POLYADIC BOOLEAN ALGEBRAS

Relation Algebras from Cylindric and Polyadic Algebras

This paper is a survey of recent results concerning connections between relation algebras (RA), cylindric algebras (CA) and polyadic equality algebras (PEA). We describe exactly which subsets of the standard axioms for RA are needed for axiomatizing RA over the RA-reducts of CA3’s, and we do the same for the class SA of semi-associative relation algebras. We also characterize the class of RA-re...

Polyadic Algebras over Nonclassical Logics

The polyadic algebras that arise from the algebraization of the first-order extensions of a SIC are characterized and a representation theorem is proved. Standard implicational calculi (SIC)’s were considered by H. Rasiowa [19] and include classical and intuitionistic logic and their various weakenings and fragments, the many-valued logics of Post and Lukasiewicz, modal logics that admit the ru...

An autobiography of Polyadic Algebras

In the 1950’s I set out to revolutionize logic. I didn’t succeed (not yet!), but it wasn’t for want of trying. Logic has always fascinated me. In the common-sense sense of the word logic was easy; I had no inclination to commit the obvious errors of reasoning, and long chains of deductions were not intimidating. When I was told about syllogisms, I said “sure, obviously”, and didn’t feel that I ...

On Automorphisms of Polyadic Algebras

Introduction. This paper belongs to the theory of polyadic algebras as developed by Haimos [11-15], but it has a bearing on the theory of models. Two central concepts are those of homogeneous(2) and of normal extensions of a polyadic algebra (see the beginning of §2 and of §6). These concepts bear some resemblance to concepts of the theory of algebraic extensions of fields; however, we have bee...

On Amalgamation of Reducts of Polyadic Algebras