1,063,422 research outputs found
A Fuzzy Petri Nets Model for Computing With Words
Motivated by Zadeh's paradigm of computing with words rather than numbers,
several formal models of computing with words have recently been proposed.
These models are based on automata and thus are not well-suited for concurrent
computing. In this paper, we incorporate the well-known model of concurrent
computing, Petri nets, together with fuzzy set theory and thereby establish a
concurrency model of computing with words--fuzzy Petri nets for computing with
words (FPNCWs). The new feature of such fuzzy Petri nets is that the labels of
transitions are some special words modeled by fuzzy sets. By employing the
methodology of fuzzy reasoning, we give a faithful extension of an FPNCW which
makes it possible for computing with more words. The language expressiveness of
the two formal models of computing with words, fuzzy automata for computing
with words and FPNCWs, is compared as well. A few small examples are provided
to illustrate the theoretical development.Comment: double columns 14 pages, 8 figure
Transition Systems for Model Generators - A Unifying Approach
A fundamental task for propositional logic is to compute models of
propositional formulas. Programs developed for this task are called
satisfiability solvers. We show that transition systems introduced by
Nieuwenhuis, Oliveras, and Tinelli to model and analyze satisfiability solvers
can be adapted for solvers developed for two other propositional formalisms:
logic programming under the answer-set semantics, and the logic PC(ID). We show
that in each case the task of computing models can be seen as "satisfiability
modulo answer-set programming," where the goal is to find a model of a theory
that also is an answer set of a certain program. The unifying perspective we
develop shows, in particular, that solvers CLASP and MINISATID are closely
related despite being developed for different formalisms, one for answer-set
programming and the latter for the logic PC(ID).Comment: 30 pages; Accepted for presentation at ICLP 2011 and for publication
in Theory and Practice of Logic Programming; contains the appendix with
proof
Extracting finite structure from infinite language
This paper presents a novel connectionist memory-rule based model capable of learning the finite-state properties of an input language from a set of positive examples. The model is based upon an unsupervised recurrent self-organizing map [T. McQueen, A. Hopgood, J. Tepper, T. Allen, A recurrent self-organizing map for temporal sequence processing, in: Proceedings of Fourth International Conference in Recent Advances in Soft Computing (RASC2002), Nottingham, 2002] with laterally interconnected neurons. A derivation of functionalequivalence theory [J. Hopcroft, J. Ullman, Introduction to Automata Theory, Languages and Computation, vol. 1, Addison-Wesley, Reading, MA, 1979] is used that allows the model to exploit similarities between the future context of previously memorized sequences and the future context of the current input sequence. This bottom-up learning algorithm binds functionally related neurons together to form states. Results show that the model is able to learn the Reber grammar [A. Cleeremans, D. Schreiber, J. McClelland, Finite state automata and simple recurrent networks, Neural Computation, 1 (1989) 372–381] perfectly from a randomly generated training set and to generalize to sequences beyond the length of those found in the training set
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
DAKS: An R Package for Data Analysis Methods in Knowledge Space Theory
Knowledge space theory is part of psychometrics and provides a theoretical framework for the modeling, assessment, and training of knowledge. It utilizes the idea that some pieces of knowledge may imply others, and is based on order and set theory. We introduce the R package DAKS for performing basic and advanced operations in knowledge space theory. This package implements three inductive item tree analysis algorithms for deriving quasi orders from binary data, the original, corrected, and minimized corrected algorithms, in sample as well as population quantities. It provides functions for computing population and estimated asymptotic variances of and one and two sample Z tests for the diff fit measures, and for switching between test item and knowledge state representations. Other features are a function for computing response pattern and knowledge state frequencies, a data (based on a finite mixture latent variable model) and quasi order simulation tool, and a Hasse diagram drawing device. We describe the functions of the package and demonstrate their usage by real and simulated data examples.
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