A General Algebraic Semantics for Sentential Logics

Font, Josep M., and Ramon Jansana

ISBN 10: 3540616993 / ISBN 13: 9783540616993

Published by Springer, Berlin and New York, 1996

About this Item

An ex-library copy in originall yellow paper covers. The usual ex-libris markings. The binding is sound, the text is clean/unmarked, and there is little wear to the covers.

Seller Inventory # 062353

Bibliographic Details

• Title: A General Algebraic Semantics for Sentential Logics
• Publisher: Springer, Berlin and New York
• Publication Date: 1996
• Language: English
• ISBN 10: 3540616993
• ISBN 13: 9783540616993
• Binding: Trade Paperback
• Edition: First Edition.
• Condition: Good
• Dust Jacket Condition: No Dust Jacket
• Book Type: Book

About this title

Synopsis

The purpose of this monograph is to develop a very general approach to the algebra­ ization of sententiallogics, to show its results on a number of particular logics, and to relate it to other existing approaches, namely to those based on logical matrices and the equational consequence developed by Blok, Czelakowski, Pigozzi and others. The main distinctive feature of our approachlies in the mathematical objects used as models of a sententiallogic: We use abstract logics, while the dassical approaches use logical matrices. Using models with more structure allows us to reflect in them the metalogical properties of the sentential logic. Since an abstract logic can be viewed as a "bundle" or family of matrices, one might think that the new models are essentially equivalent to the old ones; but we believe, after an overall appreciation of the work done in this area, that it is precisely the treatment of an abstract logic as a single object that gives rise to a useful -and beautiful- mathematical theory, able to explain the connections, not only at the logical Ievel but at the metalogical Ievel, between a sentential logic and the particular dass of models we associate with it, namely the dass of its full models. Traditionally logical matrices have been regarded as the most suitable notion of model in the algebraic studies of sentential logics; and indeed this notion gives sev­ eral completeness theorems and has generated an interesting mathematical theory.