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Super-Strict Implications
- Source :
- Bulletin of the Section of Logic, Vol 50, Iss 1, Pp 1-34 (2021)
- Publication Year :
- 2021
- Publisher :
- Uniwersytet Lodzki (University of Lodz), 2021.
-
Abstract
- 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.
- Subjects :
- 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
Subjects
Details
- ISSN :
- 2449836X and 01380680
- Volume :
- 50
- Database :
- OpenAIRE
- Journal :
- Bulletin of the Section of Logic
- Accession number :
- edsair.doi.dedup.....36dad55176f8c1417d4406c527e8d47a