Modal Deduction in Second-Order Logic and Set Theory - II

被引：4

作者：

Van Benthem J. ^{[1
]}

D'Agostino G. ^{[2
]}

Montanari A. ^{[1
]}

Policriti A. ^{[2
]}

机构：

[1] ILLC, Universiteit Van Amsterdam, Plantage Muidergracht 24

[2] Dipaitimento di Malematica E Lufuriualica, Università di Udine, Via delle Scienze 206

来源：

Studia Logica | 1998年 / 60卷 / 3期

关键词：

Modal Deduction; Modal Logic; Second-Order Logic; Set theory; Translation Methods;

D O I：

10.1023/A:1005037512998

中图分类号：

学科分类号：

摘要：

In this paper, we generalize the set-theoretic translation method for polymodal logic introduced in [11] to extended modal logics. Instead of devising an ad-hoc translation for each logic, we develop a general framework within which a number of extended modal logics can be dealt with. We first extend the basic set-theoretic translation method to weak monadic second-order logic through a suitable change in the underlying set theory that connects up in interesting ways with constructibility; then, we show how to tailor such a translation to work with specific cases of extended modal logics. © 1998 Kluwer Academic Publishers.

引用

页码：387 / 420

页数：33

共 23 条

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[3] Barwise, J., Moss, L., (1996) Vicious Circles, , CSLI, Lecture Notes No. 60
[4] Van Benthem, J., Syntactic aspects of modal incompleteness theorems (1979) Theoria, 45, pp. 67-81
[5] Van Benthem, J., Doets, K., Higher-Order Logic (1983) Handbook of Philosophical Logic., 1, pp. 275-329. , D. Gabbay and F. Guenthner (eds.)
[6] D. Reidel Pub. Comp., DordrechtHolland
[7] Van Benthem, J., (1985) Modal Logic, and Classical Logic, , Bibliopolis, Napoli and Atlantic Heights (N.J.)
[8] Van Benthem, J., D'Agostino, G., Montanari, A., Policriti, A., Modal Deduction in Second-Order Logic and Set Theory - F (1997) Journal of Logic and Computation, 7 (2), pp. 251-265
[9] Van Benthem, J., D'Agostino, G., Montanari, A., Policriti, A., Modal deduction in Second-Order Logic and Set Theory - II (1996) Research Report, in the ILLC-series, ML-96-08, , University of Amsterdam, July
[10] Bernays, P., A system of axiomatic set theory. Part F (1937) Journal of Symbolic Logic, 2, pp. 65-77

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