TPTP Axioms File: SWB003+0.ax
%------------------------------------------------------------------------------
% File : SWB003+0 : TPTP v8.2.0. Released v5.2.0.
% Domain : Semantic Web
% Axioms : RDFS
% Version : [Sch03] axioms : Especial.
% English :
% Refs : [Sch03] Schneider, M. (2011), Email to G. Sutcliffe
% Source : [Sch03]
% Names : axioms-rdfs-standard [Sch03]
% Status : Satisfiable
% Syntax : Number of formulae : 80 ( 62 unt; 0 def)
% Number of atoms : 108 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 28 ( 0 ~; 0 |; 8 &)
% ( 5 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 6 usr; 0 prp; 1-3 aty)
% Number of functors : 33 ( 33 usr; 33 con; 0-0 aty)
% Number of variables : 37 ( 37 !; 0 ?)
% SPC : FOF_SAT_EPR
% Comments :
%------------------------------------------------------------------------------
%----I(s p o) = true -> I(p) in IP
%----Note: the "iext" predicate seems to represent a true triple,
%----not quite the IEXT mapping [CHECK!]
fof(simple_iext_property,axiom,
! [S,P,O] :
( iext(P,S,O)
=> ip(P) ) ).
%----Set IR
%----The set IR is the set of all resources.
fof(simple_ir,axiom,
! [X] : ir(X) ).
%----Set LV
%----The set LV of all data values is a subset of IR.
fof(simple_lv,axiom,
! [X] :
( lv(X)
=> ir(X) ) ).
%----Axiomatic Triples for the Collection Vocabulary (Lists): rdf:first
fof(rdf_collection_first_type,axiom,
iext(uri_rdf_type,uri_rdf_first,uri_rdf_Property) ).
%----Axiomatic Triples for the Collection Vocabulary (Lists): rdf:nil
fof(rdf_collection_nil_type,axiom,
iext(uri_rdf_type,uri_rdf_nil,uri_rdf_List) ).
%----Axiomatic Triples for the Collection Vocabulary (Lists): rdf:rest
fof(rdf_collection_rest_type,axiom,
iext(uri_rdf_type,uri_rdf_rest,uri_rdf_Property) ).
%----Axiomatic Triples for the Container Vocabulary: rdf:_n
fof(rdf_container_n_type_001,axiom,
iext(uri_rdf_type,uri_rdf__1,uri_rdf_Property) ).
%----Axiomatic Triples for the Container Vocabulary: rdf:_n
fof(rdf_container_n_type_002,axiom,
iext(uri_rdf_type,uri_rdf__2,uri_rdf_Property) ).
%----Axiomatic Triples for the Container Vocabulary: rdf:_n
fof(rdf_container_n_type_003,axiom,
iext(uri_rdf_type,uri_rdf__3,uri_rdf_Property) ).
%----Axiomatic Triples for the Reification Vocabulary: rdf:object
fof(rdf_reification_object_type,axiom,
iext(uri_rdf_type,uri_rdf_object,uri_rdf_Property) ).
%----Axiomatic Triples for rdf:value--
fof(rdf_reification_predicate_type,axiom,
iext(uri_rdf_type,uri_rdf_value,uri_rdf_Property) ).
%----Axiomatic Triples for the Reification Vocabulary: rdf:subject
fof(rdf_reification_subject_type,axiom,
iext(uri_rdf_type,uri_rdf_subject,uri_rdf_Property) ).
%----IP and rdf:Property
fof(rdf_type_ip,axiom,
! [P] :
( iext(uri_rdf_type,P,uri_rdf_Property)
<=> ip(P) ) ).
%----Axiomatic Triple for rdf:type
fof(rdf_type_type,axiom,
iext(uri_rdf_type,uri_rdf_type,uri_rdf_Property) ).
