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Completeness Theory for Propositional Logics

Completeness Theory for Propositional Logics
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Completeness is one of the most important notions in the methodology of formal systems. Particularly, it 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 developed by introducing the so-called [Gamma]-completeness. It generalizes and systematizes an essential variety of the notion of completeness such as Post-completeness and structural completeness. The presented approach allows also for a new perspective on some essential properties of propositional systems, for example two-valuedness. For these purposes the theory of logical matrices and the theory of consequence operations are exploited. 
Springer; January 2008
186 pages; ISBN 9783764385187
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