Relation pm#relation_to_set_or_class (*,pm#set_or_class)
supertype: pm#relation_to_collection
subtype: sumo#closed_on (pm#function_type,sumo#set_or_class) a binary_function is closed on a set_or_class if it is defined for all instances of the set_or_class and its value is always an instance of the set_or_class
subtype: sumo#reflexive_on__reflexiveon (pm#binary_relation_type,sumo#set_or_class) a binary_relation is reflexive on a set_or_class only if every instance of the set_or_class bears the relation to itself
subtype: sumo#irreflexive_on__irreflexiveon (pm#binary_relation_type,sumo#set_or_class) a binary_relation is irreflexive on a set_or_class only if no instance of the set_or_class bears the relation to itself
subtype: sumo#partial_ordering_on (pm#binary_relation_type,sumo#set_or_class) a binary_relation is a partial ordering on a set_or_class only if the relation is reflexive_on the set_or_class, and it is both an antisymmetric_relation, and a transitive_relation
subtype: sumo#total_ordering_on (pm#binary_relation_type,sumo#set_or_class) a binary_relation ?REL is a total ordering on a set_or_class only if it is a partial ordering for which either (?REL ?INST1 ?INST2) or (?REL ?INST2 ?INST1) for every ?INST1 and ?INST2 in the set_or_class
subtype: sumo#trichotomizing_on (pm#binary_relation_type,sumo#set_or_class)
subtype: sumo#equivalence_relation_on (pm#binary_relation_type,sumo#set_or_class) a binary_relation is an equivalence_relation_on a set_or_class only if the relation is reflexive_on the set_or_class and it is both a transitive_relation and a symmetric_relation
subtype: pm#relation_to_class (*,rdfs#class)
subtype: pm#kind__type___class___instance_of__instanceof (?,rdfs#class) the '^' link in the FT notation
subtype: sumo#extension_fn__extensionfn (sumo#Attribute -> sumo#class) a unary_function that maps an attribute into the class whose condition for membership is the attribute
subtype: pm#relation_to_another_set_or_class (pm#set_or_class,pm#set_or_class+) this category is needed to group SUMO relations between classes which cannot be subtype of pm#relation_from_type because their signatures curiously also involve sets
subtype: pm#disjoint (pm#set_or_class,pm#set_or_class) like sumo#disjoint but from a a pm#set_or_class to another
subtype: sumo#disjoint (sumo#set_or_class,sumo#set_or_class) classes are exclusive/disjoint only if they share no instance (and hence no subtype), i.e. just in case the result of applying sumo#intersection_fn to them is empty
subtype: pm#exclusive_class__exclusiveclas (rdfs#class,rdfs#class) the 2 classes have no common subtype/instance; in WebKB, use the link '!'
subtype: pm#complement_class (rdfs#class -> rdfs#class) if something is not in one of the classes, then it is in the other, and vice versa; in WebKB, use the link '/'
subtype: pm#subclass_of_or_equal (pm#set_or_class,pm#set_or_class)
subtype: sumo#subclass__subclass_of (sumo#set_or_class,sumo#set_or_class) if the common reading conventions of parameters had been respected, this type would have been named subclass_of; every instance of the 1st argument is also an instance of the 2nd argument; a class may have multiple superclasses and subclasses
subtype: sumo#immediate_subclass__immediate_subclass_of (sumo#set_or_class,sumo#set_or_class) the 1st argument is a subclass of the 2nd argument and there is no other subclass of the 2nd argument such that the 1st is also a subclass of the 2nd; in WebKB, use the link '<'
subtype: rdfs#sub_class_of__subclassof__super_class__superclas (rdfs#class,rdfs#class) in WebKB, use the link '<'
subtype: sumo#power_set_fn__powersetfn (sumo#set_or_class -> sumo#set_or_class) maps the argument to the set_or_class of all its subclasses
subtype: pm#relation_to_another_class (rdfs#class,rdfs#class+)
subtype: rdfs#sub_class_of__subclassof__super_class__superclas (rdfs#class,rdfs#class) in WebKB, use the link '<'
subtype: owl#equivalent_class (rdfs#class,rdfs#class) in WebKB, use the link '='
subtype: pm#exclusive_class__exclusiveclas (rdfs#class,rdfs#class) the 2 classes have no common subtype/instance; in WebKB, use the link '!'
subtype: daml#restricted_by (rdfs#class,owl#restriction)
subtype: sumo#disjoint_decomposition (sumo#class,sumo#class+) a disjoint_decomposition of a class C is a set of mutually disjoint subclasses of C
subtype: sumo#partition (sumo#class,sumo#class+) a partition of a class C is a set of mutually disjoint classes (a subclass partition) covering C; each instance of C is instance of exactly one of the subclasses in the partition
subtype: sumo#exhaustive_decomposition (sumo#class,sumo#class+) an exhaustive_decomposition of a class C is a set of subclasses of C such that every instance of C is an instance of one of the subclasses in the set; note: this does not necessarily mean that the elements of the set are disjoint (see sumo#partition - a partition is a disjoint exhaustive decomposition)
subtype: sumo#partition (sumo#class,sumo#class+) a partition of a class C is a set of mutually disjoint classes (a subclass partition) covering C; each instance of C is instance of exactly one of the subclasses in the partition