Classical Model Existence Theorem in Subclassical Predicate Logics. II
- 133 Downloads
This paper is a sequel to Lee (2007) and Lee (2009). In Lee (2009) it is proved that there are weak subclassical predicate logics (which are classically sound but weaker than the first-order logic) which also satisfy the Classical Model Existence property (CME for short): Every consistent set has a classical model. In this paper we improve the result in Lee (2007) by showing that some weak propositional logics (extensions of the implicational linear logic BCI) also satisfy CME in propositional case. For subclassical predicate logics two types of approaches (by prenex normal form construction or by Hintikka style construction) will be considered. By this we prove that CME for predicate logics also holds for some subclassical logics with weak propositional part.
- Lee, J. -L. (2007). Classical model existence theorem in propositional logics. In J. -Y. Béziau & A. Costa-Leite (Eds.), Perspectives on Universal Logic (pp. 179–97). Italy: Polimetrica, Monza.Google Scholar
- Lee, J. -L. (2007a). Classical model existence and left resolution. Logic and Logical Philosophy, 16(4), 333–52.Google Scholar
- Lee, J. -L. (2009) Classical model existence theorem in subclassical predicate logics. I. In D. Makinson, J. Malinowski, H. Wansing (eds.), Trends in Logic: Towards mathematical philosophy Trends in logic—Studia Logica Library, vol. 28, (pp. 187-99). Dordrecht: Springer.Google Scholar
- Paoli, F. (2002). Substructural Logics: A Primer, Trends in logic—Studia Logica Library: Kluwer Academic Publishers.Google Scholar