Super-Strict Implications
| Autor: | Guido Gherardi, Eugenio Orlandelli |
|---|---|
| Přispěvatelé: | Orlandelli, Eugenio, Gherardi, Guido |
| Rok vydání: | 2021 |
| Předmět: |
sequent calculi
connexive implication Logic Computer science structural rules strict implication paradoxes of implication connexive implication sequent calculi structural rules Cube (algebra) lcsh:Logic Semantics Paradoxes of material implication Philosophy TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Modal paradoxes of implication Negation Computer Science::Logic in Computer Science Calculus strict implication Kripke semantics lcsh:BC1-199 Rule of inference |
| Zdroj: | Bulletin of the Section of Logic, Vol 50, Iss 1, Pp 1-34 (2021) |
| ISSN: | 2449-836X 0138-0680 |
| DOI: | 10.18778/0138-0680.2021.02 |
| Popis: | This paper introduces the logics of super-strict implications, where a super-strict implication is a strengthening of C.I. Lewis' strict implication that avoids not only the paradoxes of material implication but also those of strict implication. The semantics of super-strict implications is obtained by strengthening the (normal) relational semantics for strict implication. We consider all logics of super-strict implications that are based on relational frames for modal logics in the modal cube. it is shown that all logics of super-strict implications are connexive logics in that they validate Aristotle's Theses and (weak) Boethius's Theses. A proof-theoretic characterisation of logics of super-strict implications is given by means of G3-style labelled calculi, and it is proved that the structural rules of inference are admissible in these calculi. It is also shown that validity in the S5-based logic of super-strict implications is equivalent to validity in G. Priest's negation-as-cancellation-based logic. Hence, we also give a cut-free calculus for Priest's logic. |
| Databáze: | OpenAIRE |
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