Reasoning with preferences over temporal, uncertain, and conditional statements

In this thesis we consider reasoning with preferences in a number of different AI problems. We start with a specific area as, temporal reasoning, for which there is specialized reasoning machinery. In particular, we consider quantitative temporal constraints and we add preferences in such a context. We discuss the complexity for solving temporal constraint satisfaction problems with preferences in general, and we identify a tractable subclass: simple temporal problems with semi-convex preference functions. For this subclass, we consider finding optimal solutions with respect to the (fuzzy) maximin criterion and to the Pareto criterion. In the first case, we propose two solvers based on two different approaches. One enforces the notion of path consistency adapted to deal also with preferences. We show that enforcing such a property is sufficient to solve an STPP and it is a polynomial time algorithm. The second solver, reduces the problem to that of solving several hard constraint problems. We show that also this solver is polynomial. We have also designed a solver that finds Pareto optimal solutions. It applies one of the solvers for fuzzy-optimal solutions several times, to problems obtained from the original one by changing some constraints. Also this solver is polynomial. We have implemented and tested the solvers for fuzzy optimals. The tests, performed on randomly generated problems, show that the second solver is much faster, although it allows to represent less general preferences. We also consider the problem of actually obtaining the preferences on all the temporal constraints. Practically, it may not be feasible to retrieve all such preferences by a user. We,