Completeness Theory for Propositional Logics
Completeness is one of the most important notions in logic and the foundations of mathematics. Many variants of the notion have been denied in literature. We shall concentrate on the sevariants,and aspects,of completeness which are denied in propositional logic. Completeness means the possibility of...
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| Format: | Livre numérique |
| Jezik: | Anglais |
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Basel :
Birkhäuser Basel : Springer e-books
[20..].
Cham : Springer Nature |
| Serija: | Studies in Universal Logic
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L'impression du document génère 185 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
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| Edition sous un autre format: | • Completeness theory for propositional logics, Witold A. Pogorzelski, Piotr Wojtylak, Basel, Birkhäuser, 2008, 1 vol. (viii-178 p.), Studies in universal logic, 978-3-7643-8517-0 |
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| 008 | 080829q2000 xxe ||| |||| 00| 0 eng d | ||
| 009 | PPN127049533 | ||
| 020 | |a 9783764385187 | ||
| 041 | 0 | |a eng | |
| 082 | |a 511.3 | ||
| 084 | |a 03-01. 2010 | ||
| 084 | |a 03B05. 2010 | ||
| 084 | |a 03G10. 2010 | ||
| 100 | 1 | |a Pogorzelski, Witold A., |d 1927- | |
| 245 | 1 | 0 | |a Completeness Theory for Propositional Logics |c Witold A. Pogorzelski, Piotr Wojtylak. |
| 260 | |a Basel : |b Birkhäuser Basel : |b Springer e-books. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 1 | |a Studies in Universal Logic | |
| 500 | |a L'impression du document génère 185 p. | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. Index | ||
| 505 | 0 | |a Introduction -- 1. Basic notions: Propositional languages -- 2. Semantic methods in propositional logic: Preordered sets -- 3. Completeness of propositional logic: Generalized completeness -- 4. Characterization of propositional connectives: Cn-definitions -- Appendix: The fundamental metatheorem for the classical propositional logic -- A proof system for the classical logic -- Abstract algebras -- Preliminary lattice-theoretical notions -- Propositional logics -- Brief exposition of the most important propositional logics -- Preordered algebras -- Logical matrices -- Adequacy -- Propositional logic and lattice theory -- Post-completeness -- The problem of uniqueness of Lindenbaum extensions -- Some related concepts -- The system (D) -- Variants -- The system (I) -- Classical logic | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a Completeness is one of the most important notions in logic and the foundations of mathematics. Many variants of the notion have been denied in literature. We shall concentrate on the sevariants,and aspects,of completeness which are denied 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 definition 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 and many applications in logic and theoretical computer science | ||
| 650 | |a Théorème de complétude | ||
| 650 | |a Logique symbolique et mathématique | ||
| 700 | 1 | |a Wojtylak, Piotr. |4 aut | |
| 776 | 0 | |0 125303998 |t Completeness theory for propositional logics |f Witold A. Pogorzelski, Piotr Wojtylak |c Basel |n Birkhäuser |d 2008 |p 1 vol. (viii-178 p.) |s Studies in universal logic |z 978-3-7643-8517-0 | |
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