Claudia Zepeda

A general theory of confluent rewriting systems for logic programming and its applications

Abstract Recently, Brass and Dix showed (J. Automat. Reason. 20(1) (1998) 143–165) that the well founded semantics WFS can be defined as a confluent calculus of transformation rules. This led not only to a simple extension to disjunctive programs (J. Logic Programming 38(3) (1999) 167–213), but also to a new computation of the well-founded semantics which is linear for a broad class of programs. We take this approach as a starting point and generalize it considerably by developing a general theory of Confluent LP-systems CS . Such a system CS is a rewriting system on the set of all logic programs over a fixed signature L and it induces in a natural way a canonical semantics. Moreover, we show four important applications of this theory: (1) most of the well-known semantics are induced by confluent LP-systems, (2) there are many more transformation rules that lead to confluent LP-systems, (3) semantics induced by such systems can be used to model aggregation, (4) the new systems can be used to construct interesting counterexamples to some conjectures about the space of well-behaved semantics.

Inferring acceptable arguments with answer set programming

Following the argumentation framework and semantics proposed by Dung, we are interested in the problem of deciding which set of acceptable arguments support the decision making in an agent-based platform called CARREL. It is an agent-agency which mediates organ transplants. We present two possible ways to infer the stable and preferred extensions of an argumentation framework, one in a declarative way using answer set programming (ASP) and the other one in a procedure way.

A Schema for Generating Relevant Logic Programming Semantics and its Applications in Argumentation Theory

In the literature, there are several approaches which try to perform common sense reasoning. Among them, the approaches which have probably received the most attention the last two decades are the approaches based on logic programming semantics with negation as failure and argumentation theory. Even though both approaches have their own features, it seems that they share some common behaviours which can be studied by considering the close relationship between logic programming semantics and extension-based argumentation semantics. In this paper, we will present a general recursive schema for defining new logic programming semantics. This schema takes as input any basic logic programming semantics, such as the stable model semantics, and gives as output a new logic programming semantics which satisfies some desired properties such as relevance and the existence of the intended models for every normal program. We will see that these new logic programming semantics can define candidate extension-based argumentation semantics. These new argumentation semantics will overcome some of the weakness of the extension-based argumentation semantics based on admissible sets. In fact, we will see that some of these new argumentation semantics have similar behaviour to the extension-based argumentation semantics built in terms of strongly connected components.

Pstable Theories and Preferences

In this paper we introduce preference rules which allow us to specify preferences as an ordering among the possible solutions of a problem. Our approach allow us to express preferences for general theories and we define a semantics for them. The formalism used to develop our work is Pstable semantics.

Update sequences based on minimal generalized pstable models

In case intelligent agents get new knowledge and this knowledge must be added or updated to their knowledge base, it is important to avoid inconsistencies. Currently there are several approaches dealing with updates. In this paper, we propose a semantics for update sequences. We start introducing the notion of minimal generalized (MG) pstable models that, as we argue is interesting by itself. Based on MG pstable models we construct our update semantics. In this work, we also use some representative examples to compare our update semantics to other known update semantics and observe some advantages of it.

Expressing Extension-Based Semantics Based on Stratified Minimal Models

Extension-based argumentation semantics is a successful approach for performing non-monotonic reasoning based on argumentation theory. An interesting property of some extension-based argumentation semantics is that these semantics can be characterized in terms of logic programming semantics. In this paper, we present novel results in this topic. In particular, we show that one can induce an argumentation semantics (that we call Stratified Argumentation Semantics) based on a logic programming semantics that is based on stratified minimal models. We show that the stratified argumentation semantics overcome some problems of extension-based argumentation semantics based on admissible sets and we show that it coincides with the argumentation semantics CF2.

Modeling evacuation planning using A-Prolog

In this work, we present current results of our research, the goal of which is to develop a decision support system (DSS) as an extension of a geographical information system (GIS) to model evacuation plans. We presents why an A-Prolog approach seems to be appropriated to explore in order to add the planning operation as an extension of a GIS. In order to achieve our objective, first we model the disaster scenario. The disaster scenario should be described as close as possible to the real problem. We define an action language, named ALEP, to model and give a solution to the evacuation plans. The syntax and semantics of ALEP are presented. Finally, we plan to test the expressiveness of the ALEP language, defining a DSS to model evacuation plans.

Yet another application of fuzzy logic

Fuzzy logic has been mainly used for fuzzy control and other applications. Recently, it also has been studied as a symbolic logic with syntax and semantics. We know that fuzzy logic is a branch of many-valued logic based on the paradigm of inference under vagueness. In this paper, we consider a particular many valued logic to show a non-standard application of fuzzy logic. We propose to use it for knowledge representation based on logic programming.

A Formal Design Model for Mechatronic Systems

For successful mechatronic system development, the views of all developers produced should be well integrated into a whole, reducing any risks of inconsistencies and conflicts. The model-based verification techniques use models to describe the possible system behavior in a mathematically precise and unambiguous manner. In particular model checking provides the basis for a whole range of verification techniques ranging from an exhaustive exploration to experiments with a restrictive set of scenarios. Here we propose a framework for verifying mechatronic-design systems based on symbolic model checking. Moreover this framework is an approach based on a novel semantics called p-stable.

Defining Stage Argumentation Semantics in Terms of an Abducible Semantics

We define a new logic programming semantics in terms of abducible atoms. We use it to characterize the stage extensions of an argumentation framework AF by means of an associated normal program PAF. We also define the stage semantics for a special type of normal programs and present a similar characterization.