Buch, Englisch, 178 Seiten, Format (B × H): 170 mm x 244 mm, Gewicht: 342 g
Reihe: Studies in Universal Logic
Buch, Englisch, 178 Seiten, Format (B × H): 170 mm x 244 mm, Gewicht: 342 g
Reihe: Studies in Universal Logic
ISBN: 978-3-7643-8517-0
Verlag: Springer
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.
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Research
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Weitere Infos & Material
Introduction.- 1. Basic notions: Propositional languages.- Abstract algebras.- Preliminary lattice-theoretical notions.- Propositional logics.- Brief exposition of the most important propositional logics.- 2. Semantic methods in propositional logic: Preordered sets.- Preordered algebras.- Logical matrices.- Adequacy.- Propositional logic and lattice theory.- 3. Completeness of propositional logic: Generalized completeness.- Post-completeness.- The problem of uniqueness of Lindenbaum extensions.- Some related concepts.- 4. Characterization of propositional connectives: Cn-definitions.- The system (D).- Variants.- The system (I).- Classical logic.- Appendix: The fundamental metatheorem for the classical propositional logic.- A proof system for the classical logic.
