Peirce Algebras and Relation Algebras are Equipollent

Schmidt, R. A. (Sept. 1993/Aug. 1994)

Extended Abstract. Manuscript. Comments are welcome. BiBTeX, with access restriction: DVI, PostScript

In this Note, I show that the classes RA of relation algebras and PA of Peirce algebras are equivalent in a certain sense. Since relation algebras and Peirce algebras are structurally different, the former are one-sorted algebras and the latter are two-sorted algebras, the usual notion of equivalence is inappropriate. Instead, I use the notions of equipollence and equipollent extension for classes of algebras, which are defined in Tarski and Givant (1987) for logics. The result has applications in modal logic, KL-ONE based knowledge representation and other fields.

Renate A. Schmidt
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