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| %%% Implements EL reasoning based on the (optimized) encoding described here: | ||
| %%% https://link.springer.com/article/10.1007/s10817-013-9296-3 | ||
| %%% The description of rules at the bottom reference the names from Figure 3. | ||
| %%% This ruleset normalises an EL ontology in OWL/RDF encoding. | ||
| %%% Unsupported OWL EL features include: oneOf, allDisjoint. | ||
| %%% The encoding used for property chains is also slightly antique. | ||
| %%% | ||
| %%% The ruleset computes facts for the following predicates: | ||
| %%% nf:isMainClass(?C): ?C is an "interesting" class (not just an auxiliary class expression) | ||
| %%% nf:isSubClass(?C): ?C occurs in a subclass position (i.e., negatively) | ||
| %%% nf:conj(?C,?D1,?D2): ?C is the conjunction of ?D1 and ?D2 | ||
| %%% nf:exists(?C,?P,?D): ?C is the existential restriction of property ?P with values from ?D | ||
| %%% nf:subClassOf(?C,?D): ?C is syntactically specified to be a subclass of ?D | ||
| %%% nf:subPropChain(?S1,?S2,?R): there was a role chain axiom ?S1 o ?S2 -> ?R | ||
| %%% nf:subProp(?R,?S): ?R is a subproperty of ?S (directly or indirectly) | ||
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| @prefix nf: <http://rulewerk.semantic-web.org/normalForm/> . | ||
| @prefix inf: <http://rulewerk.semantic-web.org/inferred/> . | ||
| @prefix owl: <http://www.w3.org/2002/07/owl#> . | ||
| @prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> . | ||
| @prefix sct: <http://www.ihtsdo.org/owlname#> . | ||
| @prefix xsd: <http://www.w3.org/2001/XMLSchema#> . | ||
| @prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> . | ||
| @prefix owl: <http://www.w3.org/2002/07/owl#> . | ||
| @prefix genid: <https://rulewerk.semantic-web.org/.well-known/genid/> . | ||
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| %%% This file assumes a normalized owl ontology to be present | ||
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| % nf:isMainClass(?C): ?C is an "interesting" class (not just an auxiliary class expression) | ||
| @import nf:isMainClass :- csv { resource = "../data/isMainClass.csv.gz" } . | ||
| % nf:isSubClass(?C): ?C occurs in a subclass position (i.e., negatively) | ||
| @import nf:isSubClass :- csv { resource = "../data/isSubClass.csv.gz" } . | ||
| % nf:conj(?C, ?D1, ?D1): ?C is the conjunction of ?D1 and ?D2 | ||
| @import nf:conj :- csv { resource = "../data/conj.csv.gz" } . | ||
| % nf:exists(?E, ?R, ?C): Every ?E has an ?R-relation to a ?C | ||
| @import nf:exists :- csv { resource = "../data/exists.csv.gz" } . | ||
| % nf:subClassOf(?C, ?D): Every member of ?C is a member of ?D | ||
| @import nf:subClassOf :- csv { resource = "../data/subClassOf.csv.gz" } . | ||
| % nf:subPropChain(?S1, ?S2, ?S): Roles ?S1 composed with ?S2 are a subproperty of the role ?S | ||
| @import nf:subPropChain :- csv { resource = "../data/subPropChain.csv.gz" } . | ||
| % nf:subProp(?R, ?S): Role ?R is a subproperty of the role ?S | ||
| @import nf:subProp :- csv { resource = "../data/subProp.csv.gz" } . | ||
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| %%% Inference rules | ||
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| % Start classification for all named classes | ||
| inf:init(?C) :- nf:isMainClass(?C) . | ||
| % R_init | ||
| inf:init(?C) :- inf:ex(?E, ?R, ?C) . | ||
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| % R_0: Every class is a sub class of itself | ||
| inf:subClassOf(?C, ?C) :- inf:init(?C) . | ||
| % R_\top: Every class is a sub class of owl:Thing | ||
| inf:subClassOf(?C, "<http://www.w3.org/2002/07/owl#Thing>") :- nf:isMainClass(?C) . | ||
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| % R_\sqcap^-: | ||
| % If ?C is contained in the intersection of ?D1 and ?D1, | ||
