An encompassing framework for Paraconsistent Logic Programs

Abstract

We propose a framework which extends Antitonic Logic Programs [Damásio and Pereira, in: Proc. 6th Int. Conf. on Logic Programming and Nonmonotonic Reasoning, Springer, 2001, p. 748] to an arbitrary complete bilattice of truth-values, where belief and doubt are explicitly represented. Inspired by Ginsberg and Fitting's bilattice approaches, this framework allows a precise definition of important operators found in logic programming, such as explicit and default negation. In particular, it leads to a natural semantical integration of explicit and default negation through the Coherence Principle [Pereira and Alferes, in: European Conference on Artificial Intelligence, 1992, p. 102], according to which explicit negation entails default negation. We then define Coherent Answer Sets, and the Paraconsistent Well-founded Model semantics, generalizing many paraconsistent semantics for logic programs. In particular, Paraconsistent Well-Founded Semantics with eXplicit negation (WFSX p ) [Alferes et al., J. . Thus, we have a powerful mathematical formalism for dealing simultaneously with default, paraconsistency, and uncertainty reasoning. Results are provided about how our semantical framework deals with inconsistent information and with its propagation by the rules of the program.

Modularity in the Rule Interchange Format

“…The essential problem with the previous definition is that the negations of Equilibrium Logic [22] underlying Answer Set semantics [15] and extensions are ruled out by RIF-FLD semantics. The same happens to Well-founded Semantics with Explicit Negation and its extensions [2,1,12]. The reason is the same for all these semantics since the double negation law for default negation does not hold, as can be seen in Figures 3-6 (the truth-table for symmetric negation is −).…”

Paracoherent Answer Set Semantics meets Argumentation Frameworks

“…The two major paracoherent semantics for logic programs are the semi-stable (Sakama and Inoue 1995) and the semi-equilibrium semantics (Amendola et al 2016). These semantics emerged over several alternative proposals (Przymusinski 1991a;Gelder et al 1991;Saccà and Zaniolo 1991;You and Yuan 1994;Eiter et al 1997;Seipel 1997;Balduccini and Gelfond 2003;Pereira and Pinto 2005;Pereira and Pinto 2007;Alcântara et al 2005;Galindo et al 2008). However, (Amendola et al 2016) have shown that only semi-stable semantics (Sakama and Inoue 1995) and semi-equilibrium semantics (Amendola et al 2016) satisfy all the following five highly desirable -from the knowledge representation point of viewtheoretical properties: (i) every consistent answer set of a program corresponds to a paracoherent answer set (answer set coverage); (ii) if a program has some (consistent) answer set, then its paracoherent answer sets correspond to answer sets (congruence); (iii) if a program has a classical model, then it has a paracoherent answer set (classical coherence); (iv) a minimal set of atoms should be undefined (minimal undefinedness); (v) every true atom must be derived from the program (justifiability or foundedness).…”

The reliability of experts' opinions in constructing a composite environmental index: The case of ESI 2005

“…Later in 1948, Stanislaw Jaskowski constructed a system of propositional paraconsistent logic, where he distinguished between contradictory/inconsistent systems and trivial ones. In 1953 and 1954, Newton da Costa began the development of his ideas on paraconsistency motivated by mathematical problems, and developed the idea of paraconsistent logic as a field with relevant applications in applied science and technology, such as robotics (Nakamatsu et al, 2002), expert systems (Alcantara et al, 2005), and medicine (Sadegh-Zadeh, 2002).…”