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Axiomatizing the Skew Boolean Propositional Calculus
, 2007
"... Abstract. The skew Boolean propositional calculus (SBP C) is a generalization of the classical propositional calculus that arises naturally in the study of certain wellknown deductive systems. In this article, we consider a candidate presentation of SBP C and prove it constitutes a Hilbertstyle ax ..."
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Abstract. The skew Boolean propositional calculus (SBP C) is a generalization of the classical propositional calculus that arises naturally in the study of certain wellknown deductive systems. In this article, we consider a candidate presentation of SBP C and prove it constitutes a Hilbertstyle axiomatization. The problem reduces to establishing that the logic presented by the candidate axiomatization is algebraizable in the sense of Blok and Pigozzi. In turn, this is equivalent to verifying four particular formulas are derivable from the candidate presentation. Automated deduction methods played a central role in proving these four theorems. In particular, our approach relied heavily on the method of proof sketches. 1.
Orthomodular Lattices
, 2008
"... Summary. The main result of the article is the solution to the problem of short axiomatizations of orthomodular ortholattices. Based on EQP/Otter results [10], we gave a set of three equations which is equivalent to the classical, much longer equational basis of such a class. Also the basic example ..."
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Summary. The main result of the article is the solution to the problem of short axiomatizations of orthomodular ortholattices. Based on EQP/Otter results [10], we gave a set of three equations which is equivalent to the classical, much longer equational basis of such a class. Also the basic example of the lattice which is not orthomodular, i.e. benzene (or B6) is defined in two settings – as a relational structure (poset) and as a lattice. As a preliminary work, we present the proofs of the dependence of other axiomatizations of ortholattices. The formalization of the properties of orthomodular lattices follows [4].