Completeness Theory for Propositional Logics

Piotr Wojtylak

ISBN 10: 3764385170 / ISBN 13: 9783764385170

Verlag: Birkhäuser Basel, Springer Basel Apr 2008, 2008

Beschreibung

Neuware -Completeness is one of the most important notions in logic and the foundations of mathematics. Many variants of the notion have been de ned in literature. We shallconcentrateonthesevariants,andaspects,of completenesswhicharede ned in propositional logic. Completeness means the possibility of getting all correct and reliable sc- mata of inference by use of logical methods. The word ¿all¿, seemingly neutral, is here a crucial point of distinction. Assuming the de nition as given by E. Post we get, say, a global notion of completeness in which the reliability refers only to syntactic means of logic and outside the correct schemata of inference there are only inconsistent ones. It is impossible, however, to leave aside local aspects of the notion when we want to make it relative to some given or invented notion of truth. Completeness understood in this sense is the adequacy of logic in relation to some semantics, and the change of the logic is accompanied by the change of its semantics. Such completeness was e ectively used by J. ukasiewicz and investigated in general terms by A. Tarski and A. Lindenbaum, which gave strong foundations for research in logic and, in particular, for the notion of consequence operation determined by a logical system. The choice of logical means, by use of which we intend to represent logical inferences, is also important. Most of the de nitions and results in completeness theory were originally developed in terms of propositional logic. Propositional formal systems nd many applications in logic and theoretical computer science.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 192 pp. Englisch.

Bestandsnummer des Verkäufers 9783764385170

Bibliografische Details

• Titel: Completeness Theory for Propositional Logics
• Verlag: Birkhäuser Basel, Springer Basel Apr 2008
• Erscheinungsjahr: 2008
• Sprache: Englisch
• ISBN-10: 3764385170
• ISBN-13: 9783764385170
• Einband: Taschenbuch
• Zustand: Neu

Über diesen Titel

Inhaltsangabe

This book develops the theory of one of the most important notions in the methodology of formal systems. Particularly, completeness plays an important role in propositional logic where many variants of the notion have been defined. This approach allows also for a more profound view upon some essential properties of propositional systems. For these purposes, the theory of logical matrices, and the theory of consequence operations is exploited.

Críticas

From the reviews:

“The book provides a uniform treatment of the variety of results centered around the completeness property. ... book is a good introduction to the problems of completeness. A wealth of examples, comments and theorems well elucidate various difficult aspects of the theory. ... From the methodological viewpoint, the book applies the tools that were elaborated in metalogic ... . AAL also offers subtle tools for tackling some of the problems raised in the book.” (Janusz M. Czelakowski, Mathematical Reviews, Issue 2010 c)

“The book is written with exceptional clarity and precision. This combination makes it accessible to a wide spectrum of potential readers, and hence it can be recommended to anyone interested in formal logic. ... the book may stimulate to further research by opening new fields of investigation and introducing new concepts and ideas. Finally, one cannot miss the extensive and up-to-date bibliography which is included in the book. Summing up, the book ... offers a deep and intelligible exposition of completeness theory in propositional logics.”­­­ (Tomasz Połacik, Studia Logica, Vol. 95, 2010)