A General Algebraic Semantics for Sentential Logics: 7 (Lecture Notes in Logic) - Softcover

Font, Josep M.

 
9783540616993: A General Algebraic Semantics for Sentential Logics: 7 (Lecture Notes in Logic)
Softcover
ISBN 10: 3540616993 ISBN 13: 9783540616993
Verlag: Springer, 2013

Inhaltsangabe

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.

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Reseña del editor

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.

Reseña del editor

This book presents a general process of algebraization, in a wide sense, applicable to any logical system presented as a sentential logic. This process is performed through the use of abstract logics, which are pairs consisting of an algebra and closure operature on it. The main innovation of the book is the notion of full model of a logic. Besides the funda- mental properties of this notion, the relationship between this approach and the more restricted, matrix based ones are studied. Moreover abstract logics are used in a natural way as models of Gentzen calculi. In this way algebraizations of some logics are obtained that are not possible in more standard approaches. The book is addressed to logicians with an interest in the algebraic aspect of logic or an interest in general theories of sentential logics.

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Verlag
Springer
Erscheinungsdatum
2013
Sprache
Englisch
ISBN 10 
3540616993
ISBN 13 
9783540616993
Einband
Tapa blanda
Anzahl der Seiten
148
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
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