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Interpolation and DefinabilityModal and Intuitionistic Logics$
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Dov M. Gabbay and Larisa Maksimova

Print publication date: 2005

Print ISBN-13: 9780198511748

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198511748.001.0001

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MODAL AND SUPERINTUITIONISTIC LOGICS: BASIC CONCEPTS

MODAL AND SUPERINTUITIONISTIC LOGICS: BASIC CONCEPTS

Chapter:
(p.35) 2 MODAL AND SUPERINTUITIONISTIC LOGICS: BASIC CONCEPTS
Source:
Interpolation and Definability
Author(s):

D.M. Gabbay

L. Maksimova

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198511748.003.0002

This chapter presents basic definitions and known results related to modal and superintuitionistic logics. Well-known Hilbert-style axiomatizations of the most known modal systems K, D, T, K4, D4, S4, S5 and also of the intuitionistic logic are given. For each of the calculi, its relational semantics is considered. The algebraic semantics and its connection with relational semantics via representation theorems are presented.

Keywords:   Kripke semantics, pseudoboolean algebra, modal algebra, representation theorem

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