(define-theory Topo-Morphology (Topology Localization))
(in-theory 'Topo-Morphology)


(DEFINE-RELATION 3D-AREA (?A ?B) :IFF-DEF
 (AND (PART ?A ?B)
      (= (INVERSE HOLE-IN) 3D-AREA)
      (ENTITY ?A)
      (REGION ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE 3D-AREA REGION)
      (DOMAIN 3D-AREA ENTITY)))
(DEFINE-RELATION 3D-AREA-OF (?A ?B)
 "A tridimensional area of some object is some kind
of hole in that object, which has a particular morphological saliency. Probably no
saliency rule can be stated; for example, body spaces are 3d areas which are
considered parts of an anatomical structure, although the most you can say
structurally is that they are surrounded by anatomical-structures.
In other words, a 3-d area is a mereologically relevant hole in some object."
 :IFF-DEF (AND (HOLE-IN ?A ?B) (PART-OF ?A ?B)))
(DEFINE-RELATION ABNORMALLY-ATTACHED (?A ?B) :DEF
 (AND (ATTACHED ?A ?B)
      (EXISTS (?C) (AND (CONTEXT ?A ?C) (UNEXPECTED ?C ?B)))
      (MATERIAL-OBJECT ?A)
      (MATERIAL-OBJECT ?B)))
(DEFINE-RELATION ACCESS-TO (?A ?B) :IFF-DEF
 (AND (= (INVERSE ACCESSIBLE-THROUGH) ACCESS-TO)
      (*OPENING ?A)
      (ENTITY ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE ACCESS-TO ENTITY)
      (DOMAIN ACCESS-TO *OPENING)))
(DEFINE-RELATION ACCESSIBLE-THROUGH (?A ?B) :DEF
 (AND (TOPO-MORPHOLOGICAL-RELATION ?A ?B) (*OPENING ?B)))
(DEFINE-RELATION ATTACHED (?A ?B) :DEF
 (AND (CONNECTED ?A ?B)
      (TOPO-MORPHOLOGICAL-RELATION ?A ?B)
      (LOCALIZED-ENTITY ?A)
      (LOCALIZED-ENTITY ?B)))
(DEFINE-RELATION BRANCH (?A ?B) :IFF-DEF
 (= (INVERSE BRANCH-OF) BRANCH))
(DEFINE-RELATION BRANCH-OF (?A ?B)
 "Arises from the division of. For example, the arborization 
of arteries."
 :DEF (ATTACHED ?A ?B))
(DEFINE-RELATION CAN-FILL (?A ?B) :IFF-DEF
 (AND (= (INVERSE FILLABLE-WITH) CAN-FILL)
      (*LIQUID ?A)
      (*CAVITY ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE CAN-FILL *CAVITY)
      (DOMAIN CAN-FILL *LIQUID)))
(DEFINE-RELATION CONNECTED-TO (?A ?B)
 "Directly attached to another physical unit as tendons are 
connected to muscles. This includes attached to and anchored to."
 :DEF (ATTACHED ?A ?B) :AXIOM-DEF
 (MAPPING CONNECTED-TO "We cannot simply map this to topology:connected, since
the anatomical sense of this relation has a functional sugar which is absent in the
strict topological connection: two anatomical objects seem connected when they are
'attached', say when we need some physical force to divide them. We mapped it to 
morphology:attached, but maintaining the symmetric characteristic of USN. In other
words, 'connected-to' is the neutral version of 'attached'."))
