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.

Notions of justifications for logic programs under answer set semantics have been recently studied for atom-based approaches or argumentation approaches. The paper addresses the question in a rule-based answer set computation: the search algorithm does not guess on the truth or falsity of an atom but on the application or non application of a non monotonic rule. In this view, justifications are sets of ground rules with particular properties. Properties of these justifications are established; in particular the notion of blocking set (a reason incompatible with an answer set) is defined, that permits to explain computation failures. Backjumping, learning, debugging and explanations are possible applications. 1998 ACM Subject Classification D.1.6 Logic Programming, I.2.3 Logic Programming

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 proposi-tional 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.