Query answering in resource-based answer set semantics

Abstract

In recent work we defined resource-based answer set semantics, which is an extension to answer set semantics stemming from the study of its relationship with linear logic. In fact, the name of the new semantics comes from the fact that in the linear-logic formulation every literal (including negative ones) were considered as a resource. In this paper, we propose a query-answering procedure reminiscent of Prolog for answer set programs under this extended semantics as an extension of XSB-resolution for logic programs with negation. 1 We prove formal properties of the proposed procedure. Under consideration for acceptance in TPLP.

About Epistemic Negation and World Views in Epistemic Logic Programs

“…AS does not enjoy such properties because some atoms may be forced to assume certain truth values in order to prevent inconsistencies; this is no longer the case for RAS. An advantage of the property of relevance is to make top-down query-answering possible (Costantini and Formisano 2016) in prolog-style, i.e., without computing the answer sets in advance but rather via an enhanced resolution procedure. This because in RAS only the relevant rules have a role in proving/disproving any atom A.…”

“…RAS query-answering is performed via RAS-XSB-resolution, described in (Costantini and Formisano 2016). It is implemented on top of XSB-resolution (Swift and Warren 2012;Chen and Warren 1993), which is an efficient, fully described and implemented procedure, correct and complete w.r.t.…”

“…Then, in Section 4 we propose some observations on ELPs that will lead to an alternative approach to the computation of world view via epistemic scenarios. We introduce Resource-Based Answer set semantics in Section 5, and then we show in Section 6 how by means of its associated query-answering device, RAS-XSBresolution (Costantini and Formisano 2016), we are able to query ELPs so as to check the validity of guesses, and to query world views and sets of world views. In Section 7 we expand the case study introduced above, and finally we conclude.…”

“…For consistent programs, which are those for which epistemic negation makes sense as some world view may exist, RAS returns the same answer sets as AS (under very simple conditions, seen below) and therefore the same world views. RAS however features, differently from AS, a prolog-like top-down query answering facility (Costantini and Formisano 2016).…”

Better Paracoherent Answer Sets with Less Resources

“…Semantics for non-monotonic logic programs (Przymusinski 1991;van Gelder et al 1991;You and Yuan 1994;Sakama and Inoue 1995;Eiter et al 1997;Seipel 1997;Balduccini and Gelfond 2003;Pereira and Pinto 2007;Alcântara et al 2005;Galindo et al 2008;Amendola et al 2016;Costantini and Formisano 2016) that relax the definition of answer set to overcome the absence of answer sets can be considered in broader terms paracoherent semantics. Nonetheless, the first approach to the problem of handling inconsistency in ASP programs is the semi-stable semantics by (Sakama and Inoue 1995).…”