Constructive Embedding from Extensions of Logics of Strict Implication into Modal Logics

Logic in Asia: Studia Logica Library - Structural Analysis of Non-Classical Logics ◽

10.1007/978-3-662-48357-2_11 ◽

2015 ◽

pp. 223-251 ◽

Cited By ~ 2

Author(s):

Sakiko Yamasaki ◽

Katsuhiko Sano

Keyword(s):

Modal Logics ◽

Strict Implication

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Modal Logics of Strict Implication

Applied Logic Series - Goal-Directed Proof Theory ◽

10.1007/978-94-017-1713-7_4 ◽

2000 ◽

pp. 117-169

Author(s):

Dov M. Gabbay ◽

Nicola Olivetti

Keyword(s):

Modal Logics ◽

Strict Implication

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Natural Deduction Based upon Strict Implication for Normal Modal Logics

Notre Dame Journal of Formal Logic ◽

10.1305/ndjfl/1040408608 ◽

1994 ◽

Vol 35 (4) ◽

pp. 471-495 ◽

Cited By ~ 3

Author(s):

Claudio Cerrato

Keyword(s):

Natural Deduction ◽

Modal Logics ◽

Strict Implication ◽

Normal Modal Logics

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Super-Strict Implications

Bulletin of the Section of Logic ◽

10.18778/0138-0680.2021.02 ◽

2021 ◽

Author(s):

Eugenio Orlandelli ◽

Guido Gherardi

Keyword(s):

Modal Logics ◽

Relational Semantics ◽

Strict Implication ◽

Material Implication ◽

Structural Rules ◽

Relational Frames

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 $$\mathsf{S5}$$-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.

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