Abstract Several extensions of the stable model semantics are available to describe ‘intensional’ functions—functions that can be described in terms of other functions and predicates by logic programs. Such functions are useful for expressing inertia and default behaviors of systems, and can be exploited for alleviating the grounding bottleneck involving functional fluents. However, the extensions were defined in different ways under different intuitions. In this paper we provide several reformulations of the extensions, and note that they are in fact closely related to each other and coincide on large syntactic classes of logic programs.

We provide reformulations and generalizations of both the semantics of logic programs by Faber, Leone and Pfeifer and its extension to arbitrary propositional formulas by Truszczyński. Unlike the previous definitions, our generalizations refer neither to grounding nor to fixpoints, and apply to firstorder formulas containing aggregate expressions. In the same spirit as the first-order stable model semantics proposed by Ferraris, Lee and Lifschitz, the semantics proposed here are based on syntactic transformations that are similar to circumscription. The reformulations provide useful insights into the FLP semantics and its relationship to circumscription and the first-order stable model semantics.