Abstracts

Sara Ayhan @Connexive Logic

Contradictions without negation and a proof-theoretic, bilateralist account of connexive logics

In this talk I will investigate a negation-free fragment of a connexive logic from the perspective of bilateralist proof-theoretic semantics and will argue that eliminating primitive negation has two important conceptual consequences. First, it requires a reconceptualization of contradictory logics: in a bilateralist framework, contradiction need not be understood in terms of negation inconsistency, but rather as the coexistence of proofs and refutations for certain formulas within a non-trivial system. Second, it challenges the standard definition of connexive logics, which typically rely on negation-based schemata. Finally, I will also address the issue of proof/refutation duality in the absence of negation, which can be formalized and recovered at a meta-level by extending the system with a two-sorted typed lambda-calculus.

Colin Caret @BLOT

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Michael De @Relevance Logic

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Elena Ficara @BLOT

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Naoya Fujikawa @BLOT

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Nils Kürbis @Connexive Logic

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Fei Liang @BLOT

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Anna Malavisi @BLOT

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Florian Marion @Connexive Logic

On Wyman’s Theory of the Meaninglessness of Contradictions: Cancellation View of Negation and Reductio ad Absurdum

Satoru Niki @Connexive Logic

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Hitoshi Omori @Relevance Logic

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Takuro Onishi @Relevance Logic

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Graham Priest @BLOT

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Graham Priest @Connexive Logic

Cooper's Logic of Ordinary Discourse

Shuhei Shimamura @Connexive Logic

Coherence and Connexivity

Daniel Skurt @Connexive Logic

Solving a New Paradox of Deontic Logic (and a dozen other paradoxes) with RNmatrices for MC-based Modal Logics

Shawn Standefer @Relevance Logic

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Peter Verdée @BLOT

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Wen-fang Wang @BLOT

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Heinrich Wansing @BLOT

Remarks on strong dimathematism

In a sort of hostile review of Graham Priest's monograph Beyond the Limits of Thought, Cambridge University Press, 1995, that appeared in Review of Modern Logic, 1996, 437-439, Maria Frapolli comments on Priest's dialetheism, the view that there exist true contradictions, as follows:

"Contradictions are marks of error, not announcements of a deeper truth. Priest defends his position as if it were the battle of tolerance versus scholastic dogmatism. But, as I see it, we do not stand here in front of a dispute between antiquated orthodoxy and liberalizing heterodoxy, but between philosophy and charlatanism."

Thirty years after the publication of Beyond the Limits of Thought, dialetheism is widely regarded as a coherent and completely respectable view. Nevertheless, even if contradictions are not necessarily seen as marks of error, it may be irritating to consider it as theoretically rational to deal with non-trivial logics that are not only contradiction-tolerant in the sense of being paraconsistent but contain provable contradictions. In my talk, I will elaborate on a view that I have called "strong dimathematism" and that is meant as a contribution to making sense of provable contradictions in non-trivial negation inconsistent logics.

Heinrich Wansing @Connexive Logic

Constructiveness and connexivity

According to some authors, intuitionistic logic is the correct constructive logic. Sara Negri and Jan von Plato (Structural Proof Theory, Cambridge University Press, 2001, p. 25), for example, write that "[i]ntuitionistic reasoning and constructive reasoning ... are the same thing." In this talk, I will discuss the constructiveness of the non-trivial negation inconsistent hyperconnexive logic C, that is a conservative extension of positive intuitionistic logic. I will end with some comments on Leibniz-identity in second-order C.

Zach Weber @BLOT

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