1,536 research outputs found
The Integration of Connectionism and First-Order Knowledge Representation and Reasoning as a Challenge for Artificial Intelligence
Intelligent systems based on first-order logic on the one hand, and on
artificial neural networks (also called connectionist systems) on the other,
differ substantially. It would be very desirable to combine the robust neural
networking machinery with symbolic knowledge representation and reasoning
paradigms like logic programming in such a way that the strengths of either
paradigm will be retained. Current state-of-the-art research, however, fails by
far to achieve this ultimate goal. As one of the main obstacles to be overcome
we perceive the question how symbolic knowledge can be encoded by means of
connectionist systems: Satisfactory answers to this will naturally lead the way
to knowledge extraction algorithms and to integrated neural-symbolic systems.Comment: In Proceedings of INFORMATION'2004, Tokyo, Japan, to appear. 12 page
An Upper Bound on the Complexity of Recognizable Tree Languages
The third author noticed in his 1992 PhD Thesis [Sim92] that every regular
tree language of infinite trees is in a class
for some natural number , where is the game quantifier. We
first give a detailed exposition of this result. Next, using an embedding of
the Wadge hierarchy of non self-dual Borel subsets of the Cantor space
into the class , and the notions of Wadge degree
and Veblen function, we argue that this upper bound on the topological
complexity of regular tree languages is much better than the usual
Towards a Systematic Account of Different Semantics for Logic Programs
In [Hitzler and Wendt 2002, 2005], a new methodology has been proposed which
allows to derive uniform characterizations of different declarative semantics
for logic programs with negation. One result from this work is that the
well-founded semantics can formally be understood as a stratified version of
the Fitting (or Kripke-Kleene) semantics. The constructions leading to this
result, however, show a certain asymmetry which is not readily understood. We
will study this situation here with the result that we will obtain a coherent
picture of relations between different semantics for normal logic programs.Comment: 20 page
On variables with few occurrences in conjunctive normal forms
We consider the question of the existence of variables with few occurrences
in boolean conjunctive normal forms (clause-sets). Let mvd(F) for a clause-set
F denote the minimal variable-degree, the minimum of the number of occurrences
of variables. Our main result is an upper bound mvd(F) <= nM(surp(F)) <=
surp(F) + 1 + log_2(surp(F)) for lean clause-sets F in dependency on the
surplus surp(F).
- Lean clause-sets, defined as having no non-trivial autarkies, generalise
minimally unsatisfiable clause-sets.
- For the surplus we have surp(F) <= delta(F) = c(F) - n(F), using the
deficiency delta(F) of clause-sets, the difference between the number of
clauses and the number of variables.
- nM(k) is the k-th "non-Mersenne" number, skipping in the sequence of
natural numbers all numbers of the form 2^n - 1.
We conjecture that this bound is nearly precise for minimally unsatisfiable
clause-sets.
As an application of the upper bound we obtain that (arbitrary!) clause-sets
F with mvd(F) > nM(surp(F)) must have a non-trivial autarky (so clauses can be
removed satisfiability-equivalently by an assignment satisfying some clauses
and not touching the other clauses). It is open whether such an autarky can be
found in polynomial time.
As a future application we discuss the classification of minimally
unsatisfiable clause-sets depending on the deficiency.Comment: 14 pages. Revision contains more explanations, and more information
regarding the sharpness of the boun
A Coverage Criterion for Spaced Seeds and its Applications to Support Vector Machine String Kernels and k-Mer Distances
Spaced seeds have been recently shown to not only detect more alignments, but
also to give a more accurate measure of phylogenetic distances (Boden et al.,
2013, Horwege et al., 2014, Leimeister et al., 2014), and to provide a lower
misclassification rate when used with Support Vector Machines (SVMs) (On-odera
and Shibuya, 2013), We confirm by independent experiments these two results,
and propose in this article to use a coverage criterion (Benson and Mak, 2008,
Martin, 2013, Martin and No{\'e}, 2014), to measure the seed efficiency in both
cases in order to design better seed patterns. We show first how this coverage
criterion can be directly measured by a full automaton-based approach. We then
illustrate how this criterion performs when compared with two other criteria
frequently used, namely the single-hit and multiple-hit criteria, through
correlation coefficients with the correct classification/the true distance. At
the end, for alignment-free distances, we propose an extension by adopting the
coverage criterion, show how it performs, and indicate how it can be
efficiently computed.Comment: http://online.liebertpub.com/doi/abs/10.1089/cmb.2014.017
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