The Well-Founded Semantics in Normal Logic Programs with Uncertainty

Abstract

Abstract. Many frameworks of logic programming have been proposed to manage uncertain information in deductive databases and expert systems. Roughly, on the basis of how uncertainty is associated to facts and the rules in a program, they can be classified into implication-based (IB) and annotation-based (AB). However, one fundamental issue that remains unaddressed in the IB approach is the representation and the manipulation of the non-monotonic mode of negation, an important feature for real applications. Our focus in this paper is to introduce nonmonotonic negation in the parametric IB framework, a unifying umbrella for IB frameworks. The semantical approach that we will adopt is based on the well-founded semantics, one of the most widely studied and used semantics of (classical) logic programs with negation.

Managing Uncertainty and Vagueness in Description Logics, Logic Programs and Description Logic Programs

“…[35,122,130,252,276]. On the other hand, there are very few works dealing with normal logic programs [38,78,80,142,143,144,145,146,147,148,173,186,250,253,258,263], and little is know about top-down query answering procedures. The only exceptions are [250,258,263].…”

Reducing fuzzy answer set programming to model finding in fuzzy logics

“…Most notably are the probabilistic (Baral et al 2007;Damásio and Pereira 2000;Fuhr 2000;Lukasiewicz 1998;Lukasiewicz 1999;Ng and Subrahmanian 1993;Ng and Subrahmanian 1994;Straccia 2008) and possibilistic (Alsinet et al 2002;Bauters et al 2010;Nicolas et al 2005;Nicolas et al 2006) extensions to handle uncertainty, the fuzzy extensions (Cao 2000;Ishizuka and Kanai 1985;Lukasiewicz 2006;Lukasiewicz and Straccia 2007a;Lukasiewicz and Straccia 2007b;Madrid and Ojeda-Aciego 2008;Madrid and Ojeda-Aciego 2009;Saad 2009a;Straccia 2008;Van Nieuwenborgh et al 2007b;Vojtás 2001;Wagner 1998) which allow to encode the intensity to which the predicates are satisfied, and, more generally, many-valued extensions Damásio et al 2007;Damásio and Pereira 2001a;Damásio and Pereira 2001b;Damásio and Pereira 2004;Emden 1986;Fitting 1991;Kifer and Li 1988;Kifer and Subrahmanian 1992;Lakshmanan 1994;Lakshmanan and Sadri 1994;Lakshmanan and Sadri 1997;Lakshmanan and Shiri 2001;Lakshmanan 1997;Loyer and Straccia 2002;Loyer and Straccia 2003;…”

Aggregated Fuzzy Answer Set Programming

“…[10,11,24,44,45,47,48,52,53,[55][56][57][58]70]). These weights are specified manually and they reflect the minimum degree of fulfillment required for a rule.…”

“…This idea can be implemented by allowing that the last rule, constr , should not always be completely satisfied. Many of the current approaches (for example [10,11,24,44,45,47,48,52,53,55,56,70]) that allow partial rule satisfaction do so by coupling a weight to each rule, thus predefining to what degree each of the rules should be satisfied.…”

“…Most notable are the probabilistic [12,28,50,51,61,62,74] and possibilistic [2,5,63,64] extensions to handle uncertainty, the fuzzy extensions [8,33,[52][53][54][55][56]67,74,[80][81][82] which allow to encode the intensity to which the predicates are satisfied, and, more generally, many-valued extensions [10,11,[13][14][15]24,26,[38][39][40][41][43][44][45]47,48,60,70,72,73,75,76].…”