Willy Lesaint

Theoretical Foundations of Value Withdrawal Explanations for Domain Reduction

Solvers on finite domains use local consistency notions to remove values from the domains. This paper defines value withdrawal explanations. Domain reduction is formalized with chaotic iterations of monotonic operators. To each operator is associated its dual which will be described by a set of rules. For classical consistency notions, there exists a natural such system of rules. They express value removals as consequences of other value removals. The linking of these rules inductively defines proof trees. Such a proof tree clearly explains the removal of a value (the root of the tree). Explanations can be considered as the essence of domain reduction.

Property grammar parsing seen as a constraint optimization problem

Blache [1] introduced Property Grammar as a formalism where linguistic information is represented in terms of non hierarchical constraints. This feature gives it an adequate expressive power to handle complex linguistic phenomena, such as long distance dependencies, and also agrammatical sentences [2]. Recently, Duchier et al. [3] proposed a model-theoretic semantics for property grammar. The present paper follows up on that work and explains how to turn such a formalization into a constraint optimization problem, solvable using constraint programming techniques. This naturally leads to an implementation of a fully constraint-based parser for property grammars.