A logic of hypothetical conjunction

Matthew Collinson* (Corresponding Author)

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

A binary connective that can be read as a matching conjunction for conditional connectives found in many conditional logics is considered. The most natural way to read this connective is often as a conjunction and yet, hypothetically, considered to hold of a state of affairs that could be obtained under the hypothesis. The connective can be given an intensional semantics extending a standard semantics of conditional logic that uses propositionally indexed families of binary relations on possible worlds. This semantics is determined by an adjoint relationship between the operations supporting the semantics of the conditional and the new conjunction. The semantics of the hypothetical conjunction connective subsumes the semantics, supported by a ternary relation semantics, of the fusion connective that arises in connection with substructural and relevant logics, and therefore subsumes a number of other forms of conjunction. A number of applications of the hypothetical conjunction connective are discussed, including generalized forms of resource reasoning used in computer science applications.logics, and therefore subsumes a number of other forms of conjunction. A number of applications of the hypothetical conjunction connective are discussed, including to generalized forms of resource reasoning of use in computer science applications.
Original languageEnglish
Pages (from-to)975–1009
Number of pages35
JournalJournal of Logic and Computation
Volume29
Issue number6
Early online date19 Nov 2019
DOIs
Publication statusPublished - 2019

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