Adding weights or preferences to Abstract Argumentation Frameworks can help disentangle semantics from otherwise all-equivalent attacks. Having such information makes possible to distil the set of found extensions by reducing their number. In this work we provide a new definition of weighted defence: according to it, all the attacks from an argument to a set of arguments are considered with a single global weight, i.e., attacks are grouped together. This provides a coherent view w.r.t. defence, which is usually “collective” in the literature. Moreover, we model weighted defences from related works in the same algebraic framework: this allows us to compare all the different proposals together.

In this paper a planning framework based on Ant Colony Optimization techniques is presented. It is well known that finding optimal solutions to planning problems is a very hard computational problem. Stochastic methods do not guarantee either optimality or completeness, but it has been proved that in many applications they are able to find very good, often optimal, solutions. We propose several approaches based both on backward and forward search over the state space, using several heuristics and testing different pheromone models in order to solve sequential optimization planning problems.

In this paper an application of the metaheuristic Ant Colony Optimization to optimal planning is presented. It is well known that finding out optimal solutions to planning problem is a very hard computational problem. Approximate methods do not guarantee either optimality or completeness, but it has been proved that in many applications they are able to find very good solutions, often close to optimal ones. Since one of the most performing stochastic method for combinatorial optimization is ACO, we have decided to use this technique to design an algorithm which optimizes plan length in propositional planning. This algorithm has been implemented and some empirical evaluations have been performed. The results obtained are encouraging and show the feasibility of this approach.