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Comments on some completeness theorems of Urquhart and méndez & Salto
Journal of Philosophical Logic 30 (1):51-55 (2001)
Abstract
Urquhart and Méndez and Salto claim to establish completeness theorems for the system C and two of its negation extensions. In this note, we do the 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 systemsAuthor's Profile
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Citations of this work
Relational ternary semantics for a logic equivalent to Involutive Monoidal t-norm based logic IMTL.Gemma Robles & José M. Méndez - 2005 - Bulletin of the Section of Logic 34 (2):101-116.
References found in this work
A propositional calculus with denumerable matrix.Michael Dummett - 1959 - Journal of Symbolic Logic 24 (2):97-106.
Entailment: The Logic of Relevance and Necessity, Vol. II.Alan Ross Anderson, Nuel D. Belnap & J. Michael Dunn - 1992 - Princeton, NJ, USA: Princeton University Press.
Many-valued logic.Alasdair Urquhart - 1986 - In D. Gabbay & F. Guenther, Handbook of Philosophical Logic, Vol. Iii. D. Reidel Publishing Co..
A natural negation completion of Urquhart's many-valued logic C.José M. Mendez & Francisco Salto - 1998 - Journal of Philosophical Logic 27 (1):75-84.
Urquhart's C with Intuitionistic Negation: Dummett's LC without the Contraction Axiom.José M. Méndez & Francisco Salto - 1995 - Notre Dame Journal of Formal Logic 36 (3):407-413.
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