34 research outputs found
Algebraic model counting
Weighted model counting (WMC) is a well-known inference task on knowledge bases, and the basis for some of the most efficient techniques for probabilistic inference in graphical models. We introduce algebraic model counting (AMC), a generalization of WMC to a semiring structure that provides a unified view on a range of tasks and existing results. We show that AMC generalizes many well-known tasks in a variety of domains such as probabilistic inference, soft constraints and network and database analysis. Furthermore, we investigate AMC from a knowledge compilation perspective and show that all AMC tasks can be evaluated using sd-DNNF circuits, which are strictly more succinct, and thus more efficient to evaluate, than direct representations of sets of models. We identify further characteristics of AMC instances that allow for evaluation on even more succinct circuits
Hunting for Tractable Languages for Judgment Aggregation
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).Comment: To appear in the Proceedings of the 16th International Conference on
Principles of Knowledge Representation and Reasoning (KR 2018
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