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General Algebraic Semantics for Sentential Logics
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154 b
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This book presents a general process of algebraization, in a wide sense, applicable to any logical system presented as a sentential logic. This process is performed through the use of abstract logics, which are pairs consisting of an algebra and closure operature on it. The main innovation of the book is the notion of full model of a logic. Besides the funda- mental properties of this notion, the relationship between this approach and the more restricted, matrix based ones are studied. Moreover abstract logics are used in a natural way as models of Gentzen calculi. In this way algebraizations of some logics are obtained that are not possible in more standard approaches. The book is addressed to logicians with an interest in the algebraic aspect of logic or an interest in general theories of sentential logics.
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