%----Axiomatic Triple for rdf:type
fof(rdf_value_type,axiom,
iext(uri_rdf_type,uri_rdf_type,uri_rdf_Property) ).
fof(rdfs_annotation_comment_domain,axiom,
iext(uri_rdfs_domain,uri_rdfs_comment,uri_rdfs_Resource) ).
fof(rdfs_annotation_comment_range,axiom,
iext(uri_rdfs_range,uri_rdfs_comment,uri_rdfs_Literal) ).
fof(rdfs_annotation_isdefinedby_domain,axiom,
iext(uri_rdfs_domain,uri_rdfs_isDefinedBy,uri_rdfs_Resource) ).
fof(rdfs_annotation_isdefinedby_range,axiom,
iext(uri_rdfs_range,uri_rdfs_isDefinedBy,uri_rdfs_Resource) ).
fof(rdfs_annotation_isdefinedby_sub,axiom,
iext(uri_rdfs_subPropertyOf,uri_rdfs_isDefinedBy,uri_rdfs_seeAlso) ).
fof(rdfs_annotation_label_domain,axiom,
iext(uri_rdfs_domain,uri_rdfs_label,uri_rdfs_Resource) ).
fof(rdfs_annotation_label_range,axiom,
iext(uri_rdfs_range,uri_rdfs_label,uri_rdfs_Literal) ).
fof(rdfs_annotation_seealso_domain,axiom,
iext(uri_rdfs_domain,uri_rdfs_seeAlso,uri_rdfs_Resource) ).
fof(rdfs_annotation_seealso_range,axiom,
iext(uri_rdfs_range,uri_rdfs_seeAlso,uri_rdfs_Resource) ).
%----Definition of ICEXT
fof(rdfs_cext_def,axiom,
! [X,C] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) ).
%----IC and rdfs:Resource
fof(rdfs_class_instsub_resource,axiom,
! [C] :
( ic(C)
=> iext(uri_rdfs_subClassOf,C,uri_rdfs_Resource) ) ).
%----IC and rdfs:Resource
fof(rdfs_collection_first_domain,axiom,
iext(uri_rdfs_domain,uri_rdf_first,uri_rdf_List) ).
%----IC and rdfs:Resource
fof(rdfs_collection_first_range,axiom,
iext(uri_rdfs_range,uri_rdf_first,uri_rdfs_Resource) ).
fof(rdfs_collection_rest_domain,axiom,
iext(uri_rdfs_domain,uri_rdf_rest,uri_rdf_List) ).
fof(rdfs_collection_rest_range,axiom,
iext(uri_rdfs_range,uri_rdf_rest,uri_rdf_List) ).
fof(rdfs_container_alt_sub,axiom,
iext(uri_rdfs_subClassOf,uri_rdf_Alt,uri_rdfs_Container) ).
fof(rdfs_container_bag_sub,axiom,
iext(uri_rdfs_subClassOf,uri_rdf_Bag,uri_rdfs_Container) ).
%----rdfs:ContainerMembershipProperty
fof(rdfs_container_containermembershipproperty_instsub_member,axiom,
! [P] :
( icext(uri_rdfs_ContainerMembershipProperty,P)
=> iext(uri_rdfs_subPropertyOf,P,uri_rdfs_member) ) ).
fof(rdfs_container_containermembershipproperty_sub,axiom,
iext(uri_rdfs_subClassOf,uri_rdfs_ContainerMembershipProperty,uri_rdf_Property) ).
fof(rdfs_container_member_domain,axiom,
iext(uri_rdfs_domain,uri_rdfs_member,uri_rdfs_Resource) ).
fof(rdfs_container_member_range,axiom,
iext(uri_rdfs_range,uri_rdfs_member,uri_rdfs_Resource) ).
fof(rdfs_container_n_domain_001,axiom,
iext(uri_rdfs_domain,uri_rdf__1,uri_rdfs_Resource) ).
fof(rdfs_container_n_domain_002,axiom,
iext(uri_rdfs_domain,uri_rdf__2,uri_rdfs_Resource) ).
fof(rdfs_container_n_domain_003,axiom,
iext(uri_rdfs_domain,uri_rdf__3,uri_rdfs_Resource) ).
