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A General Algebraic Semantics for Sentential Logics

Josep M. Font, Ramon Jansana (Autoren)

Buch | Softcover

VI, 139 Seiten

1996
Springer Berlin (Verlag)
978-3-540-61699-3 (ISBN)

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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.

Erscheint lt. Verlag	2.10.1996
Reihe/Serie	Lecture Notes in Logic
Zusatzinfo	VI, 139 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	235 g
Themenwelt	Mathematik / Informatik ► Informatik ► Programmiersprachen / -werkzeuge
	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
Schlagworte	abstract algebraic logic • algebraizable logics • consequence operations • full model • generalized matrix • gentzen calculi • gentzen system • K-congruence • leibniz operator • logic matrix • Model • protoalgebraic logics • sentential logic • strongly adequate gentze • strongly adequate gentzen system • tarski operator
ISBN-10	3-540-61699-3 / 3540616993
ISBN-13	978-3-540-61699-3 / 9783540616993
Zustand	Neuware