Bulletin of the Section of Logic 50 (1):1-34 (2021)
AbstractThis 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 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 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.
Added to PP
Historical graph of downloads
References found in this work
Connexive Logics. An Overview and Current Trends.Hitoshi Omori & Heinrich Wansing - forthcoming - Logic and Logical Philosophy:1.
A Guide to Completeness and Complexity for Modal Logics of Knowledge and Belief.Joseph Y. Halpern & Yoram Moses - 1992 - Artificial Intelligence 54 (3):319-379.
Does the Traditional Treatment of Enthymemes Rest on a Mistake?David Hitchcock - 1998 - Argumentation 12 (1):15-37.
Citations of this work
No citations found.
Similar books and articles
Natural Deduction Based Upon Strict Implication for Normal Modal Logics.Claudio Cerrato - 1994 - Notre Dame Journal of Formal Logic 35 (4):471-495.
Strict Conditionals: A Negative Result.Jan Heylen & Leon Horsten - 2006 - Philosophical Quarterly 56 (225):536–549.
Sequent Calculi for Some Strict Implication Logics.Ryo Ishigaki & Ryo Kashima - 2008 - Logic Journal of the IGPL 16 (2):155-174.
Priorean Strict Implication, Q and Related Systems.Fabrice Correia - 2001 - Studia Logica 69 (3):411-427.
Dual-Context Sequent Calculus and Strict Implication.Kentaro Kikuchi - 2002 - Mathematical Logic Quarterly 48 (1):87-92.
Residuated Logics Based on Strict Triangular Norms with an Involutive Negation.Petr Cintula, Erich Peter Klement, Radko Mesiar & Mirko Navara - 2006 - Mathematical Logic Quarterly 52 (3):269-282.
Cut Elimination, Identity Elimination, and Interpolation in Super-Belnap Logics.Adam Přenosil - 2017 - Studia Logica 105 (6):1255-1289.
Modal Logics in the Vicinity of S.Brian F. Chellas & Krister Segerberg - 1996 - Notre Dame Journal of Formal Logic 37 (1):1-24.
An Algebraic View of Super-Belnap Logics.Hugo Albuquerque, Adam Přenosil & Umberto Rivieccio - 2017 - Studia Logica 105 (6):1051-1086.
Material and Strict Implication in Boolean Algebras, Revisited.Enric Trillas & Rudolf Seising - 2014 - Archives for the Philosophy and History of Soft Computing 2014 (2).
The Relevant Logic E and Some Close Neighbours: A Reinterpretation.Edwin Mares & Shawn Standefer - 2017 - IfCoLog Journal of Logics and Their Applications 4 (3):695--730.
On Applications of Truth-Value Connectives for Testing Arguments with Natural Connectives.Andrzej Pietruszczak - 2006 - Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):143-156.