (a -role1-> b) and (a -role2-> b) with weights > 0.

Effect

Report a consistency violation. Both edges contradict the disjointness assertion.

Inverse Inference Ruleadded since 2018

Applies to

amt:InverseAxiom

Precondition

There exists an edge (a -antecedent-> b) with weight w.

Effect

Add an edge (b -inverse-> a) with weight w. Mark the edge as inferred. Iterate to fixpoint.

Role Chain Inference Ruleadded since 2018

Applies to

amt:RoleChainAxiom

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}.

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.

Self-Disjoint Consistency Ruleadded since 2018

Applies to

amt:SelfDisjointAxiom

Precondition

There exists an edge (a -role-> a) with weight > 0.

Effect

Report a consistency violation. The role is asserted to be irreflexive.

Subsumption Inference Ruleadded since 2018

Applies to

amt:SubsumptionAxiom

Precondition

There exists an edge (a -subRole-> b) with weight w.

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.