226,345 research outputs found
Modal Logic and the Approximation Induction Principle
We prove a compactness theorem in the context of Hennessy-Milner logic. It is
used to derive a sufficient condition on modal characterizations for the
Approximation Induction Principle to be sound modulo the corresponding process
equivalence. We show that this condition is necessary when the equivalence in
question is compositional with respect to the projection operators
Approximation properties of the neuro-fuzzy minimum function
The integration of fuzzy logic systems and neural networks in data driven nonlinear modeling applications has generally been limited to functions based upon the multiplicative fuzzy implication rule for theoretical and computational reasons. We derive a universal approximation result for the minimum fuzzy implication rule as well as a differentiable substitute function that allows fast optimization and function approximation with neuro-fuzzy networks. --Fuzzy Logic,Neural Networks,Nonlinear Modeling,Optimization
Ultimate approximations in nonmonotonic knowledge representation systems
We study fixpoints of operators on lattices. To this end we introduce the
notion of an approximation of an operator. We order approximations by means of
a precision ordering. We show that each lattice operator O has a unique most
precise or ultimate approximation. We demonstrate that fixpoints of this
ultimate approximation provide useful insights into fixpoints of the operator
O.
We apply our theory to logic programming and introduce the ultimate
Kripke-Kleene, well-founded and stable semantics. We show that the ultimate
Kripke-Kleene and well-founded semantics are more precise then their standard
counterparts We argue that ultimate semantics for logic programming have
attractive epistemological properties and that, while in general they are
computationally more complex than the standard semantics, for many classes of
theories, their complexity is no worse.Comment: This paper was published in Principles of Knowledge Representation
and Reasoning, Proceedings of the Eighth International Conference (KR2002
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
DNF Sampling for ProbLog Inference
Inference in probabilistic logic languages such as ProbLog, an extension of
Prolog with probabilistic facts, is often based on a reduction to a
propositional formula in DNF. Calculating the probability of such a formula
involves the disjoint-sum-problem, which is computationally hard. In this work
we introduce a new approximation method for ProbLog inference which exploits
the DNF to focus sampling. While this DNF sampling technique has been applied
to a variety of tasks before, to the best of our knowledge it has not been used
for inference in probabilistic logic systems. The paper also presents an
experimental comparison with another sampling based inference method previously
introduced for ProbLog.Comment: Online proceedings of the Joint Workshop on Implementation of
Constraint Logic Programming Systems and Logic-based Methods in Programming
Environments (CICLOPS-WLPE 2010), Edinburgh, Scotland, U.K., July 15, 201
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