Comments on some completeness theorems of Urquhart and Mendez and Salto

2025-02-06 Classification：Philosophy Click()
Author：Harris, K; Fitelson, B

Article Title：Comments on some completeness theorems of Urquhart and Mendez and Salto

Abstract：
Urquhart and Mendez and Salto claim to establish completeness theorems for the system C and two of its negation extensions. In this note, we do that following three things: (1) provide a counterexample to all of these alleged completeness theorems, (2) attempt to diagnose the mistakes in the reported completeness proofs, and (3) provide complete axiomatizations of the desired systems.

Keywords: completeness; substructural; logic; man-valued; matrix

DOI: 10.1023/A:1017549804474

Source：JOURNAL OF PHILOSOPHICAL LOGIC

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