Logic for exact entailment

Fine, Kit; Jago, Mark

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