pm#type second-order type or more
closed_exclusion: pm#individual
exclusion: sumo#Attribute
supertype: pm#non_spatial_collection sumo#abstract (sumo)
subtype: rdfs#class__clas rdfs#class has pm#binary_relation_type as instance and hence is different from sumo#class
subtype: sumo#class__clas classes differ from sets in three important respects: 1) classes are not assumed to be extensional, i.e. distinct classes might well have exactly the same instances, 2) classes typically have an associated `condition' that determines the instances of the class, e.g., the condition `human' determines the "class of humans" (note that some classes might satisfy their own condition (e.g., the "class of abstract things" is "abstract") and hence be instances of themselves), 3) the instances of a class may occur only once within the class, i.e. a class cannot contain duplicate instances
subtype: rdfs#datatype
subtype: owl#restriction
subtype: owl#all_different__alldifferent
subtype: owl#deprecated_class
subtype: dl#rigid__RG "all" the instances of a rigid type must "necessarily" be of this type at all times; role types such as #student or pm#tired_person are "non-rigid" and even "anti-rigid" since it is always possible for "any" student or tired person to cease being student or tired without loosing its identity
subtype: dl#leaf_type__L type without subtype
subtype: dl#non-empty__nonempty__NEP such a type "necessarily" has at least one instance
subtype: pm#situation_class__situationclas all situation types are instance of this class
subtype: pm#attribute_class__attributeclas class that has for instances subclasses of sumo#Attribute
subtype: pm#substance_class__substanceclas class that has for instances subclasses of sumo#substance
subtype: pm#virtual_class__virtualclas class that should not be used directly: its subtypes should be used instead
instance: pm#class_of_inheritable_relation_type (pm)
instance: pm#thing__something___T__t___3D_or_4D_thing_or_anything_else any category (type or individual) is instance of this type; any type is also a subtype of this type
instance: pm#nothing (pm)
instance: pm#binary_relation_type all binary relation types are instance of that object
instance: pm#binary_relation (?,?) in WebKB, most relation types are binary and some have a variable number of arguments (as in KIF), hence this type is currently only specialized by types that I do not want to see as direct subtypes of pm#relation
instance: sumo#distributes__distribute (pm#binary_function_type,pm#binary_function_type) a binary_function ?F1 is distributive over another binary_function ?F2 just in case (?F1 ?INST1 (?F2 ?INST2 ?INST3)) is equal to (?F2 (?F1 ?INST1 ?INST2) (?F1 ?INST1 ?INST3)), for all ?INST1, ?INST2, and ?INST3
subtype: pm#unary_function_type class of functions requiring a single argument; if R is functional, then if R(x -> y) and P(x -> z) then y=z
subtype: pm#binary_predicate_type the class of predicates relating two items - its valence is two
subtype: pm#injective_binary_relation_type if P is injective, then if P(x,y) and P(z,y) then x=z; e.g., if nameOfMonth(m,"Feb") and nameOfMonth(n,"Feb") then m and n are the same month
subtype: pm#reflexive_relation_type a relation is reflexive if (?REL ?INST ?INST) for all ?INST
subtype: pm#trichotomizing_relation_type binary_relation such that all ordered pairs consisting of distinct individuals are element of this binary_relation
subtype: pm#irreflexive_relation_type r is irreflexive if r(?i,?i) holds for no value of ?i
subtype: pm#symmetric_relation_type when (?REL ?INST1 ?INST2) implies (?REL ?INST2 ?INST1), for all ?INST1 and ?INST2
subtype: pm#antisymmetric_relation_type when for distinct ?INST1 and ?INST2, (?REL ?INST1 ?INST2) implies not (?REL ?INST2 ?INST1), that is, for all ?INST1 and ?INST2, (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST1) imply that ?INST1 and ?INST2 are identical; it is possible for an antisymmetric relation to be a reflexive relation
subtype: pm#transitive_relation_type a binary_relation ?REL is transitive if (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST3) imply (?REL ?INST1 ?INST3), for all ?INST1, ?INST2, and ?INST3
subtype: pm#intransitive_relation_type a binary_relation ?REL is intransitive only if (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST3) imply not (?REL ?INST1 ?INST3), for all ?INST1, ?INST2, and ?INST3
subtype: owl#annotation_property
subtype: owl#deprecated_property
subtype: owl#ontology_property
subtype: rdfs#constraint_property
subtype: rdfs#container_membership_property
subtype: owl#datatype_property
subtype: owl#object_property if rel is an ObjectProperty, and rel(x,y), then y is an object
instance: pm#binary_relation sumo#distributes__distribute
subtype: dolce#universal__UNIVERSAL
subtype: dolce#rigid_universal__rigiduniversal__X
instance: dolce#particular a 0-order type
instance: dolce#entity dolce#abstract dolce#region dolce#temporal_region dolce#time_interval dolce#physical_region dolce#space_region__spaceregion dolce#abstract_region dolce#quality dolce#temporal_quality dolce#temporal_location dolce#physical_quality dolce#spatial_location__spatiallocation dolce#abstract_quality dolce#endurant dolce#amount_of_matter dolce#physical_endurant dolce#feature dolce#physical_object dolce#agentive_physical_object dolce#non-agentive_physical_object dolce#non-physical_endurant dolce#non-physical_object dolce#mental_object dolce#social_object dolce#agentive_social_object dolce#social_agent dolce#society dolce#non-agentive_social_object dolce#arbitrary_sum__arbitrarysum dolce#perdurant dolce#event dolce#achievement dolce#accomplishment dolce#stative dolce#state dolce#process__proces
subtype: pm#1st_order_type__1stordertype__type1 all 1st order types are implicitely or explicitely instance of that 2nd-order type
subtype: pm#relation_type there are three kinds of relation(_types): pm#predicate_type, pm#function_type and sumo#list; both predicates and functions denote sets of ordered n-tuples; the difference between these two classes is that predicates cover formula-forming operators, while functions cover term-forming operators; a list, on the other hand, is a particular ordered n-tuple
subtype: pm#predicate_type__predicatetype a sentence-forming relation with each tuple being a finite, ordered sequence of objects
