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Erschienen in:
2008 | OriginalPaper | Buchkapitel
Semantic methods in propositional logic
Erschienen in: Completeness Theory for Propositional Logics
Verlag: Birkhäuser Basel
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In the first chapter we have introduced syntactic notions concerning propositional logics. The purpose of the present chapter is to give a semantic approach to the further study of formal systems. This approach is algebraic in its nature and therefore we will use elementary notions and results of the theory of abstract algebra. Our discussion is based on the notion of the consequence operation generated by a given relational system. (Pre)ordered algebras are examined first and next we consider logical matrices. Then these structures are applied to define propositional logics. In Section 2.5 some relationships between propositional logics and lattice theory are presented.