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Birkhäuser - Birkhäuser Mathematics | Completeness Theory for Propositional Logics

Completeness Theory for Propositional Logics

Pogorzelski, Witold A., Wojtylak, Piotr


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  • 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

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. Global variants of the notion mean the possibility of getting all correct and reliable schemata of inference. Its local variants refer to the notion of truth given by some semantics. A uniform theory of completeness in its general and local meaning is carried out and it generalizes and systematizes some variety of the notion of completeness such as Post-completeness, structural completeness and many others. 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.

Content Level » Research

Keywords » Completeness - Consequence operation - Logical matrix - Post-completeness - Structural completeness - Universal Logic - logic - proof

Related subjects » Birkhäuser Mathematics

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