We analyse preference inference, through consistency, for general preference languages based on lexicographic models. We identify a property, which we call strong compositionality, that applies for many natural kinds of preference statement, and that allows a greedy algorithm for determining consistency of a set of preference statements. We also consider different natural definitions of optimality, and their relations to each other, for general preference languages based on lexicographic models. Based on our framework, we show that testing consistency, and thus inference, is polynomial for a specific preference language LpqT, which allows strict and non-strict statements, comparisons between outcomes and between partial tuples, both ceteris paribus and strong statements, and their combination. Computing different kinds of optimal sets is also shown to be polynomial; this is backed up by our experimental results.

Judgment aggregation is a general framework for collective decision making that can be used to model many different settings. Due to its general nature, the worst case complexity of essentially all relevant problems in this framework is very high. However, these intractability results are mainly due to the fact that the language to represent the aggregation domain is overly expressive. We initiate an investigation of representation languages for judgment aggregation that strike a balance between (1) being limited enough to yield computational tractability results and (2) being expressive enough to model relevant applications. In particular, we consider the languages of Krom formulas, (definite) Horn formulas, and Boolean circuits in decomposable negation normal form (DNNF). We illustrate the use of the positive complexity results that we obtain for these languages with a concrete application: voting on how to spend a budget (i.e., participatory budgeting).

Formula compilation by generation of prime implicates or implicants finds a wide range of applications in AI. Recent work on formula compilation by prime implicate/implicant generation often assumes a Conjunctive/Disjunctive Normal Form (CNF/DNF) representation. However, in many settings propositional formulae are naturally expressed in non-clausal form. Despite a large body of work on compilation of non-clausal formulae, in practice existing approaches can only be applied to fairly small formulae, containing at most a few hundred variables. This paper describes two novel approaches for the compilation of non-clausal formulae either with prime implicants or implicates, that is based on propositional Satisfiability (SAT) solving. These novel algorithms also find application when computing all prime implicates of a CNF formula. The proposed approach is shown to allow the compilation of non-clausal formulae of size significantly larger than existing approaches.

Minimal explanations of infeasibility find a wide range of uses. In the Boolean domain, these are referred to as Minimal Unsatisfiable Subsets (MUSes). In some settings, one needs to enumerate MUSes of a Boolean formula. Most often the goal is to enumerate all MUSes. In cases where this is computationally infeasible, an alternative is to enumerate some MUSes. This paper develops a novel approach for partial enumeration of MUSes, that complements existing alternatives. If the enumeration of all MUSes is viable, then existing alternatives represent the best option. However, for formulas where the enumeration of all MUSes is unrealistic, our approach provides a solution for enumerating some MUSes within a given time bound. The experimental results focus on formulas for which existing solutions are unable to enumerate MUSes, and shows that the new approach can in most cases enumerate a non-negligible number of MUSes within a given time bound.