A comparison of sceptical NAF-free logic programming approaches

Recently there has been increased interest in logic programming-based default reasoning approaches which are not using negation-as-failure in their object language. Instead, default reasoning is modelled by rules and a priority relation among them. Historically the first logic in this class was Defeasible Logic. In this paper we will study its relationship to other approaches which also rely on the idea of using logic rules and priorities. In particular we will study sceptical LPwNF, courteous logic programs, and priority logic

A comparison between non-monotonic formalisms

It is interesting and important to compare, analyze and assess the alternative tools that could be used in the area of Knowledge Representation. In this paper we present a reasearch line associated to this goal: to formally establish the relation among Knowledge Representation formalisms in order to make a sensible use of them. As a part of this main task, we present a comparison between Normal Default Theory and Defeasible Logic Programming. This comparison is achieved introducing a DELP variant, called DELP;, which allows to associate the answers of a DELP interpreter to the consequences, credulous and skeptical, of a Normal Default Theory.Eje: Agentes y Sistemas InteligentesRed de Universidades con Carreras en Informática (RedUNCI

On the connection between default logic and DELP

In this paper, we establish a relation between an argumentation based system: Defeasible Logic Programming (DELP), and a nonmonotonic system: Reiter’s Default Logic. This relation is achieved by introducing a variant of DELP and a transformation that maps default theories to defeasible logic programs. The transformation allows to associate the answers of a DELP Interpreter with the consequences, credulous and skeptical, of the default theory. Thus, this work establishes a link between a well understood nonmonotonic system and a argumentation based system. This link could be studied separately and could be exploited for the development of the latter system.Red de Universidades con Carreras en Informática (RedUNCI

A comparison between non-monotonic formalisms

It is interesting and important to compare, analyze and assess the alternative tools that could be used in the area of Knowledge Representation. In this paper we present a reasearch line associated to this goal: to formally establish the relation among Knowledge Representation formalisms in order to make a sensible use of them. As a part of this main task, we present a comparison between Normal Default Theory and Defeasible Logic Programming. This comparison is achieved introducing a DELP variant, called DELP;, which allows to associate the answers of a DELP interpreter to the consequences, credulous and skeptical, of a Normal Default Theory.Eje: Agentes y Sistemas InteligentesRed de Universidades con Carreras en Informática (RedUNCI

Semantics of logic programs with explicit negation

After a historical introduction, the bulk of the thesis concerns the study of a declarative semantics for logic programs. The main original contributions are: ² WFSX (Well–Founded Semantics with eXplicit negation), a new semantics for logic programs with explicit negation (i.e. extended logic programs), which compares favourably in its properties with other extant semantics. ² A generic characterization schema that facilitates comparisons among a diversity of semantics of extended logic programs, including WFSX. ² An autoepistemic and a default logic corresponding to WFSX, which solve existing problems of the classical approaches to autoepistemic and default logics, and clarify the meaning of explicit negation in logic programs. ² A framework for defining a spectrum of semantics of extended logic programs based on the abduction of negative hypotheses. This framework allows for the characterization of different levels of scepticism/credulity, consensuality, and argumentation. One of the semantics of abduction coincides with WFSX. ² O–semantics, a semantics that uniquely adds more CWA hypotheses to WFSX. The techniques used for doing so are applicable as well to the well–founded semantics of normal logic programs. ² By introducing explicit negation into logic programs contradiction may appear. I present two approaches for dealing with contradiction, and show their equivalence. One of the approaches consists in avoiding contradiction, and is based on restrictions in the adoption of abductive hypotheses. The other approach consists in removing contradiction, and is based in a transformation of contradictory programs into noncontradictory ones, guided by the reasons for contradiction

On the equivalence between assumption-based argumentation and logic programming

Assumption-Based Argumentation (ABA) has been shown to subsume various other non-monotonic reasoning formalisms, among them normal logic programming (LP). We re-examine the relationship between ABA and LP and show that normal LP also subsumes (flat) ABA. More precisely, we specify a procedure that given a (flat) ABA framework yields an associated logic program with almost the same syntax whose semantics coincide with those of the ABA framework. That is, the 3-valued stable (respectively well-founded, regular, 2-valued stable, and ideal) models of the associated logic program coincide with the complete (respectively grounded, preferred, stable, and ideal) assumption labellings and extensions of the ABA framework. Moreover, we show how our results on the translation from ABA to LP can be reapplied for a reverse translation from LP to ABA, and observe that some of the existing results in the literature are in fact special cases of our work. Overall, we show that (flat) ABA frameworks can be seen as normal logic programs with a slightly different syntax. This implies that methods developed for one of these formalisms can be equivalently applied to the other by simply modifying the syntax

On the connection between default logic and DELP

In this paper, we establish a relation between an argumentation based system: Defeasible Logic Programming (DELP), and a nonmonotonic system: Reiter’s Default Logic. This relation is achieved by introducing a variant of DELP and a transformation that maps default theories to defeasible logic programs. The transformation allows to associate the answers of a DELP Interpreter with the consequences, credulous and skeptical, of the default theory. Thus, this work establishes a link between a well understood nonmonotonic system and a argumentation based system. This link could be studied separately and could be exploited for the development of the latter system.Red de Universidades con Carreras en Informática (RedUNCI