Quantified Equilibrium Logic and Foundations for Answer Set Programs

A Revised Concept of Safety for General Answer Set Programs

“…Satisfaction in classical logic can be encoded by satisfaction by total models in here-and-there logic [19]; so we can characterise the classical models of the formula in the previous lemma by the total models of a formula in QHT, as follows: Corollary 1. Let ϕ be a ground sentence and α = (α 1 , .…”

“…As a logical basis the non-classical logic of quantified here-and-there, QHT, is used (see also [14]). By expanding the language to include new predicates, this logic can be embedded in classical first-order logic, [19], and this permits an alternative but equivalent formulation of the concept of stable model for first-order formulas, expressed in terms of classical, second-order logic [6]. The latter definition of answer set has been further studied in [10,11] where the basis of a first-oder programming language, RASPL-1, is described.…”

Connecting First-Order ASP and the Logic FO(ID) through Reducts

“…Recently researchers have sought to address these limitations. In particular, Pearce and Valverde [19] introduced the quantified equilibrium logic. That logic is a first-order extension of the equilibrium logic by Pearce [18], a propositional logic with the semantics of equilibrium models.…”

“…For the class of theories that we call programs, the concept of the reduct can be extended in two ways. We use one of them as a bridge to the first-order ASP as developed by Pearce and Valverde [19] and Ferraris et al [8]. We use the other as the connection to the logic FO(ID), and note here in passing that it also provides an alternative characterization of a version of the first-order ASP proposed by Denecker et al [3].…”

“…We show that our definition of stable models of a sentence is equivalent to the one based on the operator SM . We proceed in a roundabout way through a connection between our concept of stability and that based on the quantified logic here-and-there [19].…”