Completeness Theory for Propositional Logics

• Κύριοι συγγραφείς: Pogorzelski, Witold A. (Συγγραφέας), Wojtylak, Piotr (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Basel : Birkhäuser Basel, 2008.
• Σειρά: Studies in Universal Logic
• Θέματα: Mathematics.; Mathematical logic.; Mathematical Logic and Foundations.

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...

Πίνακας περιεχομένων:

• 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.