Studies in Universal Logic

Completeness Theory for Propositional Logics

Authors: Pogorzelski, Witold A., Wojtylak, Piotr

  • Develops theory for one of the most important notions in the methodology of formal systems
  • Allows a more profound view upon essential properties of propositional systems
  • Theory of logical matrices and of consequence operations is exploited
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About this book

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.

Reviews

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)


Table of contents (4 chapters)

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-3-7643-8518-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.00
price for USA
  • ISBN 978-3-7643-8517-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Completeness Theory for Propositional Logics
Authors
Series Title
Studies in Universal Logic
Copyright
2008
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-7643-8518-7
DOI
10.1007/978-3-7643-8518-7
Softcover ISBN
978-3-7643-8517-0
Series ISSN
2297-0282
Edition Number
1
Number of Pages
VIII, 178
Topics