(DEFINE-RELATION CONNECTS (?A ?B ?C) :DEF
 (AND (CONNECTED ?A ?B) (CONNECTED ?B ?C) (STRUCTURING-TERNARY ?A ?B ?C))
 :AXIOM-DEF (AND (ARITY CONNECTS 3) (TERNARY CONNECTS)))
(DEFINE-RELATION DETACHED (?A ?B) :DEF
 (AND (NOT (ATTACHED ?A ?B))
      (TOPO-MORPHOLOGICAL-RELATION ?A ?B)
      (EXISTS (?C) (AND (CONTEXT ?A ?C) (UNEXPECTED ?C ?B)))
      (MATERIAL-OBJECT ?A)
      (MATERIAL-OBJECT ?B)))
(DEFINE-RELATION FILLABLE-WITH (?A ?B) :DEF
 (AND (TOPO-MORPHOLOGICAL-RELATION ?A ?B) (*CAVITY ?A) (*LIQUID ?B)))
(DEFINE-RELATION FORMS-SEQUENCE (?A ?B) :IFF-DEF
 (AND (= (INVERSE SEQUENCE-OF) FORMS-SEQUENCE)
      (OBJECT ?A)
      (ABSTRACTION ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE FORMS-SEQUENCE ABSTRACTION)
      (DOMAIN FORMS-SEQUENCE OBJECT)))
(DEFINE-RELATION HAS-ABNORMALLY-ATTACHED-PART (?A ?B) :IFF-DEF
 (AND (= (INVERSE ABNORMALLY-ATTACHED)
         HAS-ABNORMALLY-ATTACHED-PART)
      (MATERIAL-OBJECT ?A)
      (MATERIAL-OBJECT ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE HAS-ABNORMALLY-ATTACHED-PART MATERIAL-OBJECT)
      (DOMAIN HAS-ABNORMALLY-ATTACHED-PART
       MATERIAL-OBJECT)))
(DEFINE-RELATION HAS-ATTACHED (?A ?B) :IFF-DEF
 (= (INVERSE ATTACHED) HAS-ATTACHED))
(DEFINE-RELATION HAS-DETACHED-PART (?A ?B) :IFF-DEF
 (AND (= (INVERSE DETACHED) HAS-DETACHED-PART)
      (MATERIAL-OBJECT ?A)
      (MATERIAL-OBJECT ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE HAS-DETACHED-PART MATERIAL-OBJECT)
      (DOMAIN HAS-DETACHED-PART MATERIAL-OBJECT)))
(DEFINE-RELATION HOLE-IN (?A ?B)
 "Some region is a hole in some host (object or region)
when it is wholly located at the unique region of the host."
 :DEF
 (AND (TOPO-MORPHOLOGICAL-RELATION ?A ?B)
      (REGION ?A)
      (EXISTS (?C) (AND (WHOLLY-LOCATED ?A ?C) (IS-REGION-OF ?C ?B)))))
(DEFINE-RELATION HOST-OF (?A ?B) :IFF-DEF
 (AND (= (INVERSE HOLE-IN) HOST-OF) (ENTITY ?A) (REGION ?B))
 :AXIOM-CONSTRAINTS
 (AND (RANGE HOST-OF REGION)
      (DOMAIN HOST-OF ENTITY)))
(DEFINE-RELATION INTERCONNECTED-BY (?A ?B) :IFF-DEF
 (= (INVERSE INTERCONNECTS) INTERCONNECTED-BY))
(DEFINE-RELATION INTERCONNECTS (?A ?B)
 "Serves to link or join together two or more other 
physical units. This includes joins, links, conjoins, articulates, separates, and bridges."
 :DEF (AND (TOPO-MORPHOLOGICAL-RELATION ?A ?B) (OBJECT ?A) (OBJECT ?B))
 :AXIOM-DEF
 (MAPPING INTERCONNECTS
  "New entry. Used only in two templates: one relevant, 'Body-Space 
interconnects Cell'. Anyway, this should be a ternary relation."))
(DEFINE-RELATION SEQUENCE-OF (?A ?B) :DEF
 (AND (ELEMENT-OF ?B ?A)
      (FORALL (?Z)
       (=> (ELEMENT-OF ?Z ?A)
        (EXISTS (?W) (AND (ELEMENT-OF ?W ?A) (CONNECTED ?Z ?W)))))
      (TOPO-MORPHOLOGICAL-RELATION ?A ?B)
      (EXISTS (?C) (AND (REPRESENTS ?A ?C) (ELEMENT ?C ?B)))
      (OBJECT ?B)))
(DEFINE-RELATION TRIBUTARY (?A ?B) :IFF-DEF
 (= (INVERSE TRIBUTARY-OF) TRIBUTARY))
(DEFINE-RELATION TRIBUTARY-OF (?A ?B)
 "Merges with. For example, the confluence of veins." :DEF (BRANCH-OF ?A ?B)
 :AXIOM-DEF
 (MAPPING TRIBUTARY-OF "Functionally-charged topological notion: branching with
carrying fluids. Still to be modelled."))
(DEFINE-RELATION _CAVITY (?A ?B)
 "A cavity is a hole inside an object (eg, a body part),
say an internal hole (not connected to its host's complement."
 :DEF
 (AND (EXISTS (?Z ?W ?K)
       (AND (MATERIAL-OBJECT ?Z)
            (REGION ?W)
            (HOST-OF ?Z ?W)
            (EXISTS (?C) (AND (T-COMPLEMENT ?Z ?C) (IDENTITY ?K ?C)))
            (NOT (CONNECTED ?A ?K))))
      (_HOLE ?A ?B)
      (REGION ?A)))
(DEFINE-RELATION _CHAIN (?A ?B) :DEF
 (TOPO-MORPHOLOGICAL-PROPERTY ?A ?B))
(DEFINE-RELATION _CHANNEL (?A ?B)
 "A channel is the host of an elongate cavity 
within a (complex) system of fluid circulation. A morphological (and functional) 
extension is needed for this definition."
