Abstract
An intermediate predicate logic L is called finite iff it is characterized by a finite partially ordered set M, i.e., iff L is the logic of the class of all predicate Kripke frames based on M. In this paper we study axiomatizability of logics of this kind. Namely, we consider logics characterized by finite trees M of a certain type (‘levelwise uniform’ trees) and establish the finite axiomatizability criterion for this case.
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References
Gabbay D., and D. de Jongh, 'Sequence of decidable finitely axiomatizable intermediate logics with the disjunction property', Journal of Symbolic Logic 39, No.1 (1974), 67–78.
Ghilardi S., 'Presheaf semantics and independence results for some non-classical first-order logics', Archive for Math. Logic 29, No.2 (1989), 125–136.
Hosoi T., 'On the axiomatic method and the algebraic method for dealing with propositional logics', Journal of the Faculty of Science, Univ. of Tokyo, Sect. I, 14, No.1 (1967), 131–169.
McKay C. G., 'On finite logics', Indag. Math. 29, No.3 (1967), 363–365.
Ono H., 'A study of intermediate predicate logics', Publications of RIMS, Kyoto Univ. 8, No.3, 1972–1973, pp. 619–649.
Ono H., 'Model extension theorem and Craig's interpolation theorem for intermediate predicate logics', Reports on Math. Logic 15 (1983), 41–58.
Ono H., 'Some problems in intermediate predicate logics', Reports on Math. Logic 21 (1987), 55–67.
Ono H., 'On finite linear intermediate predicate logics', Studia Logica 47, No.4 (1988), 391–399.
Shimura T., 'Kripke completeness of some intermediate predicate logics with the axiom of constant domain and a variant of canonical formulas', Studia Logica 52, No.1 (1993), 23–40.
Skvortsov D., 'On axiomatizability of some intermediate predicate logics (summary)', Reports on Math. Logic 22 (1988), 115–116.
Skvortsov D., 'On the predicate logic of finite Kripke frames', Studia Logica 54, No.1 (1995), 79–88.
Skvortsov D., 'On finite intersections of intermediate predicate logics', in A. Ursini and P. Agliano, (eds.), Logic and Algebra, Marcel-Dekker, N.Y., 1996 (Proc. of Intern. Conf. on Logic and Algebra in memory of R. Magari, Siena, 1994), pp. 667–688.
Skvortsov D., 'Not every “tabular” predicate logic is finitely axiomatizable', Studia Logica 59 (1997), 387–396.
Skvortsov D., 'The superintuitionistic predicate logic of finite Kripke frames is not recursively axiomatizable'. In preparation.
Smorynski C., 'Applications of Kripke models', in A. S. Troelstra (ed.), Metamathematical investigation of intuitionistic arithmetic and analysis, Lecture Notes Math. 344, Springer, 1973, pp. 324–391.
Yokota S., Axiomatization of the first-order intermediate logics of bounded Kripkean heights, I. Zeitschr. für math. Logik und Grundl. der Math. 35, No.5 (1989), 415–421.
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Skvortsov, D. On Intermediate Predicate Logics of some Finite Kripke Frames, I. Levelwise Uniform Trees. Studia Logica 77, 295–323 (2004). https://doi.org/10.1023/B:STUD.0000039028.22017.4f
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DOI: https://doi.org/10.1023/B:STUD.0000039028.22017.4f