Igor Stéphan

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.

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.

A possibilistic inconsistency handling in answer set programming

Both in classical logic and in Answer Set Programming, inconsistency is characterized by non existence of a model. Whereas every formula is a theorem for inconsistent set of formulas, an inconsistent program has no answer. Even if these two results seem opposite, they share the same drawback: the knowledge base is useless since one can not draw valid conclusions from it. Possibilistic logic is a logic of uncertainty able to deal with inconsistency in classical logic. By putting on every formula a degree of certainty, it defines a way to compute, with regard to these degrees, a consistent subset of formulas that can be then used in a classical inference process. In this work, we address the treatment of inconsistency in Answer Set Programming by a possibilistic approach that takes into account the non monotonic aspect of the framework.

A new parallel architecture for QBF tools

In this paper, we present the main lines and a first implementation of an open general parallel architecture that we propose for various computation problems about Quantified Boolean Formulae. One main feature of our approach is to deal with QBF without syntactic restrictions, as prenex form or conjunctive normal form. Another main point is to develop a general parallel framework in which we will be able in the future to introduce various specialized algorithms dedicated to particular subproblems.

HEURISTICS FOR A DEFAULT LOGIC REASONING SYSTEM

In Artificial Intelligence, Default Logic is recognized as a powerful framework for knowledge representation when one has to deal with incomplete information. Its expressive power is suitable for non monotonic reasoning, but the counterpart is its very high level of theoretical complexity. Today, some operational systems are able to deal with real world applications. However, finding a default logic extension in a practical way is not yet possible in whole generality. This paper which is an extended version of18 shows how heuristics such as Genetic Algorithms and Local Search techniques can be used and combined to build an automated default reasoning system. We give a general description of the required basic components and we exhibit experimental results.

From (Quantified) Boolean Formulae to Answer Set Programming

We propose in this article a translation from quantified Boolean formulae to answer set programming. The computation of a solution of a quantified Boolean formula is then equivalent to the computation of a stable model for a normal logic program. The case of unquantified Boolean formulae is also considered since it is equivalent to the case of quantified Boolean formulae with only existential quantifiers.

Answer Set Programming by Ant Colony Optimization

Answer Set Programming is a very convenient framework to represent various problems issued from Artificial Intelligence (nonmonotonic reasoning, planning, diagnosis...). Furthermore, it can be used to neatly encode combinatorial problems. In all cases, the solutions are obtained as sets of literals: the Answer Sets.Ant Colony Optimization is a general metaheuristics that has been already successfully used to solve hard combinatorial problems (traveling salesman problem, graph coloring, quadratic assignment...). It is based on the collective behavior of artificial ants exploring a graph and exchanging pieces of information by means of pheromone traces.The purpose of this work is to show how Ant Colony Optimization can be used to compute an answer set of a logic program.

New Generation Systems for Non-monotonic Reasoning

Default Logic is recognized as a powerful framework for knowledge representation and incomplete information management. Its expressive power is suitable for non monotonic reasoning, but the counterpart is its very high level of computational complexity. The purpose of this paper is to show how heuristics such as Genetic Algorithms, Ant Colony Optimization and Local Search can be used to elaborate an efficient non monotonic reasoning system.

Combining heuristics for default logic reasoning systems

In Artificial Intelligence, Default Logic is recognized as a powerful framework for knowledge representation when one has to deal with incomplete information. Its expressive power is suitable for nonmonotonic reasoning, but the counterpart is its very high level of theoretical complexity. Today, some operational systems are able to deal with real world applications. However finding a default logic extension in a practical way is not yet possible in whole generality. This paper shows how modern heuristics such as genetic algorithms and local search techniques can be used and combined to build an automated default reasoning system. We give a general description of the required basic components and we exhibit experimental results.

On Implementation of Tree Synchronized Languages

Tree languages have been extensively studied and have many applications related to the rewriting framework such as order sorted speci fications, higher order matching or unification. In this paper, we focus on the implementation of such languages and, inspired by the Definite Clause Grammars that allows to write word grammars as Horn clauses in a Prolog environment, we propose to build a similar framework for particular tree languages (TTSG) which introduces a notion of synchronization between production rules. Our main idea is to define a proof theoretical semantics for grammars and thus to change from syntactical tree manipulations to logical deduction. This is achieved by a sequent calculus proof system which can be refined and translated into Prolog Horn clauses. This work provides a scheme to build goal directed procedures for the recognition of tree languages.