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A Possibilistic Argumentation Decision Making Framework with Default Reasoning

Nieves J.C., Confalonieri R.

Fundamenta Informaticae

2011

Vol. 113, nr 1

41-61

In this paper, we introduce a possibilistic argumentation-based decision making framework which is able to capture uncertain information and exceptions/defaults. In particular, we define the concept of a possibilistic decision making framework which is based on a possibilistic default theory, a set of decisions and a set of prioritized goals. This set of goals captures user preferences related to the achievement of a particular state in a decision making problem. By considering the inference of the possibilistic well-founded semantics, the concept of argument with respect to a decision is defined. This argument captures the feasibility of reaching a goal by applying a decision in a given context. The inference in the argumentation decision making framework is based on basic argumentation semantics. Since some basic argumentation semantics can infer more than one possible scenario of a possibilistic decision making problem, we define some criteria for selecting potential solutions of the problem.

SLGAD Resolution for Inference on Logic Programs with Annotated Disjunctions

Riguzzi F.

Fundamenta Informaticae

2010

Vol. 102, nr 3/4

429-466

Logic Programs with Annotated Disjunctions (LPADs) allow to express probabilistic information in logic programming. The semantics of an LPAD is given in terms of the well-founded models of the normal logic programs obtained by selecting one disjunct from each ground LPAD clause. Inference on LPADs can be performed using either the system Ailog2, that was developed for the Independent Choice Logic, or SLDNFAD, an algorithm based on SLDNF. However, both of these algorithms run the risk of going into infinite loops and of performing redundant computations. In order to avoid these problems, we present SLGAD resolution that computes the (conditional) probability of a ground query from a range-restricted LPAD and is based on SLG resolution for normal logic programs. As SLG, it uses tabling to avoid some infinite loops and to avoid redundant computations. The performances of SLGAD are evaluated on classical benchmarks for normal logic programs under the well-founded semantics, namely a 2-person game and the ancestor relation, and on games of dice. SLGAD is compared with Ailog2 and SLDNFAD on the problems in which they do not go into infinite loops, namely those that are described by a modularly acyclic program. The results show that SLGAD is sometimes slower than Ailog2 and SLDNFAD but, if the program requires the repeated computations of the same goals, as for the dice games, then SLGAD is faster than both.

A New Partial Semantics for Disjunctive Deductive Databases

Gire F, Plourde C.

Fundamenta Informaticae

2005

Vol. 67, nr 4

323--342

We propose a new partial semantics for disjunctive deductive databases that we call disjunctive well-founded semantics. This semantics extends the classical well-founded semantics of normal databases for disjunctive databases. We give a declarative definition as well as a computational procedure for this new semantics. We prove that, in the case of disjunctive positive databases, i.e. disjunctive databases without negation, the disjunctive well-founded semantics coincides with the intersection of the minimal models.