Possibilistic uncertainty handling for answer set programming

Abstract

In this work, we introduce a new framework able to deal with a reasoning that is at the same time non monotonic and uncertain. In order to take into account a certainty level associated to each piece of knowledge, we use possibility theory to extend the non monotonic semantics of stable models for logic programs with default negation. By means of a possibility distribution we define a clear semantics of such programs by introducing what is a possibilistic stable model. We also propose a syntactic process based on a fix-point operator to compute these particular models representing the deductions of the program and their certainty. Then, we show how this introduction of a certainty level on each rule of a program can be used in order to restore its consistency in case of the program has no model at all. Furthermore, we explain how we can compute possibilistic stable models by using available softwares for Answer Set Programming and we describe the main lines of the system that we have developed to achieve this goal.

Characterizing and extending answer set semantics using possibility theory

“…Possibilistic ASP (PASP) extends upon ASP by associating a weight with every rule, which is interpreted as the necessity with which we can derive the head of the rule when the body is known to hold. Semantics for PASP have been introduced in Nicolas et al (2006) for possibilistic normal programs and later extended to possibilistic disjunctive programs in Nieves et al (2013). Under these semantics, a possibilistic rule with certainty λ allows us to derive head with certainty min (λ, N(body)), where N(body) denotes the necessity of the body, i.e.…”

“…the certainty of head is restricted by the least certain piece of information in the derivation chain. Specifically, to deal with the PASP rules without negation-as-failure (NAF), the semantics from Nicolas et al (2006) treat such rules as implications in possibilistic logic (Dubois et al 1994). When faced with negation-as-failure, the semantics from Nicolas et al (2006) rely on the reduct operation from classical ASP.…”

“…Specifically, to deal with the PASP rules without negation-as-failure (NAF), the semantics from Nicolas et al (2006) treat such rules as implications in possibilistic logic (Dubois et al 1994). When faced with negation-as-failure, the semantics from Nicolas et al (2006) rely on the reduct operation from classical ASP. Essentially, this means that the weights associated with the rules are initially ignored, the classical reduct is determined and the weights are then reassociated with the corresponding rules in the reduct.…”

Fuzzy Methods on the Web: A Critical Discussion

“…Note however, that there exist several ways to implement this intuition, leading to different semantics of fuzzy logic programming [44,64,102,107]. In parallel, some possibilistic extensions to logic programming have been considered [5,20,26,71,74], in which it is possible to encode that a given rule or fact is more or less certain (or important, preferred, etc.). Although the idea of uncertainty or preference is clearly different from the idea of graded truth, at the formal level, extensions of answer set programming that deal with uncertainty are closely related to extensions dealing with graded truth [5,24].…”

Fuzzy Answer Set Programming: An Introduction

“…To deal with uncertainty, among others, ASP can be extended with possibility theory (e.g. [15]) or with probability theory (e.g. [3]).…”