(define-theory Meronymy (Topology Top-Level))

(in-theory 'Meronymy)


(DEFINE-RELATION COMPONENT (?A ?B) :IFF-DEF
 (AND (= (INVERSE COMPONENT-OF) COMPONENT)
      (LOCALIZED-ENTITY ?A)
      (LOCALIZED-ENTITY ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE COMPONENT LOCALIZED-ENTITY)
      (DOMAIN COMPONENT LOCALIZED-ENTITY)))
(DEFINE-RELATION COMPONENT-OF (?A ?B)
 "A specialized common sense notion of part for 
heterogeneous parts of complexes. Consider the difficult issue of componentiality 
for substances and masses in general."
 :DEF
 (AND (_COMPLEX ?B TRUE)
      (PART-OF ?A ?B)
      (LOCALIZED-ENTITY ?A)
      (LOCALIZED-ENTITY ?B)))
(DEFINE-RELATION CONSTITUENT-MATERIAL (?A ?B)
 "Is structurally made up of in whole or in part of some 
material or matter. This includes composed of, made of, and formed of."
 :IFF-DEF
 (AND (= (INVERSE CONSTITUENT-MATERIAL-OF) CONSTITUENT-MATERIAL)
      (MATERIAL-OBJECT ?A)
      (MATERIAL-OBJECT ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE CONSTITUENT-MATERIAL MATERIAL-OBJECT)
      (DOMAIN CONSTITUENT-MATERIAL MATERIAL-OBJECT)))
(DEFINE-RELATION CONSISTS-OF (?A ?B)
 "Is structurally made up of in whole or in part of some 
material or matter. This includes composed of, made of, and formed of."
 :IFF-DEF (CONSTITUENT-MATERIAL ?A ?B))
(DEFINE-RELATION CONSTITUENT-MATERIAL-OF (?A ?B) :DEF
 (AND (PART-OF ?A ?B) (MATERIAL-OBJECT ?A) (MATERIAL-OBJECT ?B)))
(DEFINE-RELATION CONSTITUTES (?A ?B) :IFF-DEF
 (CONSTITUENT-MATERIAL-OF ?A ?B))
(DEFINE-RELATION CONSTITUTIVE-PHASE (?A ?B) :IFF-DEF
 (AND (= (INVERSE CONSTITUTIVE-PHASE-OF) CONSTITUTIVE-PHASE)
      (TEMPORALIZED-ENTITY ?A)
      (TEMPORALIZED-ENTITY ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE CONSTITUTIVE-PHASE TEMPORALIZED-ENTITY)
      (DOMAIN CONSTITUTIVE-PHASE TEMPORALIZED-ENTITY)))
(DEFINE-RELATION CONSTITUTIVE-PHASE-OF (?A ?B) :DEF
 (AND (TEMPORAL-PART-OF ?A ?B) (STRICTLY-NECESSARY-TO ?A ?B)))
(DEFINE-RELATION DIRECTIONAL-PART (?A ?B) :IFF-DEF
 (AND (= (INVERSE DIRECTIONAL-PART-OF) DIRECTIONAL-PART)
      (ENTITY ?A)
      (ENTITY ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE DIRECTIONAL-PART ENTITY)
      (DOMAIN DIRECTIONAL-PART ENTITY)))
(DEFINE-RELATION DIRECTIONAL-PART-OF (?A ?B)
 "A part focalized by means of a directional schema 
applied to the whole."
 :DEF (SEGMENT-OF ?A ?B))
(DEFINE-RELATION ELEMENT (?A ?B) :IFF-DEF
 (AND (= (INVERSE ELEMENT-OF) ELEMENT) (ENTITY ?A) (ENTITY ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE ELEMENT ENTITY)
      (DOMAIN ELEMENT ENTITY)))
(DEFINE-RELATION ELEMENT-OF (?A ?B)
 "A specialized common sense notion of part for uniform 
parts of collections. Quasi-synonyms: item, member."