 :DEF
 (AND (EXISTS (?Y)
       (AND (_CAVITY ?Y TRUE)
            (_ELONGATE ?Y TRUE)
            (HOST-OF ?A ?Y)
            (EXISTS ?Z (AND (_CHANNEL ?Z TRUE) (CONNECTED ?A ?Y)))))
      (_HOST ?A ?B)
      (MATERIAL-OBJECT ?A)))
(DEFINE-RELATION _DUCT (?A ?B)
 "A duct is the host of an elongate opening.
A morphological extension is needed for this definition. The additional axiom
restricts duct to anatomy."
 :DEF
 (AND (EXISTS ?Y
       (AND (_OPENING ?Y TRUE) (_ELONGATE ?Y TRUE) (HOST-OF ?A ?Y)))
      (_HOST ?A ?B)
      (MATERIAL-OBJECT ?A))
 :CONSTRAINTS
 (EXISTS (?X ?Y)
  (AND (MATERIAL-OBJECT ?X)
       (MATERIAL-OBJECT ?Y)
       (CONNECTS ?A ?X ?Y))))
(DEFINE-RELATION _HOLE (?A ?B) :DEF
 (AND (EXISTS (?Z) (AND (MATERIAL-OBJECT ?Z) (HOLE-IN ?A ?Z)))
      (TOPO-MORPHOLOGICAL-PROPERTY ?A ?B)
      (REGION ?A)))
(DEFINE-RELATION _HOLLOW (?A ?B)
 "A hollow is an external hole, such as a depression.
It is a region connected to the complement of its host."
 :DEF
 (AND (EXISTS (?Y ?Z)
       (AND (MATERIAL-OBJECT ?Z)
            (HOST-OF ?Z ?A)
            (EXISTS (?C) (AND (T-COMPLEMENT ?Z ?C) (IDENTITY ?Y ?C)))
            (CONNECTED ?A ?Y)))
      (_HOLE ?A ?B)
      (REGION ?A)))
(DEFINE-RELATION _HOST (?A ?B) :DEF
 (AND (EXISTS (?Z ?W)
       (AND (MATERIAL-OBJECT ?Z)
            (REGION ?W)
            (HOLE-IN ?W ?Z)
            (HOST-OF ?A ?W)))
      (TOPO-MORPHOLOGICAL-PROPERTY ?A ?B)))
(DEFINE-RELATION _OPENING (?A ?B)
 "An opening is a hole which connects two holes 
within two distinct objects; eg, in anatomy, it can exist by default in 
the organism or there can be another object regulating its existence in time 
(eg, pilorum, glottis)."
 :DEF
 (AND (EXISTS (?X ?Y ?Z ?W)
       (AND (HOLE-IN ?X ?Z)
            (HOLE-IN ?Y ?W)
            (DIFFERENT ?Z ?W)
            (CONNECTS ?A ?X ?Y)))
      (_HOLE ?A ?B)))
(DEFINE-CLASS *CAVITY (?SELF)
:IFF-DEF
 (AND (REGION ?SELF) (VALUE-CARDINALITY ?SELF _CAVITY 1)) :AXIOM-DEF
 (THE-ARCHETYPE *CAVITY REIFIED-PROPERTY))
(DEFINE-CLASS *LINK (?SELF)
:DEF
 (AND (EXISTS (?Y ?Z) (AND (CONNECTED ?SELF ?Y) (CONNECTED ?Y ?Z)))
      (MATERIAL-OBJECT ?SELF))
 :AXIOM-DEF (THE-ARCHETYPE *LINK REIFIED-PROPERTY))
(DEFINE-CLASS *OPENING (?SELF)
:IFF-DEF
 (AND (REGION ?SELF) (VALUE-CARDINALITY ?SELF _OPENING 1))
 :AXIOM-DEF (THE-ARCHETYPE *OPENING REIFIED-PROPERTY))
(DEFINE-CLASS *UNBOUND-STRUCTURE (?SELF)
 "No material object can be completely unbound 
-say, not connected to anything-. This reified property is defined as not 
connected to anything which it rigidly depends on."
 :IFF-DEF
 (AND (NOT (EXISTS ?Y
            (AND (MATERIAL-OBJECT ?Y)
                 (CONNECTED ?SELF ?Y)
                 (STRICTLY-DEPENDS-ON ?SELF ?Y))))
      (MATERIAL-OBJECT ?SELF))
 :AXIOM-DEF (THE-ARCHETYPE *UNBOUND-STRUCTURE REIFIED-PROPERTY))