subtype: sumo#list a particular ordered n-tuple of items; generally speaking, lists are created by means of the list_fn function, which takes any number of items as arguments and returns a list with the items in the same order; anything, including other lists, may be an item in a list; note too that lists are extensional - two lists that have the same items in the same order are identical; note too that a list (the null_list) may contain no items
subtype: pm#single_valued_relation_type when an assignment of values to every argument position except the last one determines at most one assignment for the last argument position; not all single_valued_relations are total_valued_relations
subtype: pm#total_valued_relation_type when there exists an assignment for the last argument position of the relation given any assignment of values to every argument position except the last one; note that declaring a relation to be both a total_valued_relation and a single_valued_relation means that it is a total function
subtype: pm#partial_valued_relation_type relation type that is not a total_valued_relation_type, i.e. just in case assigning values to every argument position except the last one does not necessarily mean that there is a value assignment for the last argument position; note that, if a sumo#relation is both a partial_valued_relation and a single_valued_relation, then it is a partial function
subtype: pm#binary_relation_type all binary relation types are instance of that object
subtype: pm#ternary_relation_type relates three items
subtype: pm#quaternary_relation_type relates four items
subtype: pm#quintary_relation_type relates five items
subtype: pm#variable_arity_relation_type class of relations that do not have a fixed number of arguments
subtype: pm#many_to_many_relation_type
subtype: pm#many_to_one_relation_type
subtype: pm#one_to_many_relation_type
subtype: pm#type_of_relation_extended_to_quantities relation that, when it is true on a sequence of arguments that are real_numbers, it is also true on a sequence of constant_quantites with those magnitudes in some unit of measure; for example, the less_than relation is extended to quantities; this means that for all pairs of quantities ?q1 and ?q2, [?q1, sumo#less_than: ?q2] if and only if, for some numbers ?n1 and ?n2 and unit ?u, [q1 = sumo#measure_fn(?n1,?u)], [q2 = sumo#measure_fn(?n2,?u)] and [?n1, less_than: ?n2] for all units on which ?q1 and ?q2 can be measured; note that, when a relation_extended_to_quantities is extended from real_numbers to constant_quantities, the constant_quantities must be measured along the same physical dimension
subtype: pm#probability_relation_type the class of relations that permit assessment of the probability of an event or situation
subtype: pm#spatial_relation_type the class of relations that are spatial in a wide sense, e.g., mereological relations and topological relation
subtype: pm#temporal_relation_type the class of temporal relations, e.g., notions of (temporal) topology of intervals, (temporal) schemata, and (temporal) extension
subtype: pm#intentional_relation_type the class of relations between an agent and one or more entities, where the relation requires that the agent has awareness of the entity
instance: pm#relation__related_thing__relatedthing___related_with type for any relation (unary, binary, ..., *-ary) and instance of pm#relation_type
subtype: pm#2nd_order_type__2ndordertype__type2 all 2nd order types are implicitely or explicitely instance of that 3rd order type
subtype: pm#class_of_inheritable_relation_type each instance RT of this class is a subclass of the 2nd-order_type pm#relation_type and the properties of RT can be inherited downward in the class hierarchy via the "subrelation" predicate
instance: pm#relation_type there are three kinds of relation(_types): pm#predicate_type, pm#function_type and sumo#list; both predicates and functions denote sets of ordered n-tuples; the difference between these two classes is that predicates cover formula-forming operators, while functions cover term-forming operators; a list, on the other hand, is a particular ordered n-tuple
instance: pm#binary_relation_type all binary relation types are instance of that object
instance: pm#ternary_relation_type relates three items
instance: pm#quaternary_relation_type relates four items
instance: pm#quintary_relation_type relates five items
instance: pm#type_of_relation_extended_to_quantities
instance: pm#single_valued_relation_type when an assignment of values to every argument position except the last one determines at most one assignment for the last argument position; not all single_valued_relations are total_valued_relations
instance: pm#total_valued_relation_type pm#case_relation_type pm#probability_relation_type pm#spatial_relation_type pm#temporal_relation_type
instance: pm#intentional_relation_type the class of relations between an agent and one or more entities, where the relation requires that the agent has awareness of the entity
instance: pm#propositional_attitude__propositionalattitude pm#object_attitude_relation_type
instance: pm#function_type term-forming relation that maps from a n-tuple of arguments to a range and that associates this n-tuple with at most one range element; note that the range is a set_or_class, and each element of the range is an instance of the set_or_class
instance: pm#unary_function_type class of functions requiring a single argument; if R is functional, then if R(x -> y) and P(x -> z) then y=z
instance: pm#binary_function_type class of functions requiring two arguments
instance: pm#ternary_function_type pm#quaternary_function_type
instance: pm#predicate_type__predicatetype a sentence-forming relation with each tuple being a finite, ordered sequence of objects
instance: pm#binary_predicate_type the class of predicates relating two items - its valence is two
instance: pm#ternary_predicate_type__ternarypredicatetype pm#quaternary_predicate_type pm#quintary_predicate_type
1 schema is about pm#type
[lis#graph1_on_type
[any pm#type,
may be pm#object of: (a #removal,
pm#time: a pm#time_measure,
pm#purpose: a pm#situation)]
](06/05/2024);
No statement uses a specialization of pm#type; click here to add a statement.
71 categories printed (given exploration depth: 3)