 :DEF
 (AND (_COLLECTION ?B TRUE)
      (FORALL (?W ?Z)
       (=> (AND (ELEMENT-OF ?W ?B) (ELEMENT-OF ?Z ?B))
        (EQUAL-BUT-LOCALIZATION ?W ?Z)))
      (PART-OF ?A ?B)))
(DEFINE-RELATION FINER-GRAIN-COMPONENT (?A ?B) :IFF-DEF
 (AND (COARSER-GRANULARITY ?A ?B)
      (COMPONENT ?A ?B)
      (MATERIAL-OBJECT ?A)
      (MATERIAL-OBJECT ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE FINER-GRAIN-COMPONENT MATERIAL-OBJECT)
      (DOMAIN FINER-GRAIN-COMPONENT MATERIAL-OBJECT)))
(DEFINE-RELATION FINER-GRAIN-COMPONENT-OF (?A ?B) :IFF-DEF
 (AND (COMPONENT-OF ?A ?B)
      (FINER-GRANULARITY ?A ?B)
      (MATERIAL-OBJECT ?A)
      (MATERIAL-OBJECT ?B)))
(DEFINE-RELATION FINER-GRAIN-PART (?A ?B) :IFF-DEF
 (AND (= (INVERSE FINER-GRAIN-PART-OF) FINER-GRAIN-PART)
      (ENTITY ?A)
      (ENTITY ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE FINER-GRAIN-PART ENTITY)
      (DOMAIN FINER-GRAIN-PART ENTITY)))
(DEFINE-RELATION FINER-GRAIN-PART-OF (?A ?B) :DEF
 (AND (PART-OF ?A ?B) (FINER-GRANULARITY ?A ?B)) :AXIOM-CONSTRAINTS
 (AND (RANGE FINER-GRAIN-PART-OF MATERIAL-OBJECT)
      (DOMAIN FINER-GRAIN-PART-OF MATERIAL-OBJECT)))
(DEFINE-RELATION MEREOLOGICAL-MEMBER (?A ?B) :IFF-DEF
 (AND (= (INVERSE MEREOLOGICAL-MEMBER-OF) MEREOLOGICAL-MEMBER)
      (ENTITY ?A)
      (ENTITY ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE MEREOLOGICAL-MEMBER ENTITY)
      (DOMAIN MEREOLOGICAL-MEMBER ENTITY)))
(DEFINE-RELATION MEREOLOGICAL-MEMBER-OF (?A ?B)
 "A specialized notion of element for uniform social 
parts of collections. Quasi-synonyms: participant, adept."
 :DEF (ELEMENT-OF ?A ?B) :AXIOM-CONSTRAINTS
 (DOMAIN MEREOLOGICAL-MEMBER-OF SOCIAL-OBJECT))
(DEFINE-RELATION PIECE (?A ?B) :IFF-DEF
 (AND (= (INVERSE PIECE-OF) PIECE) (ENTITY ?A) (ENTITY ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE PIECE ENTITY)
      (DOMAIN PIECE ENTITY)))
(DEFINE-RELATION PIECE-OF (?A ?B)
 "A specialized common sense notion of part for arbitrary 
parts of masses, usually characterized by quantitative measure (either in a numerical 
or an analogic scale). It is transitive. Quasi-synonyms: chunk, quantity, amount."
 :DEF
 (AND (=> (AND (PART-OF ?A ?B) (PART-OF ?B ?A)) (IDENTITY ?A ?B))
      (PART-OF ?A ?B)
      (ENTITY ?A)
      (ENTITY ?B))
 :CONSTRAINTS (AND (ENTITY ?A) (ENTITY ?B)) :AXIOM-CONSTRAINTS
 (AND (RANGE PIECE-OF ENTITY)
      (DOMAIN PIECE-OF ENTITY)))
(DEFINE-RELATION PORTION (?A ?B) :IFF-DEF
 (AND (= (INVERSE PORTION-OF) PORTION) (ENTITY ?A) (ENTITY ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE PORTION ENTITY)
      (DOMAIN PORTION ENTITY)))
(DEFINE-RELATION PORTION-OF (?A ?B)
 "A specialized common sense notion for parts selected by 
means of features which are not primary in the structure of the whole: color, judgment 
(truehe annoying part'), sex (truehe female part'), matter (truehe wooden part'). In some 
cases primariness is debatable (a complex may be structured according to matter or 
color): this is solved by contextual interpretation."
 :DEF (PART-OF ?A ?B))
(DEFINE-RELATION POSITIONAL-PART (?A ?B) :IFF-DEF
 (AND (= (INVERSE POSITIONAL-PART-OF) POSITIONAL-PART)
      (ENTITY ?A)
      (ENTITY ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE POSITIONAL-PART ENTITY)
      (DOMAIN POSITIONAL-PART ENTITY)))
(DEFINE-RELATION POSITIONAL-PART-OF (?A ?B)
 "A part focalized by means of a positional relation 
with another object."