fof(rdfs_container_n_range_001,axiom,
iext(uri_rdfs_range,uri_rdf__1,uri_rdfs_Resource) ).
fof(rdfs_container_n_range_002,axiom,
iext(uri_rdfs_range,uri_rdf__2,uri_rdfs_Resource) ).
fof(rdfs_container_n_range_003,axiom,
iext(uri_rdfs_range,uri_rdf__3,uri_rdfs_Resource) ).
fof(rdfs_container_n_type_001,axiom,
iext(uri_rdf_type,uri_rdf__1,uri_rdfs_ContainerMembershipProperty) ).
fof(rdfs_container_n_type_002,axiom,
iext(uri_rdf_type,uri_rdf__2,uri_rdfs_ContainerMembershipProperty) ).
fof(rdfs_container_n_type_003,axiom,
iext(uri_rdf_type,uri_rdf__3,uri_rdfs_ContainerMembershipProperty) ).
fof(rdfs_container_seq_sub,axiom,
iext(uri_rdfs_subClassOf,uri_rdfs_Seq,uri_rdfs_Container) ).
fof(rdfs_dat_xmlliteral_sub,axiom,
iext(uri_rdfs_subClassOf,uri_rdf_XMLLiteral,uri_rdfs_Literal) ).
%----type of rdf:XMLLiteral
fof(rdfs_dat_xmlliteral_type,axiom,
iext(uri_rdf_type,uri_rdf_XMLLiteral,uri_rdfs_Datatype) ).
%----rdfs:Datatype and rdfs:Literal
fof(rdfs_datatype_instsub_literal,axiom,
! [D] :
( icext(uri_rdfs_Datatype,D)
=> iext(uri_rdfs_subClassOf,D,uri_rdfs_Literal) ) ).
%----rdfs:Datatype is a sub class of rdfs:Class
fof(rdfs_datatype_sub,axiom,
iext(uri_rdfs_subClassOf,uri_rdfs_Datatype,uri_rdfs_Class) ).
%----domain of rdfs:domain
fof(rdfs_domain_domain,axiom,
iext(uri_rdfs_domain,uri_rdfs_domain,uri_rdf_Property) ).
%----Semantic Condition for rdfs:domain
fof(rdfs_domain_main,axiom,
! [P,C,X,Y] :
( ( iext(uri_rdfs_domain,P,C)
& iext(P,X,Y) )
=> icext(C,X) ) ).
%----range of rdfs:domain
fof(rdfs_domain_range,axiom,
iext(uri_rdfs_range,uri_rdfs_domain,uri_rdfs_Class) ).
%----Definition of set IC based on class extensions of rdfs:Class
fof(rdfs_ic_def,axiom,
! [X] :
( ic(X)
<=> icext(uri_rdfs_Class,X) ) ).
%----Definition of set IR based on class extensions of rdfs:Resource
fof(rdfs_ir_def,axiom,
! [X] :
( ir(X)
<=> icext(uri_rdfs_Resource,X) ) ).
%----Definition of set LV based on class extensions of rdfs:Literal
fof(rdfs_lv_def,axiom,
! [X] :
( lv(X)
<=> icext(uri_rdfs_Literal,X) ) ).
%----type of rdf:Property (derivable RDFS-valid triple)
fof(rdfs_property_type,axiom,
iext(uri_rdf_type,uri_rdf_Property,uri_rdfs_Class) ).
%----domain of rdfs:range
fof(rdfs_range_domain,axiom,
iext(uri_rdfs_domain,uri_rdfs_range,uri_rdf_Property) ).
%----Semantic Condition for rdfs:range
fof(rdfs_range_main,axiom,
! [P,C,X,Y] :
( ( iext(uri_rdfs_range,P,C)
& iext(P,X,Y) )
=> icext(C,Y) ) ).
