Claire Lefèvre

Possibilistic uncertainty handling for answer set programming

In this work, we introduce a new framework able to deal with a reasoning that is at the same time non monotonic and uncertain. In order to take into account a certainty level associated to each piece of knowledge, we use possibility theory to extend the non monotonic semantics of stable models for logic programs with default negation. By means of a possibility distribution we define a clear semantics of such programs by introducing what is a possibilistic stable model. We also propose a syntactic process based on a fix-point operator to compute these particular models representing the deductions of the program and their certainty. Then, we show how this introduction of a certainty level on each rule of a program can be used in order to restore its consistency in case of the program has no model at all. Furthermore, we explain how we can compute possibilistic stable models by using available softwares for Answer Set Programming and we describe the main lines of the system that we have developed to achieve this goal.

The First Version of a New ASP Solver: ASPeRiX

We present the first version of our ASP solver ASPeRiX that implements a new approach of answer set computation. The main specifity of our system is to realize a forward chaining of first order rules that are grounded on the fly. So, unlike all others available ASP systems ASPeRiX does not need a pregrounding processing.

A First Order Forward Chaining Approach for Answer Set Computing

The natural way to use Answer Set Programming (ASP) to represent knowledge in Artificial Intelligence or to solve a Constraint Satisfaction Problem is to elaborate a first order logic program with default negation. In a preliminary step this program, with variables, is translated in an equivalent propositional one by a first tool: the grounder. Then, the propositional program is given to a second tool: the solver. This last one computes (if they exist) one or many answer sets (models) of the program, each answer set encoding one solution of the initial problem. Until today, almost all ASP systems apply this two steps computation. In this work, our major contribution is to introduce a new approach of answer set computing that escapes the preliminary phase of rule instantiation by integrating it in the search process. Our methodology applies a forward chaining of first order rules that are grounded on the fly by means of previously produced constants. We have implemented this strategy in our new ASP solver ASPeRiX . The first benefit of our work is to avoid the bottleneck of instantiation phase arising for some problems because of the huge amount of memory needed to ground all rules of a program, even if these rules are not really useful in certain cases. The second benefit is to make the treatment of function symbols easier and without syntactic restriction provided that rules are safe.

ASPeRiX, a first-order forward chaining approach for answer set computing

The natural way to use Answer Set Programming (ASP) to represent knowledge in Artificial Intelligence or to solve a combinatorial problem is to elaborate a first order logic program with default negation. In a preliminary step this program with variables is translated in an equivalent propositional one by a first tool: the grounder. Then, the propositional program is given to a second tool: the solver. This last one computes (if they exist) one or many answer sets (stable models) of the program, each answer set encoding one solution of the initial problem. Until today, almost all ASP systems apply this two steps computation. In this article, the project ASPeRiX is presented as a first order forward chaining approach for Answer Set Computing. This project was amongst the first to introduce an approach of answer set computing that escapes the preliminary phase of rule instantiation by integrating it in the search process. The methodology applies a forward chaining of first order rules that are grounded on the fly by means of previously produced atoms. Theoretical foundations of the approach are presented, the main algorithms of the ASP solver ASPeRiX are detailed and some experiments and comparisons with existing systems are provided.

Dialectical Proofs for Constrained Argumentation

Constrained argumentation frameworks (CAF) generalize Dungs frameworks by allowing additional constraints on arguments to be taken into account in the definition of acceptability of arguments. These constraints are expressed by means of a logical formula which is added to Dungs framework. The resulting system captures several other extensions of Dungs original system. To determine if a set of arguments is credulously inferred from a CAF, the notion of dialectical proof (alternating pros and cons arguments) is extended for Dungs frameworks in order to respect the additional constraint. The new constrained dialectical proofs are computed by using Answer Set Programming.

Possibilistic ASP Base Revision by Certain Input

Belief base revision has been studied within the answer set programming framework. We go a step further by introducing uncertainty and studying belief base revision when beliefs are represented by possibilistic logic programs under possibilistic answer set semantics and revised by certain input. The paper proposes two approaches of rule-based revision operators and presents their semantic characterization in terms of possibilistic distribution. This semantic characterization allows for equivalently considering the evolution of syntactic logic programs and the evolution of their semantic content. It then studies the logical properties of the proposed operators and gives complexity results.

Bringing existential variables in answer set programming and bringing non-monotony in existential rules: two sides of the same coin

This article deals with the combination of ontologies and rules by means of existential rules and answer set programming. Existential rules have been proposed for representing ontological knowledge, specifically in the context of Ontology- Based Data Access. Furthermore Answer Set Programming (ASP) is an appropriate formalism to represent various problems issued from Artificial Intelligence and arising when available information is incomplete. The combination of the two formalisms requires to extend existential rules with nonmonotonic negation and to extend ASP with existential variables. In this article, we present the syntax and semantics of Existential Non Monotonic Rules (ENM-rules) using skolemization which join together the two frameworks. We formalize its links with standard ASP. Moreover, since entailment with existential rules is undecidable, we present conditions that ensure the termination of a breadth-first forward chaining algorithm known as the chase and we discuss extension of these results in the nonmonotonic case.

A Semantic Characterization for ASP Base Revision

The paper deals with base revision for Answer Set Programming (ASP). Base revision in classical logic is done by the removal of formulas. Exploiting the non-monotonicity of ASP allows one to propose other revision strategies, namely addition strategy or removal and/or addition strategy. These strategies allow one to define families of rule-based revision operators. The paper presents a semantic characterization of these families of revision operators in terms of answer sets. This characterization allows one to equivalently consider the evolution of syntactic logic programs and the evolution of their semantic content.