Towards the implementation of a preference-and uncertain-aware solver using answer set programming

Logic programs with possibilistic ordered disjunction (or LPPODs) are a recently defined logic-programming framework based on logic programs with ordered disjunction and possibilistic logic. The framework inherits the properties of such formalisms and merging them, it supports a reasoning which is nonmonotonic, preference-and uncertain-aware. The LPPODs syntax allows to specify 1) preferences in a qualitative way, and 2) necessity values about the certainty of program clauses. As a result at semantic level, preferences and necessity values can be used to specify an order among program solutions. This class of program therefore fits well in the representation of decision problems where a best option has to be chosen taking into account both preferences and necessity measures about information. In this paper we study the computation and the complexity of the LPPODs semantics and we describe the algorithm for its implementation following on Answer Set Programming approach. We describe some decision scenarios where the solver can be used to choose the best solutions by checking whether an outcome is possibilistically preferred over another considering preferences and uncertainty at the same time.Postprint (published version

A Complete Solver for Constraint Games

Game Theory studies situations in which multiple agents having conflicting objectives have to reach a collective decision. The question of a compact representation language for agents utility function is of crucial importance since the classical representation of a $n$-players game is given by a $n$-dimensional matrix of exponential size for each player. In this paper we use the framework of Constraint Games in which CSP are used to represent utilities. Constraint Programming --including global constraints-- allows to easily give a compact and elegant model to many useful games. Constraint Games come in two flavors: Constraint Satisfaction Games and Constraint Optimization Games, the first one using satisfaction to define boolean utilities. In addition to multimatrix games, it is also possible to model more complex games where hard constraints forbid certain situations. In this paper we study complete search techniques and show that our solver using the compact representation of Constraint Games is faster than the classical game solver Gambit by one to two orders of magnitude.Comment: 17 page