 :DEF (AND (EXISTS ?Z (POSITION-RELATION ?A ?Z)) (SEGMENT-OF ?A ?B)))
(DEFINE-RELATION PRIME-COMPONENT (?A ?B) :IFF-DEF
 (AND (= (INVERSE PRIME-COMPONENT-OF) PRIME-COMPONENT)
      (LOCALIZED-ENTITY ?A)
      (LOCALIZED-ENTITY ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE PRIME-COMPONENT LOCALIZED-ENTITY)
      (DOMAIN PRIME-COMPONENT LOCALIZED-ENTITY)))
(DEFINE-RELATION PRIME-COMPONENT-OF (?A ?B)
 "A strong relation of componentiality, connected 
to integrity of complexes, specially systems. Quasi-synonym: essential part."
 :DEF
 (AND (=> (ABSENT-IN ?A ?B) (NOT (_INTEGRAL ?B TRUE))) (COMPONENT ?A ?B)))
(DEFINE-RELATION SAMPLE-OF (?A ?B) :DEF (PIECE-OF ?A ?B)
 :AXIOM-CONSTRAINTS (RANGE SAMPLE-OF MATERIAL-OBJECT))
(DEFINE-RELATION SAMPLE-SOURCE (?A ?B) :IFF-DEF
 (AND (= (INVERSE SAMPLE-OF) SAMPLE-SOURCE) (ENTITY ?A) (ENTITY ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE SAMPLE-SOURCE ENTITY)
      (DOMAIN SAMPLE-SOURCE ENTITY)))
(DEFINE-RELATION SEGMENT (?A ?B) :IFF-DEF
 (AND (= (INVERSE SEGMENT-OF) SEGMENT) (ENTITY ?A) (ENTITY ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE SEGMENT ENTITY)
      (DOMAIN SEGMENT ENTITY)))
(DEFINE-RELATION SEGMENT-OF (?A ?B)
 "A specialized common sense notion for parts selected 
by means of external schemata: usually a dimensional or topological scheme (top, left, 
front, exterior, border, interior, side, edge, half, phase) (Gerstl-Pribbenow96)."
 :DEF (PART-OF ?A ?B))
(DEFINE-RELATION SHELF-PART (?A ?B) :IFF-DEF
 (AND (= (INVERSE SHELF-PART-OF) SHELF-PART) (ENTITY ?A) (ENTITY ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE SHELF-PART ENTITY)
      (DOMAIN SHELF-PART ENTITY)))
(DEFINE-RELATION SHELF-PART-OF (?A ?B) :DEF (SEGMENT-OF ?A ?B)
 :AXIOM-CONSTRAINTS
 (AND (RANGE SHELF-PART-OF MATERIAL-OBJECT)
      (DOMAIN SHELF-PART-OF MATERIAL-OBJECT)))
(DEFINE-RELATION TEMPORAL-PART (?A ?B) :IFF-DEF
 (AND (= (INVERSE TEMPORAL-PART-OF) TEMPORAL-PART)
      (TEMPORALIZED-ENTITY ?A)
      (TEMPORALIZED-ENTITY ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE TEMPORAL-PART TEMPORALIZED-ENTITY)
      (DOMAIN TEMPORAL-PART TEMPORALIZED-ENTITY)))
(DEFINE-RELATION TEMPORAL-PART-OF (?A ?B) :DEF
 (AND (=> (AND (PART-OF ?A ?B) (PART-OF ?B ?A)) (IDENTITY ?A ?B))
      (PART-OF ?A ?B)
      (TEMPORALIZED-ENTITY ?A)
      (TEMPORALIZED-ENTITY ?B))
 :CONSTRAINTS (AND (TEMPORALIZED-ENTITY ?A) (TEMPORALIZED-ENTITY ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE TEMPORAL-PART-OF TEMPORALIZED-ENTITY)
      (DOMAIN TEMPORAL-PART-OF TEMPORALIZED-ENTITY)))
(DEFINE-RELATION _COLLECTION (?A ?B)
 "Common sense wholes having an elementary uniform 
compositional structure, but parts are distinguished only with respect to each other, 
not to the whole (Gerstl-Pribbenow96)."
 :DEF
 (AND (FORALL (?Y ?Z)
       (=> (AND (ELEMENT-OF ?Y ?A) (ELEMENT-OF ?Z ?A))
        (NOT (COMMON-PART ?Y ?Z))))
      (_WEAK-WHOLE ?A ?B)))
(DEFINE-RELATION _COMPLEX (?A ?B)
 "Common sense wholes having a (multiple) heterogeneous 
compositional structure: systems, composites, compounds, etc. (Gerstl-Pribbenow96)."
