Logic for exact entailment
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2018
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| Online Access: | https://eprints.nottingham.ac.uk/54996/ |
| _version_ | 1848799096269176832 |
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| author | Fine, Kit Jago, Mark |
| author_facet | Fine, Kit Jago, Mark |
| author_sort | Fine, Kit |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:30:14Z |
| format | Article |
| id | nottingham-54996 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:30:14Z |
| publishDate | 2018 |
| publisher | Cambridge University Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-549962018-10-20T04:30:59Z https://eprints.nottingham.ac.uk/54996/ Logic for exact entailment Fine, Kit Jago, Mark 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. Cambridge University Press 2018-08-17 Article PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/54996/1/Logic%20for%20Exact%20Entailment%20RSL.pdf Fine, Kit and Jago, Mark (2018) Logic for exact entailment. Review of Symbolic Logic . ISSN 1755-0203 (In Press) Truthmaking; Exact entailment; Non-classical logic; Semantics; Mereology; Sequent calculus |
| spellingShingle | Truthmaking; Exact entailment; Non-classical logic; Semantics; Mereology; Sequent calculus Fine, Kit Jago, Mark Logic for exact entailment |
| title | Logic for exact entailment |
| title_full | Logic for exact entailment |
| title_fullStr | Logic for exact entailment |
| title_full_unstemmed | Logic for exact entailment |
| title_short | Logic for exact entailment |
| title_sort | logic for exact entailment |
| topic | Truthmaking; Exact entailment; Non-classical logic; Semantics; Mereology; Sequent calculus |
| url | https://eprints.nottingham.ac.uk/54996/ |