52 research outputs found
First-order integer programming for MAP problems
Finding the most probable (MAP) model in SRL frameworks such as Markov logic
and Problog can, in principle, be solved by encoding the problem as a
`grounded-out' mixed integer program (MIP). However, useful first-order
structure disappears in this process motivating the development of first-order
MIP approaches. Here we present mfoilp, one such approach. Since the syntax and
semantics of mfoilp is essentially the same as existing approaches we focus
here mainly on implementation and algorithmic issues. We start with the
(conceptually) simple problem of using a logic program to generate a MIP
instance before considering more ambitious exploitation of first-order
representations.Comment: corrected typo
Stable Model Counting and Its Application in Probabilistic Logic Programming
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.Comment: Accepted in AAAI, 201
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