Igor Stéphan

Martín Diéguez, Susana Hahn, Torsten Schaub et al.

Metric temporal equilibrium logic (\MEL) extends temporal equilibrium logic (\TEL) by incorporating quantitative timing constraints, enabling the specification and analysis of deadlines and durations. \MEL\ is particularly suited for domains where time-bound properties are crucial, such as embedded systems, cyber-physical systems, and real-time software. It facilitates the precise expression of timing behaviors, such as the requirement that an event must occur within 5 milliseconds of a trigger, which often elude traditional qualitative temporal logics. In this paper, we present a Tseitin-like translation that maps any metric temporal formula into a logic programming fragment restricted to past operators. This translation provides a formal bridge to leverage existing Answer Set Programming (ASP) solvers for reasoning about metric temporal constraints. By restricting the target fragment to past operators, we enable more effective evaluation and integration with current ASP-based toolchains for multi-shot solving.

Pedro Cabalar, Martín Diéguez, François Olivier et al.

Reasoning about dynamic systems with a fine-grained temporal and numeric resolution presents significant challenges for logic-based approaches like Answer Set Programming (ASP). To address this, we introduce and elaborate upon a novel temporal and constraint-based extension of the logic of Here-and-There and its nonmonotonic equilibrium extension, representing, to the best of our knowledge, the first approach to nonmonotonic temporal reasoning with constraints specifically tailored for ASP. This expressive system is achieved by a synergistic combination of two foundational ASP extensions: the linear-time logic of Here-and-There, providing robust nonmonotonic temporal reasoning capabilities, and the logic of Here-and-There with constraints, enabling the direct integration and manipulation of numeric constraints, among others. This work establishes the foundational logical framework for tackling complex dynamic systems with high resolution within the ASP paradigm.

Vincent Barichard, Igor Stéphan

We shift the QCSP (Quantified Constraint Satisfaction Problems) framework to the QCHR (Quantified Constraint Handling Rules) framework by enabling dynamic binder and access to user-defined constraints. QCSP offers a natural framework to express PSPACE problems as finite two-players games. But to define a QCSP model, the binder must be formerly known and cannot be built dynamically even if the worst case won't occur. To overcome this issue, we define the new QCHR formalism that allows to build the binder dynamically during the solving. Our QCHR models exhibit state-of-the-art performances on static binder and outperforms previous QCSP approaches when the binder is dynamic.

Claire Lefèvre, Christopher Béatrix, Igor Stéphan et al.

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.