A continuum of incomplete intermediate logics

• Autorzy: Litak T.
• Języki publikacji: EN

Abstrakty

EN

Although in 1977 V.B. Shehtman constructed the first Kripke incomplete intermediate logic, no-one in the known literature has completed his work by constructing a continuum of such logics. After a substantial reminder on how an incomplete logic can be obtained, I will construct a sequence of frames similar to those used by Jankov and Fine. None of these frames can be reduced by a p-morphism to another; at the same time, there are no p-morphisms from generated subframes of the Fine frame onto any frame from the considered sequence. All of the frames satisfy all of Shehtman's axioms. Therefore, by using the characteristic formulas of the frames from the sequence it is possible to obtain the desired conclusion.

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2002
• Tom: No. 36
• Strony: 131--142
• Opis fizyczny: Bibliogr. 12 poz., rys.

Twórcy

autor

Litak T.

• Department of Logic Jagiellonian University Grodzka 52 31-044 Cracow,

Bibliografia

• [1] R.A. Bull, Review, Journal of Symbolic Logic, 47 (1982), pp.440-445.
• [2] R.A. Bull, Review, Journal of Symbolic Logic, 48 (1983), pp.488-495.
• [3] A.V. Chagrov and M.V. Zakharyaschev, Modal Logic, Clarendon Press, Oxford 1997.
• [4] K. Fine, An Ascending Chain of S4 Logics, Theoria, 40 (1974), pp.110-116.
• [5] K. Fine, An Incomplete Logic Containing S4, Theoria, 40 (1974), pp.23-29.
• [6] D.M. Gabbay and D.H.J. de Jongh, A Sequence of Decidable Finitely Axiomatizable Intermediate Logics with the Disjunction Property, Journal of Symbolic Logic, 39 (1974), pp.67-78.
• [7] V.A. Jankov, Constructing a Sequence of Strongly Independent Superintuitionistic Propositional Calculi, Soviet Mathematics Doklady, 9 (1968), pp.806-807.
• [8] T. Litak. Incompleteness revisited, Forthcoming.
• [9] H. Ono, A Study of Intermediate Predicate Logics, Publ. RIMS, Kyoto University, 8(19 72/73), pp.619-649.
• [10] V.V. Rybakov, Noncompact Extensions of the Logic S4, Algebra and logic, 16 (1977), pp.321-334.
• [11] V.B. Shehtman, On Incomplete Propositional Logics, Soviet Mathematics Doklady, 18 (1977), pp.985-989.
• [12] V.B. Shehtman, Topological models of propositional logics, Semiotics and Information Science, 15 (1980), pp.74–98. (Russian)