Routledge Dictionary of Language and Linguistics
disjunction [Lat. disiunctio ‘separation’]
1 In formal logic the conjunction of two elementary propositions p and q by the logical particle or1 which is true if and only if at least one of the elementary propositions is true. Or1 corresponds to Lat. vel (‘or also’) which can be paraphrased by ‘one or the other, or both.’ This inclusive (i.e. non-exclusive) or, which is basic to disjunction, must be differentiated from the exclusive or2 (Lat. aut…aut…) which means ‘either one or the other, but not both’), compare or1 (Louise is either sad or tired, (or perhaps both)) with or2 (Louise is either older or younger than her friend, (but in no case both)). In everyday usage the exclusive or2 is more common (expressed by either/or or otherwise), since the inclusive reading is usually barred by the pragmatic context. This relation is represented as follows in the (two-place) truth table:
| p | q | p  q1 | p  q2 |
| t | t | t | f |
| t | f | t | t |
| f | t | t | t |
| f | f | f | f |
The term ‘disjunction’ refers to the operation of the two-place sentence operator or as well as to the propositional connective defined by it. The propositions connected by or are not necessarily semantically cohesive. For that reason the connection Socrates is a philosopher or Aristotle is a unicorn is ‘true’ (because the first part of the sentence is true), while it would have to be rejected as an utterance in an actual speech situation as an unsuccessful speech act (
speech act theory). With the aid of set theory, disjunction can be semantically characterized as the union of both model sets that make the propositions connected with each other true.
References
Pelletier, J.F. 1977. Or. TL 4. 61–74.
formal logic
2 In unification grammar the dual of the operation of unification, used, for example, in Functional Unification Grammar (FUG), lexical Unification Grammar (LUG), and Headdriven Phrase Structure Grammar (HPSG).
The disjunction of two feature structures indicates the unification bundle of the denotata of their two disjuncts. The disjunctive feature structure (in curly brackets) in the following example stands for the group of all verbs, which are in the plural or in the first or second person singular:
Equivalent notations for disjunction:
For discussion of the necessity of disjunction in unification grammar, see Karttunen (1984), for algorithms for the implementation of disjunctive unification grammars, see Kasper (1987) and Eisele and Dörre (1988).
References
Eisele, A. and J.Dörre. 1988. Unification of disjunctive feature descriptions. In ACL Proceedings. New York. 26. 286–94.
Karttunen, L. 1984. Features and values. In Coling 84. Stanford, CA. 28–33.
Kasper, R.T. 1987. A unification method for disjunctive feature descriptions. In ACL Proceedings. Stanford, CA. 25. 235–42.
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