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Cathoristic logic. A logic for capturing inferences between atomic sentences. (English) Zbl 1440.03042

Di Pierro, Alessandra (ed.) et al., From lambda calculus to cybersecurity through program analysis. Essays dedicated to Chris Hankin on the occasion of his retirement. Cham: Springer. Lect. Notes Comput. Sci. 12065, 17-85 (2020).
Summary: Cathoristic logic is a multi-modal logic where negation is replaced by a novel operator allowing the expression of incompatible sentences. We present the syntax and semantics of the logic including complete proof rules, and establish a number of results such as compactness, a semantic characterisation of elementary equivalence, the existence of a quadratic-time decision procedure, and Brandom’s incompatibility semantics property. We demonstrate the usefulness of the logic as a language for knowledge representation.
For the entire collection see [Zbl 1435.68026].

MSC:

03B45 Modal logic (including the logic of norms)
03B65 Logic of natural languages
68T27 Logic in artificial intelligence
68T30 Knowledge representation
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