In natural languages, roles are usually represented by nouns, such as mother, brother, author, or driver, but in predicate calculus, they are often represented by dyadic relations, such as motherOf, brotherOf, authorOf, or driverOf. This representation makes the mapping from language to logic unsystematic, since the noun woman is mapped to a type or a monadic predicate woman(x), but the noun mother is mapped to a dyadic predicate motherOf(x,y).
To make the mapping more systematic, the KR ontology, which is presented in the book Knowledge Representation, introduces a primitive dyadic relation Has, which converts roles into relations. The nouns mother, brother, author, and driver are represented by the role types Mother, Brother, Author, and Driver. Those types can be used as type labels in a typed logic, such as conceptual graphs or typed predicate calculus, and they can be used as monadic predicates in untyped predicate calculus. The corresponding dyadic relations, in any typed or untyped version of logic, can be defined in terms of the role and the relation Has.
Figure 1 divides the type Actuality, which is discussed in the top-level ontology, into three subtypes, Phenomenon, Role, and Sign. A phenomenal entity is an actual entity considered by itself; a role is considered in relation to something else; and a sign is considered as representing something to some agent. The trichotomy of Phenomenon, Role, and Sign in Figure 1 and the trichotomy of Independent, Relative, and Mediating in the top-level ontology are both based on Peirce's distinction of Firstness, Secondness, and Thirdness, but they are applied to different aspects: the trichotomy at the top level is applied to the nature of the entities in themselves, but the trichotomy in Figure 1 is applied to the way entities are viewed by some observer. The same person, for example, might be classified as a woman by appearance (phenomenon) or as a mother by role. For further discussion of these distinctions, see Sections 2.4 and 6.6 of Knowledge Representation.
Figure 1: Classification of roles
In Whitehead's ontology, roles result from prehensions: one entity prehends another. In terms of the Has relation, the prehending entity x has the prehended entity y in the relationship Has(x,y). The kinds of prehensions are further distinguished as extrinsic or intrinsic. If either entity in a prehension could disappear without affecting the form or existence of the other, the relationship between them is extrinsic. If the disappearance of one entity in a prehension changes the structure or even the existence of the other, the relationship between them is intrinsic. That distinction generates three further categories:
At the lower right of Figure 1, the categories Part and Property are further classified by the distinction between continuants and occurrents. That subdivision is not completely symmetric because continuants have only spatial parts, but occurrents have both spatial and temporal parts. With those distinctions, the categories Part and Property are subdivided in five more categories:
These categories, which are defined by purely semantic distinctions, have a strong correlation with the syntactic categories of natural languages. Continuants are commonly expressed by nouns, and occurrents by verbs. Attributes are expressed by adjectives, and manners by adverbs. Participants are expressed by the case relations or thematic roles associated with verbs. Stages are often expressed by nouns derived from verbs, such as retirement, or by suffixes on role words, such as infancy and motherhood.
In the following list, every role type is specified as a subtype of some type that is independent of an observer and a role type shown in Figure 1. Accompaniment, for example, is a subtype of Object in the role of Participant, which is written Object∩Participant. The corresponding dyadic relation HasAccompaniment may be abbreviated by the shorter name Accm. The signature of the relation is (Object,Object), which indicates that it relates an object to an object. For each role, there is a sample sentence, which is translated to a conceptual graph that uses the role. Then the CG is translated to an English paraphrase that uses the role with some form of the verb have; the subject of have is the prehending entity and the object is the prehended entity.
Example: Ronnie left with Nancy.
(Past)→[Situation: [Leave]→(Agnt)→[Person: Ronnie]→(Accm)→[Person: Nancy]].Paraphrase: When leaving, Ronnie had Nancy as accompaniment.
Example: The ski has a length of 167 cm.
[Ski: #]→(Chrc)→[Length]→(Amt)→[Measure: <167,cm>].By measure contraction, which is discussed in Section 1.4, this graph may be simplfied to
[Ski: #]→(Chrc)→[Length: @167cm].Paraphrase: The ski has a characteristic length whose amount is 167 cm.
[Number: 16]←(Arg)←[Sqrt]→(Rslt)→[Number: 4].Paraphrase: The square root function has 16 as argument and 4 as result.
Example: The rose is red.
[Rose: #]→(Attr)→[Red].Paraphrase: The rose has red as attribute.
Example: Sam is a good musician.
[Person: Sam]→(Attr)→[Good]→(Base)→[Type: Musician].Paraphrase: Sam has the attribute good as musician.
Example: You are wet because it is raining.
[Situation: [Person: #you]←(Attr)←[Wet]]→(Bcas)→[Situation: [Rain]].Paraphrase: Your being wet has rain as cause.
Example: Lillian is Katie's mother.
[Mother: Lillian]→(Chld)→[Child: Katie].Paraphrase: Lillian has Katie as child.
Example: Bob is taller than Mary.
[Person: Bob]→(Attr)→[Tall]→(Comp)→[Comparand: Mary].Paraphrase: Bob is tall in comparison to Mary.
Example: The rose's color is red.
[Rose: #]→(Chrc)→[Color: Red].Paraphrase: The rose has a color red as characteristic.
Example: The ambulance arrived quickly.
[Ambulance:#]←(Thme)←[Arrive]→(Manr)→[Quick].Paraphrase: The arrival of the ambulance had a quick manner.
Example: The ski is 167 cm long.
[Ski: #]→(Attr)→[Long]→(Meas)→[Measure: <167,cm>].Paraphrase: The ski has an attribute long, whose measure is 167 cm.
Example: A finger is a part of a hand.
[Hand]→(Part)→[Finger].Paraphrase: A hand has a finger as part.
Example: Niurka's watch stopped.
[Person: Niurka]→(Poss)→[Watch]←(Thme)←[Stop].Paraphrase: Niurka had as possession a watch that stopped.
Example: After Billy ate the pretzel, he drank some beer.
[Situation: [Person: Billy *x]←(Agnt)←[Eat]→(Ptnt)→[Pretzel: #]]- (Succ)→[Situation: [?x]←(Agnt)←[Drink]→(Ptnt)→[Beer]].Paraphrase: The situation of Billy's eating the pretzel had as successor the situation of his drinking some beer.
The roles derived from the participants associated with verbs form a linguistically important class that are described separately as thematic roles.
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