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Logic for exact entailment

Fine, Kit; Jago, Mark

Authors

Kit Fine

MARK JAGO mark.jago@nottingham.ac.uk
Professor of Philosophy



Abstract

An exact truthmaker for A is a state which, as well as guaranteeing A's truth, is wholly relevant to it. States with parts irrelevant to whether A is true do not count as exact truthmakers for A. Giving semantics in this way produces a very unusual consequence relation, on which conjunctions do not entail their conjuncts. This feature makes the resulting logic highly unusual. In this paper, we set out formal semantics for exact truthmaking and characterise the resulting notion of entailment, showing that it is compact and decidable. We then investigate the effect of various restrictions on the semantics. We also formulate a sequent-style proof system for exact entailment and give soundness and completeness results.

Citation

Fine, K., & Jago, M. (2019). Logic for exact entailment. Review of Symbolic Logic, 12(3), 536-556. https://doi.org/10.1017/s1755020318000151

Journal Article Type Article
Acceptance Date Aug 17, 2018
Online Publication Date Feb 1, 2019
Publication Date Feb 1, 2019
Deposit Date Aug 20, 2018
Publicly Available Date Apr 2, 2019
Journal The Review of Symbolic Logic
Print ISSN 1755-0203
Electronic ISSN 1755-0211
Publisher Cambridge University Press (CUP)
Peer Reviewed Peer Reviewed
Volume 12
Issue 3
Pages 536-556
DOI https://doi.org/10.1017/s1755020318000151
Keywords Truthmaking; Exact entailment; Non-classical logic; Semantics; Mereology; Sequent calculus
Public URL https://nottingham-repository.worktribe.com/output/1039822
Publisher URL https://www.cambridge.org/core/journals/review-of-symbolic-logic/article/logic-for-exact-entailment/7473CAC3341CFA357C0857C817B32260
Additional Information This article has been published in a revised form in The Review of Sybolic Logic http://doi.org/10.1017/S1755020318000151. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Association for Symbolic Logic 2019

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