Monadic Bounded Algebras

摘要

We introduce the equational notion of a monadic bounded algebra (MBA), intended to capture algebraic properties of bounded quantification. The variety of all MBA’s is shown to be generated by certain algebras of two-valued propositional functions that correspond to models of monadic free logic with an existence predicate. Every MBA is a subdirect product of such functional algebras, a fact that can be seen as an algebraic counterpart to semantic completeness for monadic free logic. The analysis involves the representation of MBA’s as powerset algebras of certain directed graphs with a set of “marked” points.