instruction:
In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
question:
Model counting is the problem of computing the number of models that satisfy a given propositional theory. It has recently been applied to solving inference tasks in probabilistic logic programming, where the goal is to compute the probability of given queries being true provided a set of mutually independent random variables, a model (a logic program) and some evidence. The core of solving this inference task involves translating the logic program to a propositional theory and using a model counter. In this paper, we show that for some problems that involve inductive definitions like reachability in a graph, the translation of logic programs to SAT can be expensive for the purpose of solving inference tasks. For such problems, direct implementation of stable model semantics allows for more efficient solving. We present two implementation techniques, based on unfounded set detection, that extend a propositional model counter to a stable model counter. Our experiments show that for particular problems, our approach can outperform a state-of-the-art probabilistic logic programming solver by several orders of magnitude in terms of running time and space requirements, and can solve instances of significantly larger sizes on which the current solver runs out of time or memory.
answer:
Stable Model Counting and Its Application in Probabilistic Logic Programming


question:
In many domains it is desirable to assess the pref­ erences of users in a qualitative rather than quan­ titative way. Such representations of qualitative preference orderings form an important compo­ nent of automated decision tools. We propose a graphical representation of preferences that re­ flects conditional dependence and independence of preference statements under a ceteris paribus (all else being equal) interpretation. Such a rep­ resentation is often compact and arguably natural. We describe several search algorithms for domi­ nance testing based on this representation; these algorithms are quite effective, especially in spe­ cific network topologies, such as chainand tree­ structured networks, as well as polytrees.
answer:
Reasoning With Conditional Ceteris Paribus Preference Statements


question:
One of the better studied properties for operators in judgment aggregation is independence, which essentially dictates that the collective judgment on one issue should not depend on the individual judgments given on some other issue(s) in the same agenda. Independence, although considered a desirable property, is too strong, because together with mild additional conditions it implies dictatorship. We propose here a weakening of independence, named agenda separability: a judgment aggregation rule satisfies it if, whenever the agenda is composed of several independent sub-agendas, the resulting collective judgment sets can be computed separately for each sub-agenda and then put together. We show that this property is discriminant, in the sense that among judgment aggregation rules so far studied in the literature, some satisfy it and some do not. We briefly discuss the implications of agenda separability on the computation of judgment aggregation rules.
answer:

Agenda Separability in Judgment Aggregation