| % then ?C is contained in ?D1 and ?C is contained in ?D2. | ||
| inf:subClassOf(?C,?D1), inf:subClassOf(?C,?D2) :- inf:subClassOf(?C,?Y), nf:conj(?Y,?D1,?D2) . | ||
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| % R_\sqcap^+: | ||
| % If ?C is contained in ?D1 and ?D2, | ||
| % then ?C is contained in the intersection ?I of ?D1 ?D2 | ||
| inf:subClassOf(?C, ?I) :- | ||
| inf:subClassOf(?C, ?D1), inf:subClassOf(?C, ?D2), | ||
| nf:conj(?I, ?D1, ?D2), nf:isSubClass(?I) . | ||
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| % R_\exists^-: | ||
| % If every ?Y has an R-relation to a ?C | ||
| % and every ?E is a ?Y, | ||
| % then every ?E has an ?R-relation to a ?C | ||
| inf:ex(?E, ?R, ?C) :- inf:subClassOf(?E, ?Y), nf:exists(?Y, ?R, ?C) . | ||
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| % R_\exists^+: | ||
| % If every ?E has an ?R-relation to a ?C, | ||
| % and every ?C is a ?D, | ||
| % and ?R is a subproperty of ?S, | ||
| % then every ?E has an ?S-relation to a ?D | ||
| % (i.e. every ?E is an ?Y where ?Y is the class of | ||
| % of individuals that have an ?S-relation to a ?D) | ||
| inf:subClassOf(?E, ?Y) :- | ||
| inf:ex(?E, ?R, ?C), inf:subClassOf(?C, ?D), nf:subProp(?R, ?S), | ||
| nf:exists(?Y, ?S, ?D), nf:isSubClass(?Y) . | ||
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| % R_\circ: | ||
| % If ?E has an ?R1-relation to a ?C and ?C has an ?R2-relation to a ?D, | ||
| % and ?R1 is a subproperty of ?S1 and ?R2 is a subproperty of ?S2 | ||
| % then ?E has an ?S-relation to a ?D | ||
| inf:ex(?E, ?S, ?D) :- | ||
| inf:ex(?E, ?R1, ?C), inf:ex(?C, ?R2, ?D), | ||
| nf:subProp(?R1, ?S1), nf:subProp(?R2, ?S2), | ||
| nf:subPropChain(?S1, ?S2, ?S) . | ||
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| % R_\sqsubseteq: Transitive closure of the subclass-of relation | ||
| inf:subClassOf(?C,?E) :- inf:subClassOf(?C,?D), nf:subClassOf(?D,?E) . | ||
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| % R_\bot: If every ?E has an R-relation to a ?C but ?C is empty, then ?E is also empty | ||
| inf:subClassOf(?E, "<http://www.w3.org/2002/07/owl#Nothing>") :- | ||
| inf:ex(?E,?R,?C), inf:subClassOf(?C,"<http://www.w3.org/2002/07/owl#Nothing>") . | ||
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| %%% Extract final results for main classes | ||
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| mainSubClassOf(?A,?B) :- | ||
| inf:subClassOf(?A,?B), nf:isMainClass(?A), nf:isMainClass(?B) . | ||
| @import TRIPLE :- rdf { resource = "galen-el.nt.gz" } . | ||
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| %%% Mark classes: | ||
| ClassObject(owl:someValuesFrom) . | ||
| ClassObject(rdf:first) . | ||
| ClassObject(rdfs:subClassOf) . | ||
| ClassObject(owl:equivalentClass) . | ||
| ClassSubject(rdfs:subClassOf) . | ||
| ClassSubject(owl:equivalentClass) . | ||
| class(?O) :- TRIPLE(?X, ?P, ?O), ClassObject(?P) . | ||
| class(?X) :- TRIPLE(?X, ?P, ?O), ClassSubject(?P) . | ||
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| %%% Distinguish auxiliary class expressions from primary classes: | ||
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| % Mark auxiliary existential role restrictions: | ||
| synEx(?Y,?P,?X), auxClass(?X) :- TRIPLE(?X, owl:someValuesFrom, ?Y), TRIPLE(?X, owl:onProperty, ?P) . | ||
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| %%% Mark auxiliary conjunctions: | ||
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| next(?L1,?L2) :- TRIPLE(?L1,rdf:rest,?L2) . | ||
| first(?L1) :- TRIPLE(?X, owl:intersectionOf, ?L1) . | ||
| nonfirst(?L2) :- first(?L1), next(?L1,?L2) . | ||
| nonfirst(?L2) :- nonfirst(?L1), next(?L1,?L2) . | ||
| last(?Ln) :- next(?Ln,rdf:nil) . | ||
| nonlast(?L) :- next(?L,?Ln), last(?Ln) . | ||
| nonlast(?L1) :- next(?L1,?L2), nonlast(?L2) . | ||
| in(?L,?C) :- TRIPLE(?L,rdf:first,?C) . | ||
