Errata Corrige to “Pragmatic and dialogic interpretation of bi-intuitionism. Part I”

Abstract. This paper considers a topos-theoretic structure for the interpretation of co-constructive logic for proofs and refutations following [49]. It is notoriously tricky to define a proof-theoretic semantics for logics that adequately represent constructivity over proofs and refutations. By developing abstractions of elementary topoi, we consider an elementary topos as structure for proofs, and complement topos as structure for refutation. In doing so, it is possible to consider a dialogue structure between these topoi, and also control their relation such that classical logic (interpreted in a Boolean topos) is simulated where proofs and refutations are conclusive.

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On an intuitionistic logic for pragmatics

Bellin

Carrara

Chiffi

2015

J Logic Computation

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We reconsider the pragmatic interpretation of intuitionistic logic [21] regarded as a logic of assertions and their justifications and its relations with classical logic. We recall an extension of this approach to a logic dealing with assertions and obligations, related by a notion of causal implication [14, 45]. We focus on the extension to co-intuitionistic logic, seen as a logic of hypotheses [8, 9, 13] and on polarized bi-intuitionistic logic as a logic of assertions and conjectures: looking at the S4 modal translation, we give a definition of a system AHL of bi-intuitionistic logic that correctly represents the duality between intuitionistic and co-intuitionistic logic, correcting a mistake in previous work [7, 10]. A computational interpretation of cointuitionism as a distributed calculus of coroutines is then used to give an operational interpretation of subtraction. Work on linear co-intuitionism is then recalled, a linear calculus of co-intuitionistic coroutines is defined and a probabilistic interpretation of linear co-intuitionism is given as in [9]. Also we remark that by extending the language of intuitionistic logic we can express the notion of expectation, an assertion that in all situations the truth of p is possible and that in a logic of expectations the law of double negation holds. Similarly, extending co-intuitionistic logic, we can express the notion of conjecture that p, defined as a hypothesis that in some situation the truth of p is epistemically necessary.

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Errata Corrige to “Pragmatic and dialogic interpretation of bi-intuitionism. Part I”

Cited by 3 publications

References 5 publications

Rules in Dialogue

Rules in Dialogue

Structuring Co-constructive Logic for Proofs and Refutations

On an intuitionistic logic for pragmatics

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