Abstract
Pseudo EQ-algebras were introduced by X.L. Xin as possible algebraic semantics for fuzzy type theory. The main goal of this paper is to investigate pseudo EQ-algebras with internal states. To begin with, we introduce the notion of pseudo EQ-algebras with internal state(simplify, ISPEQ-algebra) and study its properties. Moreover, we discuss the relation between ISPEQ-algebras and states on pseudo EQ-algebras. In the following, we study state filters(simplify S-fliters) and state prefilters(simplify S-prefliters) of ISPEQ-algebras. We construct ISPEQ-algebras from S-fliters and derive congruence relation θ of ISPEQ-algebras. In the end, we give the generating formula of prefilters on residuated pseudo EQ-algebras and based on that we get the generating formula of S-prefilters on residuated pseudo EQ-algebras.
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