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| %%% Mark conjunctions: | ||
| synConj(?X,?C1,?C2), auxClass(?X) :- | ||
| TRIPLE(?X, owl:intersectionOf, ?L1), next(?L1,?L2), last(?L2), in(?L1,?C1), in(?L2,?C2) . | ||
| synConj(?X,?C1,?L2), auxClass(?X) :- | ||
| TRIPLE(?X, owl:intersectionOf, ?L1), next(?L1,?L2), nonlast(?L2), in(?L1,?C1) . | ||
| synConj(?L1,?C1,?L2), auxClass(?L1) :- | ||
| nonfirst(?L1), next(?L1,?L2), nonlast(?L2), in(?L1,?C1) . | ||
| synConj(?L1,?C1,?C2), auxClass(?L1) :- | ||
| nonfirst(?L1), next(?L1,?L2), last(?L2), in(?L1,?C1), in(?L2,?C2) . | ||
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| %%% The other classes are "main classes" that are not normalised: | ||
| nf:isMainClass(?X) :- class(?X), ~auxClass(?X) . | ||
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| %%% Normalise auxiliary nested class expressions: | ||
| repOf(?X,?X) :- nf:isMainClass(?X) . % keep main classes unchanged | ||
| synExRep(?X,?P,?Rep) :- synEx(?Y,?P,?X), repOf(?Y,?Rep) . | ||
| nf:exists(!New,?P,?Rep) :- synExRep(?X,?P,?Rep) . | ||
| repOf(?X,?N) :- synExRep(?X,?P,?Rep), nf:exists(?N,?P,?Rep) . | ||
| % nf:exists(!New,?P,?Rep) :- synEx(?Y,?P,?X), repOf(?Y,?Rep) . | ||
| % repOf(?X,?N) :- synEx(?Y,?P), repOf(?Y,?Rep), nf:exists(?N,?P,?Rep) . | ||
| nf:conj(!New,?R1,?R2) :- synConj(?X,?C1,?C2), repOf(?C1,?R1), repOf(?C2,?R2) . | ||
| repOf(?X,?N) :- synConj(?X,?C1,?C2), repOf(?C1,?R1), repOf(?C2,?R2), nf:conj(?N,?R1,?R2) . | ||
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| %%% Extract old-style property chains: | ||
| nf:subPropChain(?S,?T,?R), nf:subProp(?R,?R) :- | ||
| TRIPLE(?L,rdfs:subPropertyOf,?R), TRIPLE(?L,owl:propertyChain,?L1), | ||
| in(?L1,?S), next(?L1,?L2), in(?L2,?T) . | ||
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| %%% Initialise subsumption axioms: | ||
| prepareSco(?X,?Y) :- TRIPLE(?X, rdfs:subClassOf, ?Y) . | ||
| prepareSco(?X,?Y), prepareSco(?Y,?X) :- TRIPLE(?X, owl:equivalentClass, ?Y) . | ||
| nf:subClassOf(?RX,?RY), nf:isSubClass(?RX) :- prepareSco(?X,?Y), repOf(?X,?RX), repOf(?Y,?RY) . | ||
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| %%% Initialise disjointness: | ||
| nf:subClassOf(!C,owl:Nothing), nf:conj(!C,?X,?Y), nf:isSubClass(!C), nf:isSubClass(?X), nf:isSubClass(?Y) | ||
| :- TRIPLE(?X,owl:disjointWith,?Y) . | ||
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| %%% Mark classes in subclass position recursively: | ||
| nf:isSubClass(?D) :- nf:exists(?C, ?P, ?D), nf:isSubClass(?C) . | ||
| nf:isSubClass(?C1), nf:isSubClass(?C2) :- nf:conj(?X, ?C1, ?C2), nf:isSubClass(?X) . | ||
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| %%% Precompute role hierarchy: | ||
| directSubProp(?R,?S) :- TRIPLE(?R,rdfs:subPropertyOf,?S) . | ||
| % Initialise role hierarchy only for roles in subclass positions: | ||
| nf:subProp(?P,?P) :- nf:exists(?C,?P,?D), nf:isSubClass(?C) . | ||
| nf:subProp(?R,?T) :- nf:subProp(?R,?S), directSubProp(?S,?T) . | ||
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| @export nf:isMainClass :- csv{format=(any), compression="gzip", resource="isMainClass.csv.gz"} . | ||
| @export nf:isSubClass :- csv{format=(any), compression="gzip", resource="isSubClass.csv.gz"} . | ||
| @export nf:conj :- csv{format=(any, any, any), compression="gzip", resource="conj.csv.gz"} . | ||
| @export nf:exists :- csv{format=(any, any, any), compression="gzip", resource="exists.csv.gz"} . | ||
| @export nf:subClassOf :- csv{format=(any, any), compression="gzip", resource="subClassOf.csv.gz"} . | ||
| @export nf:subPropChain :- csv{format=(any, any, any), compression="gzip", resource="subPropChain.csv.gz"} . | ||
| @export nf:subProp :- csv{format=(any, any), compression="gzip", resource="subProp.csv.gz"} . | ||
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