Resumen de Modeling arguments and uncertain information -a non-monotonic resoning approach
Juan Carlos Nieves Sánchez
In this thesis, we define a possibilistic disjunctive logic programming approach for modeling uncertain, incomplete and inconsistent information, This approach introduces the use of possibilistic disjunctive clauses which are able to capture incomplete information and incomplete states of a knowledge base at the same time. This approach is computable and moreover allows encoding uncertain information by using either numerical values or relative likelihoods. In order to define the semantics of the possibilistic disjunctive programs, three approaches are defined:
1.- the first is strictly close to the proof theory of possibilistic logic and answer set models;
2.- the second is based on partial evaluation, a fix-point operator and answer set models; and 3.- the last is also based on the proof theory of possibilistic logic and pstable semantics.
In order to manage inconsistent possibilistic logic programs, a preference criterion between inconsistent possibilistic models is defined; in addition, the approach of cuts for restoring consistency of an inconsistent possibilistic knowledge base is adopted.
Argumentation theory is also explored in this work. In particular, we explore how to model abstract argumentation semantics from a point of view of non-monotonic logic programming semantics. Based on a suitable mapping of an argumentation framework into a normal logic program, we define a direct relationship between argumentation semantics (e .g. , the preferred semantics) and logic programming with answer sets models (which is may be the most successful approach of non-monotonic reasoning of the last two decades). As a consequence of this result, we are able to suggest an easy-to-use method for implementing argumentation systems under the platform of answer set solvers. In fact, we point out that we can use answer sets solvers as DLV-system for implementing argumentations systems under the preferred semantics.
Another interesting point of exploring argumentation semantics, from the point of view of logic programming semantics, is that one can deal with part of the problems of the argumentation semantics e.g., emptiness, non-existence. Hence, by considering the idea that argumentation semantics can be viewed as a special form of logic programming semantics with negation as failure, we show that any logic programming semantics as the answer set semantics, the minimal models, the pstable semantics etc., can define candidate argumentation semantics. These candidate argumentation semantics will overcome some of the problems of the Dung's argumentation semantics that have been discussed in the literature. The new argumentation semantics are based on a new recursive framework for logic programming semantics. This framework generalizes any logic programming semantics in order to build logic programming semantics which are always defined, satisfy the property of relevance and agree with the answer set semantics for the class of stratified programs.
As an extension of our possibilistic logic programming approach, we also present a possibilistic argumentation approach which is based on our possibilistic logic programming approach. This approach offers some natural mechanisms for dealing with reasoning under inconsistent information. In fact, this approach does not requite to apply cuts to an inconsistent possibilistic knowledge base, as it is done in possibilistic logic programming, in order to manage the non-existence of possibilistic models.