%----range of rdfs:range
fof(rdfs_range_range,axiom,
iext(uri_rdfs_range,uri_rdfs_range,uri_rdfs_Class) ).
fof(rdfs_reification_object_domain,axiom,
iext(uri_rdfs_domain,uri_rdf_object,uri_rdfs_Statement) ).
fof(rdfs_reification_object_range,axiom,
iext(uri_rdfs_range,uri_rdf_predicate,uri_rdfs_Resource) ).
fof(rdfs_reification_predicate_domain,axiom,
iext(uri_rdfs_domain,uri_rdf_predicate,uri_rdfs_Statement) ).
fof(rdfs_reification_predicate_range,axiom,
iext(uri_rdfs_range,uri_rdf_predicate,uri_rdfs_Resource) ).
fof(rdfs_reification_subject_domain,axiom,
iext(uri_rdfs_domain,uri_rdf_subject,uri_rdfs_Statement) ).
fof(rdfs_reification_subject_range,axiom,
iext(uri_rdfs_range,uri_rdf_subject,uri_rdfs_Resource) ).
%----domain of rdfs:subClassOf
fof(rdfs_subclassof_domain,axiom,
iext(uri_rdfs_domain,uri_rdfs_subClassOf,uri_rdfs_Class) ).
%----Main Semantic Conditions for rdfs:subClassOf
fof(rdfs_subclassof_main,axiom,
! [C,D] :
( iext(uri_rdfs_subClassOf,C,D)
=> ( ic(C)
& ic(D)
& ! [X] :
( icext(C,X)
=> icext(D,X) ) ) ) ).
%----range of rdfs:subClassOf
fof(rdfs_subclassof_range,axiom,
iext(uri_rdfs_range,uri_rdfs_subClassOf,uri_rdfs_Class) ).
%----Reflexivity of rdfs:subClassOf on IC
fof(rdfs_subclassof_reflex,axiom,
! [C] :
( ic(C)
=> iext(uri_rdfs_subClassOf,C,C) ) ).
%----Transitivity of rdfs:subClassOf on IC
fof(rdfs_subclassof_trans,axiom,
! [C,D,E] :
( ( iext(uri_rdfs_subClassOf,C,D)
& iext(uri_rdfs_subClassOf,D,E) )
=> iext(uri_rdfs_subClassOf,C,E) ) ).
%----domain of rdfs:subPropertyOf
fof(rdfs_subpropertyof_domain,axiom,
iext(uri_rdfs_domain,uri_rdfs_subPropertyOf,uri_rdf_Property) ).
%----Main Semantic Condition for rdfs:subPropertyOf
fof(rdfs_subpropertyof_main,axiom,
! [P,Q] :
( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X,Y] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) ) ) ).
%----range of rdfs:subPropertyOf
fof(rdfs_subpropertyof_range,axiom,
iext(uri_rdfs_range,uri_rdfs_subPropertyOf,uri_rdf_Property) ).
%----Reflexivity of rdfs:subPropertyOf on IP
fof(rdfs_subpropertyof_reflex,axiom,
! [P] :
( ip(P)
=> iext(uri_rdfs_subPropertyOf,P,P) ) ).
%----Transitivity of rdfs:subPropertyOf on IP
fof(rdfs_subpropertyof_trans,axiom,
! [P,Q,R] :
( ( iext(uri_rdfs_subPropertyOf,P,Q)
& iext(uri_rdfs_subPropertyOf,Q,R) )
=> iext(uri_rdfs_subPropertyOf,P,R) ) ).
%----domain of rdf:type
fof(rdfs_type_domain,axiom,
iext(uri_rdfs_domain,uri_rdf_type,uri_rdfs_Resource) ).
%----range of rdf:type
fof(rdfs_type_range,axiom,
iext(uri_rdfs_range,uri_rdf_type,uri_rdfs_Class) ).
fof(rdfs_value_domain,axiom,
iext(uri_rdfs_domain,uri_rdf_value,uri_rdfs_Resource) ).
fof(rdfs_value_range,axiom,
iext(uri_rdfs_range,uri_rdf_value,uri_rdfs_Resource) ).
%------------------------------------------------------------------------------