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It is known that every α-dimensional quasi polyadic equality algebra (QPEA α ) can be considered as an α-dimensional cylindric algebra satisfying the merrygo- round properties . The converse of this proposition fails to be true. It is investigated in the paper how to get algebras in QPEA from algebras in CA. Instead of QPEA the class of the finitary polyadic equality algebras (FPEA) is investigated, this class is definitionally equivalent to QPEA. It is shown, among others, that from every (...) |
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We study algebras whose elements are relations, and the operations are natural “manipulations” of relations. This area goes back to 140 years ago to works of De Morgan, Peirce, Schröder . Well known examples of algebras of relations are the varieties RCAn of cylindric algebras of n-ary relations, RPEAn of polyadic equality algebras of n-ary relations, and RRA of binary relations with composition. We prove that any axiomatization, say E, of RCAn has to be very complex in the following sense: (...) |
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We study algebras whose elements are relations, and the operations are natural “manipulations” of relations. This area goes back to 140 years ago to works of De Morgan, Peirce, Schröder . Well known examples of algebras of relations are the varieties RCAn of cylindric algebras of n-ary relations, RPEAn of polyadic equality algebras of n-ary relations, and RRA of binary relations with composition. We prove that any axiomatization, say E, of RCAn has to be very complex in the following sense: (...) |
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Treating the existential quantification ∃ν i as a diamond $\diamond_i$ and the identity ν i = ν j as a constant δ ij , we study restricted versions of first order logic as if they were modal formalisms. This approach is closely related to algebraic logic, as the Kripke frames of our system have the type of the atom structures of cylindric algebras; the full cylindric set algebras are the complex algebras of the intended multidimensional frames called cubes. The main (...) |
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Three classes are introduced which are closely related to the class included in the title. It is proven that the class obtained from by replacing axiom C4 by the commutativity of single substitutions can be considered as the abstract class in the Resek–Thompson theorem, thus it is representable by set algebras. Then the class is defined and it is shown that the necessary and sufficient condition for neat embeddability of an algebra in CAα into is the validity of the merry-go-round (...) |
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The aim of this paper is to study the n-variable fragment of first order logic from a modal perspective. We define a modal formalism called cylindric mirror modal logic, and show how it is a modal version of first order logic with substitution. In this approach, we can define a semantics for the language which is closely related to algebraic logic, as we find Polyadic Equality Algebras as the modal or complex algebras of our system. The main contribution of the (...) |
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