On the Complexity of Optimization Problems based on Compiled NNF Representations

Optimization is a key task in a number of applications. When the set of feasible solutions under consideration is of combinatorial nature and described in an implicit way as a set of constraints, optimization is typically NP-hard. Fortunately, in many problems, the set of feasible solutions does not often change and is independent from the user's request. In such cases, compiling the set of constraints describing the set of feasible solutions during an off-line phase makes sense, if this compilation step renders computationally easier the generation of a non-dominated, yet feasible solution matching the user's requirements and preferences (which are only known at the on-line step). In this article, we focus on propositional constraints. The subsets L of the NNF language analyzed in Darwiche and Marquis' knowledge compilation map are considered. A number of families F of representations of objective functions over propositional variables, including linear pseudo-Boolean functions and more sophisticated ones, are considered. For each language L and each family F, the complexity of generating an optimal solution when the constraints are compiled into L and optimality is to be considered w.r.t. a function from F is identified

Scaling Construction Grammar up to Production Systems: the SCIM

While a great effort has concerned the development of fully integrated modular understanding systems, few researches have focused on the problem of unifying existing linguistic formalisms with cognitive processing models. The Situated Constructional Interpretation Model is one of these attempts. In this model, the notion of "construction" has been adapted in order to be able to mimic the behavior of Production Systems. The Construction Grammar approach establishes a model of the relations between linguistic forms and meaning, by the mean of constructions. The latter can be considered as pairings from a topologically structured space to an unstructured space, in some way a special kind of production rules