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In this study, a new paraconsistent four-valued logic called bi-classical connexive logic (BCC) is introduced as a Gentzen-type sequent calculus. Cut-elimination and completeness theorems for BCC are proved, and it… Click to show full abstract
In this study, a new paraconsistent four-valued logic called bi-classical connexive logic (BCC) is introduced as a Gentzen-type sequent calculus. Cut-elimination and completeness theorems for BCC are proved, and it is shown to be decidable. Duality property for BCC is demonstrated as its characteristic property. This property does not hold for typical paraconsistent logics with an implication connective. The same results as those for BCC are also obtained for MBCC, a modal extension of BCC.
Keywords:
classical connexive;
logic;
connexive logic;
modal extension;
cut elimination;
elimination completeness
Journal Title: Logic and Logical Philosophy
Year Published: 2019
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Journal Title: Logic and Logical Philosophy
Year Published: 2019
Link to full text (if available)
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recommendations!