 :IFF-DEF (AND (NOT (_HOMOGENEOUS ?A ?B)) (_WEAK-WHOLE ?A ?B)))
(DEFINE-RELATION _CONFIGURATION (?A ?B)
 "The special kind of complex which features only one 
additional structure: stacks, piles, series, etc. (Gerstl-Pribbenow96)."
 :DEF (_WEAK-WHOLE ?A ?B))
(DEFINE-RELATION _HOMOGENEOUS (?A ?B)
 "Something is homogeneous when it has only arbitrary 
pieces as parts; ie any parts have similar properties."
 :DEF
 (AND (FORALL (?P ?Q ?C1 ?C2)
       (=>
        (AND (PART-OF ?P ?A)
             (PART-OF ?Q ?A)
             (INSTANCE-OF ?C1 CONCEPT)
             (INSTANCE-OF ?C2 CONCEPT)
             (INSTANCE-OF ?P ?C1)
             (INSTANCE-OF ?Q ?C2))
        (IDENTITY ?C1 ?C2)))
      (MEREOLOGICAL-PROPERTY ?A ?B)))
(DEFINE-RELATION _MASS (?A ?B)
 "Common sense wholes having no compositional 
structure (Gerstl-Pribbenow96)."
 :IFF-DEF (AND (_WEAK-WHOLE ?A ?B) (_HOMOGENEOUS ?A ?B) (MATERIAL-OBJECT ?A)))
(DEFINE-RELATION _SYSTEM (?A ?B) :DEF
 (AND (_COMPLEX ?A ?B) (OBJECT ?A)))
(DEFINE-RELATION _WEAK-WHOLE (?A ?B)
 "The most general notion of whole, and merges both the 
notion of mereologic whole (theory: 'mereology') and the common-sense notions of 
specialized wholes; thus, nothing is said about self-connexity. A weak whole can be
either concentrated or distributed."
 :DEF (MEREOLOGICAL-PROPERTY ?A ?B))
(DEFINE-CLASS *ATOMIC-WHOLE (?SELF)
 "The whole containing no proper parts: this concept 
is useful in domain ontologies which assume atomicity, say that there are irreducible 
objects in the domain (eg, an ontology for the storage of original, pre-packaged car 
accessories versus an ontology for car parts recycling dealers)."
 :IFF-DEF (AND (OBJECT ?SELF) (VALUE-CARDINALITY ?SELF _ATOM 1))
 :AXIOM-DEF (THE-ARCHETYPE *ATOMIC-WHOLE REIFIED-PROPERTY))
(DEFINE-CLASS *DISTRIBUTED-WHOLE (?SELF) "Distributed wholes."
 :IFF-DEF
 (AND (OBJECT ?SELF) (VALUE-CARDINALITY ?SELF _DISTRIBUTED 1))
 :CONSTRAINTS (VALUE-CARDINALITY ?SELF _WEAK-WHOLE 1) :AXIOM-DEF
 (THE-ARCHETYPE *DISTRIBUTED-WHOLE REIFIED-PROPERTY))
(DEFINE-CLASS *INTEGRAL-WHOLE (?SELF)
 "Common sense wholes with integrity, to be distinguished 
according to the presence of a compositional structure."
 :IFF-DEF (AND (OBJECT ?SELF) (VALUE-CARDINALITY ?SELF _INTEGRAL 1))
 :CONSTRAINTS (VALUE-CARDINALITY ?SELF _WEAK-WHOLE 1) :AXIOM-DEF
 (THE-ARCHETYPE *INTEGRAL-WHOLE REIFIED-PROPERTY))
(DEFINE-CLASS *MASS (?SELF)
:IFF-DEF
 (AND (MATERIAL-OBJECT ?SELF)
      (VALUE-CARDINALITY ?SELF _MASS 1)
      (EXISTS (?A) (AND (CONSTITUENT-MATERIAL ?SELF ?A) (SUBSTANCE ?A)))))
(DEFINE-CLASS *SCATTERED-WHOLE (?SELF)
 "Common sense wholes without integrity." :IFF-DEF
 (AND (OBJECT ?SELF) (VALUE-TYPE ?SELF _INTEGRAL INCOHERENT))
 :CONSTRAINTS (VALUE-CARDINALITY ?SELF _WEAK-WHOLE 1) :AXIOM-DEF
 (THE-ARCHETYPE *SCATTERED-WHOLE REIFIED-PROPERTY))