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Boolean Algebras with Functions - Correspondence, Completeness and Quantifier Elimination


Ohlbach,  Hans Jürgen
Programming Logics, MPI for Informatics, Max Planck Society;

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Ohlbach, H. J. (1995). Boolean Algebras with Functions - Correspondence, Completeness and Quantifier Elimination.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-ACEE-F
It is shown how axiomatic specifications of Boolean Algebras with extra functions as well as propositional extension of standard propositional logic can be transformed and simplified using syntactic methods, in particular quantifier elimination algorithms for second--order predicate logic. This enables us to exploit representation theorems and model theoretic semantics for these algebras and logics in such a way that for special instances of these systems, i.e. particular algebras and particular logics the corresponding specializations on the semantic side can be computed automatically. Special cases of the results of this paper are the theorem proving aspects of J{\'o}nsson and Traski's representation theorem for Boolean Algebras with operators, completeness of different possible worlds semantics for modal logics and a clarification of the correlation between correspondence and completeness in modal logics.