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 systems | |||||||||
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Jos� M. M.�Ndez & Francisco Salto (1995). Urquhart's C with Intuitionistic Negation: Dummett's LC Without the Contraction Axiom. Notre Dame Journal of Formal Logic 36 (3):407-413.
Pierluigi Minari (1983). Completeness Theorems for Some Intermediate Predicate Calculi. Studia Logica 42 (4):431 - 441.
Paolo Gentilini (1993). Syntactical Results on the Arithmetical Completeness of Modal Logic. Studia Logica 52 (4):549 - 564.
Giovanna Corsi (2002). A Unified Completeness Theorem for Quantified Modal Logics. Journal of Symbolic Logic 67 (4):1483-1510.
Adriana Galli, Marta Sagastume & Gonzalo E. Reyes (2000). Completeness Theorems Via the Double Dual Functor. Studia Logica 64 (1):61-81.
Norihiro Kamide (2009). Proof Systems Combining Classical and Paraconsistent Negations. Studia Logica 91 (2):217 - 238.
José M. Mendez & Francisco Salto (1998). A Natural Negation Completion of Urquhart's Many-Valued Logic C. Journal of Philosophical Logic 27 (1):75-84.
Kenneth Harris & Branden Fitelson (2001). Comments on Some Completeness Theorems of Urquhart and Méndez & Salto. Journal of Philosophical Logic 30 (1):51-55.
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