19,147 research outputs found
Knowledge Compilation of Logic Programs Using Approximation Fixpoint Theory
To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of
ICLP 2015
Recent advances in knowledge compilation introduced techniques to compile
\emph{positive} logic programs into propositional logic, essentially exploiting
the constructive nature of the least fixpoint computation. This approach has
several advantages over existing approaches: it maintains logical equivalence,
does not require (expensive) loop-breaking preprocessing or the introduction of
auxiliary variables, and significantly outperforms existing algorithms.
Unfortunately, this technique is limited to \emph{negation-free} programs. In
this paper, we show how to extend it to general logic programs under the
well-founded semantics.
We develop our work in approximation fixpoint theory, an algebraical
framework that unifies semantics of different logics. As such, our algebraical
results are also applicable to autoepistemic logic, default logic and abstract
dialectical frameworks
Aggregated fuzzy answer set programming
Fuzzy Answer Set programming (FASP) is an extension of answer set programming (ASP), based on fuzzy logic. It allows to encode continuous optimization problems in the same concise manner as ASP allows to model combinatorial problems. As a result of its inherent continuity, rules in FASP may be satisfied or violated to certain degrees. Rather than insisting that all rules are fully satisfied, we may only require that they are satisfied partially, to the best extent possible. However, most approaches that feature partial rule satisfaction limit themselves to attaching predefined weights to rules, which is not sufficiently flexible for most real-life applications. In this paper, we develop an alternative, based on aggregator functions that specify which (combination of) rules are most important to satisfy. We extend upon previous work by allowing aggregator expressions to define partially ordered preferences, and by the use of a fixpoint semantics
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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