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2 results

  • PROOF SYSTEMS FOR EXACT ENTAILMENT

  • Part of
  • JOHANNES KORBMACHER
  • Journal:
    The Review of Symbolic Logic / Volume 16 / Issue 4 / December 2023
    Published online by Cambridge University Press:
    11 May 2022, pp. 1260-1295
    Print publication:
    December 2023
    • Article
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  • We present a series of proof systems for exact entailment (i.e., relevant truthmaker preservation from premises to conclusion) and prove soundness and completeness. Using the proof systems, we observe that exact entailment is hyperintensional not only in the sense of Cresswell, but also in the sense recently proposed by Odintsov and Wansing.

  • LOGIC FOR EXACT ENTAILMENT

  • KIT FINE, MARK JAGO
  • Journal:
    The Review of Symbolic Logic / Volume 12 / Issue 3 / September 2019
    Published online by Cambridge University Press:
    01 February 2019, pp. 536-556
    Print publication:
    September 2019

  • 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.