On Coherence and Consistence in Fuzzy Answer Set Semantics for Residuated Logic Programs

Abstract

Abstract. In this work we recall the first steps towards the definition of an answer set semantics for residuated logic programs with negation, and concentrate on the development of relationships between the notions of coherence and consistence of an interpretation.

Weighted logics for artificial intelligence – an introductory discussion

“…Finally, we would like to mention that, although we have mainly focused on logical issues, many of the concerns discussed here have also echoes in closely related areas like description logics, logic programming and answer set programming when they come to handle uncertainty, preferences or fuzziness, see for instance [90,108,62,75,92,9,17] for a variety of logic programming approaches coping with graded uncertainty and/or truth.…”

Stable Models of Fuzzy Propositional Formulas

“…Our adaptation in the fuzzy stable model semantics is similar to the method from [9], in which the consistency of an interpretation is guaranteed by imposing the extra restriction I(∼p) ≤ ∼I(p) for all atom p. Strong negation and consistency have also been studied in [13,14].…”

Reducing fuzzy answer set programming to model finding in fuzzy logics

“…Over the years many different fuzzy answer set programming formalisms have been developed (Lukasiewicz 2006;Lukasiewicz and Straccia 2007a;Madrid and Ojeda-Aciego 2008;Madrid and Ojeda-Aciego 2009;Saad 2009a;Straccia 2008;Van Nieuwenborgh et al 2007b). Most of these base their semantics on fixpoints or minimal models, in combination with a reduct operation.…”

“…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;…”