A Proof Theoretic View of Constraint Programming

We provide here a proof theoretic account of constraint programming that attempts to capture the essential ingredients of this programming style. We exemplify it by presenting proof rules for linear constraints over interval domains, and illustrate their use by analyzing the constraint propagation process for the {\tt SEND + MORE = MONEY} puzzle. We also show how this approach allows one to build new constraint solvers.Comment: 25 page

Constraint Programming viewed as Rule-based Programming

We study here a natural situation when constraint programming can be entirely reduced to rule-based programming. To this end we explain first how one can compute on constraint satisfaction problems using rules represented by simple first-order formulas. Then we consider constraint satisfaction problems that are based on predefined, explicitly given constraints. To solve them we first derive rules from these explicitly given constraints and limit the computation process to a repeated application of these rules, combined with labeling.We consider here two types of rules. The first type, that we call equality rules, leads to a new notion of local consistency, called {\em rule consistency} that turns out to be weaker than arc consistency for constraints of arbitrary arity (called hyper-arc consistency in \cite{MS98b}). For Boolean constraints rule consistency coincides with the closure under the well-known propagation rules for Boolean constraints. The second type of rules, that we call membership rules, yields a rule-based characterization of arc consistency. To show feasibility of this rule-based approach to constraint programming we show how both types of rules can be automatically generated, as {\tt CHR} rules of \cite{fruhwirth-constraint-95}. This yields an implementation of this approach to programming by means of constraint logic programming. We illustrate the usefulness of this approach to constraint programming by discussing various examples, including Boolean constraints, two typical examples of many valued logics, constraints dealing with Waltz's language for describing polyhedral scenes, and Allen's qualitative approach to temporal logic.Comment: 39 pages. To appear in Theory and Practice of Logic Programming Journa

Extensional and Intensional Strategies

This paper is a contribution to the theoretical foundations of strategies. We first present a general definition of abstract strategies which is extensional in the sense that a strategy is defined explicitly as a set of derivations of an abstract reduction system. We then move to a more intensional definition supporting the abstract view but more operational in the sense that it describes a means for determining such a set. We characterize the class of extensional strategies that can be defined intensionally. We also give some hints towards a logical characterization of intensional strategies and propose a few challenging perspectives

Strategic Rewriting

AbstractThis is a position paper preparing the round table organized during the 4th International Workshop on Reduction Strategies in Rewriting and Programming. I sketch what I believe to be important challenges of strategic rewriting

Modelling Planning Problems with Rules & Strategies

Rapport interne.The ELAN system provides an environment for specifying and prototyping deduction systems in a language based on rewrite rules controlled by strategies. We design in ELAN a specific planning problem, namely a controller for printing tasks, by combining rules, strategies and constraint solving on finite domains

Coordinated constraint relaxation using a distributed agent protocol

The interactions among agents in a multi-agent system for coordinating a distributed, problem solving task can be complex, as the distinct sub-problems of the individual agents are interdependent. A distributed protocol provides the necessary framework for specifying these interactions. In a model of interactions where the agents' social norms are expressed as the message passing behaviours associated with roles, the dependencies among agents can be specified as constraints. The constraints are associated with roles to be adopted by agents as dictated by the protocol. These constraints are commonly handled using a conventional constraint solving system that only allows two satisfactory states to be achieved - completely satisfied or failed. Agent interactions then become brittle as the occurrence of an over-constrained state can cause the interaction between agents to break prematurely, even though the interacting agents could, in principle, reach an agreement. Assuming that the agents are capable of relaxing their individual constraints to reach a common goal, the main issue addressed by this thesis is how the agents could communicate and coordinate the constraint relaxation process. The interaction mechanism for this is obtained by reinterpreting a technique borrowed from the constraint satisfaction field, deployed and computed at the protocol level.The foundations of this work are the Lightweight Coordination Calculus (LCC) and the distributed partial Constraint Satisfaction Problem (CSP). LCC is a distributed interaction protocol language, based on process calculus, for specifying and executing agents' social norms in a multi-agent system. Distributed partial CSP is an extension of partial CSP, a means for managing the relaxation of distributed, over-constrained, CSPs. The research presented in this thesis concerns how distributed partial CSP technique, used to address over-constrained problems in the constraint satisfaction field, could be adopted and integrated within the LCC to obtain a more flexible means for constraint handling during agent interactions. The approach is evaluated against a set of overconstrained Multi-agent Agreement Problems (MAPs) with different levels of hardness. Not only does this thesis explore a flexible and novel approach for handling constraints during the interactions of heterogeneous and autonomous agents participating in a problem solving task, but it is also grounded in a practical implementation