Abstract
To describe semantics of a logical system one should define notions of a model and the truth in a model. A major part of classical first order model theory can be developed within the standard semantics, while alternative types of semantics (such as sheaves, forcing, polyadic algebras) play an auxiliary role.
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References
van Benthem, J. F. A. K., 1978, Two simple incomplete logics, Theoria 44:No. 1, 25–37.
Dragalin, A. G., 1979, “Mathematical Intuitionism. Introduction to Proof Theory”, Nauka, Moscow (in Russian).
Ellerman, D., 1974, Sheaves of structures and generalized ultraproducts, Ann. Math. Log. 7:No. 2–3, 163–195.
Fine, K., 1974, An incomplete logic containing S4, Theoria 40:No. 1, 23–29.
Fine, K., 1978, Model theory for modal logics, I: De re/de dicto distinction, J. Phil. Log. 7:125–156.
Fourman, M.P., and Scott, D.S., 1979, Sheaves and logic, in: “Lect. Notes Math.”, 753:302–401.
Gerson, M. S., The inadequacy of neighborhood semantics for modal logics, J. Symb. Logic. 40:No. 2, 141–147.
Godement, R., 1958, “Topologie Algebrique et Theorie de Faisceaux”, Hermann, Paris.
Goldblatt, R., 1979, “Topoi”, Studies in Logic and Found. Math., v.98.
Görnemann, S., 1971, A logic stronger than intuitionism, J. Symb. Logic 36:No. 2, 249–261.
Higgs, D., 1973, “A Category Approach to Boolean-Valued Set Theory”, Lect. Notes, Univ. of Waterloo.
Kripke, S. A., 1963, Semantical considerations on modal logic, Acta Philos. Fennica, 16:83–94.
Kripke, S. A., 1965, Semantical analysis of intuitionistic logic, in: “Formal Systems and Recursive Functions”, J. N. Crossley and M. A. E. Dummett, eds., North-Holland, pp 92–130.
Montagna, F., 1984, The predicate modal logic of provability, Notre Dame J. of Form. Log., 25:No. 2, 179–189.
Montague, R., 1970, Pragmatics and intensional logic, Synthese 22:No. 112, 68–94.
Ono, H., 1973, Incompleteness of semantics for intermediate predicate logics. I: Kripke’s semantics, Proc. Jap. Acad. 49:No. 9, 711–713.
Ono, H., 1983, Model extension theorem and Craig’s interpolation theorem for intermediate predicate logics, Reports in Math. Logic, 15:41–58.
Rasiowa, H., and Sikorski, R., 1963, “The Mathematics of Metamathematics”,Warsaw.
Reyes, G., 1978, Théorie des modeles et faisceaux, Adv. Math., 30:No. 2, 156–170.
Schütte, K., 1968, Vollständige Systeme modaler and intuitionistischer Logik, Ergebn. Math., v. 42.
Shehtman, V. B., 1977, On incomplete propositional logics, Dokl. AN SSSR. 235:No. 3, 542–545 (in Russian).
Shehtman, V. B., 1980, Topological models of propositional logics, Semiotika i informatika No. 15:74–98 (in Russian).
Thomason, R. H., 1968, On the strong semantical completeness of the intuitionistic predicate calculus, J. Symb. Logic, 33:1–7.
Thomason, S. K., 1972, Semantic analysis of tense logic, J. Symb. Logic 37: No. 1, 150–158.
Thomason, S. K., 1974, An incompleteness theorem in modal logic, Theoria 40:No. 1, 30–34.
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© 1990 Plenum Press, New York
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Shehtman, V., Skvortsov, D. (1990). Semantics of Non-Classical First Order Predicate Logics. In: Petkov, P.P. (eds) Mathematical Logic. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0609-2_9
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DOI: https://doi.org/10.1007/978-1-4613-0609-2_9
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