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Algebraic semantics for modal logics I

Published online by Cambridge University Press:  12 March 2014

E. J. Lemmon
E. J. Lemmon*
Affiliation:
Claremont Graduate School, Claremont, California
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Extract

Modal logic received its modern impetus from the work of Lewis and Langford [10]. In recent years, however, their axiomatic approach, aided by somewhat ad hoc matrices for distinguishing different modal systems, has been supplemented by other techniques. Two of the most profound of these were, first, the algebraic methods employed by McKinsey and Tarski (see [11] and [12]) and, second, the semantic method of Kripke (see [5] and [6]); and there have been others. The aim of the present series of papers is to afford a synthesis of these methods. Thus, though new results are given, the interest lies rather in revealing interconnexions between familiar results and in providing a general framework for future research. In general, we show that semantic completeness results of the Kripke kind can be deduced from the algebraic results by means of one central theorem (Theorem 21).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 31 , Issue 1 , March 1966 , pp. 46 - 65
Copyright
Copyright © Association for Symbolic Logic 1996

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