  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.
