Showing papers on "Disjunctive normal form published in 2001"

Learning of Boolean Functions Using Support Vector Machines

Abstract: This paper concerns the design of a Support Vector Machine (SVM) appropriate for the learning of Boolean functions. This is motivated by the need of a more sophisticated algorithm for classification in discrete attribute spaces. Classification in discrete attribute spaces is reduced to the problem of learning Boolean functions from examples of its input/output behavior. Since any Boolean function can be written in Disjunctive Normal Form (DNF), it can be represented as a weighted linear sum of all possible conjunctions of Boolean literals. This paper presents a particular kernel function called the DNF kernel which enables SVMs to efficiently learn such linear functions in the high-dimensional space whose coordinates correspond to all possible conjunctions. For a limited form of DNF consisting of positive Boolean literals, the monotone DNF kernel is also presented. SVMs employing these kernel functions can perform the learning in a high-dimensional feature space whose features are derived from given basic attributes. In addition, it is expected that SVMs' well-founded capacity control alleviates overfitting. In fact, an empirical study on learning of randomly generated Boolean functions shows that the resulting algorithm outperforms C4.5. Furthermore, in comparison with SVMs employing the Gaussian kernel, it is shown that DNF kernel produces accuracy comparable to best adjusted Gaussian kernels.

Kernel Machines and Boolean Functions

Abstract: We give results about the learnability and required complexity of logical formulae to solve classification problems. These results are obtained by linking propositional logic with kernel machines. In particular we show that decision trees and disjunctive normal forms (DNF) can be represented by the help of a special kernel, linking regularized risk to separation margin. Subsequently we derive a number of lower bounds on the required complexity of logic formulae using properties of algorithms for generation of linear estimators, such as perceptron and maximal perceptron learning.

Semantics for Fuzzy Disjunctive Programs with Weak Similarity.

Abstract: In the paper, we present declarative, model, and fixpoint semantics for fuzzy disjunctive programs with weak similarity — sets of graded strong literal disjunctions. We shall suppose that truth values (degrees) constitute a regular residuated lattice L = (L, ≤, *, ⇒, ∪, ∩, 0, 1). A graded strong literal disjunction will be viewed as a pair (d, c) where d is a formula of the form ¬(d 1 & … & d n ), i.e. a negation of a strong conjunction of literals d i ; and c is a truth value belonging to the lattice L. A graded literal disjunction can be understood as a means of representation of incomplete and imprecise information, where the incompleteness is formalised by its strong literal disjunction (a negation of a strong conjunction of literals), while the impreciseness by its truth degree. Such programs may contain the binary predicate symbol for weak similarity, denoted as ∼, which is the fuzzy counterpart of the ‘classical’ equality.

On Formulation of Disjunctive Coupling Queries in WHOWEDA

Abstract: We describe how to formulate coupling query to glean relevant Web data in the context of our web warehousing system called WHOWEDA (Warehouse Of Web Data) One of the important feature of our query mechanism is the ability to express disjunctive query conditions compactly We describe how to formulate coupling queries in text form as well as pictorially using coupling text and coupling graph We explore the limitations of coupling graph with respect to coupling text We found out that AND, OR and AND/OR-coupling graphs are less expressive than their textual counterparts To address this shortcoming we introduced another query formulation technique called hybrid graph which is a special type of p-connected coupling graph

An Algorithm for Dual Transformation in First-Order Logic

Abstract: The transformation between conjunctive and disjunctive canonical forms is useful in domains such as theorem proving, function minimization, and knowledge representation. In this paper, we present a concurrent algorithm for this transformation, suitable for first-order logic theories. The proposed algorithm use the holographic relation between these normal forms in order to avoid the generation of noncondensed and subsumed (dual) clauses. We also stress the facts that, in first-order logic, this transformation is asymmetric and that disjunctive normal form, in some special cases, may be not unique, depending on choices about which subsumptions are allowed or not. The algorithm, which is part of a theorem-proving knowledge representation project, has been implemented and tested.

Semantic Forcing in Disjunctive Logic Programs

Abstract: We propose a semantics for disjunctive logic programs, based on the single notion of forcing. We show that the semantics properly extends, in a natural way, previous approaches. A fixpoint characterization is also provided. We also take a closer look at the relationship between disjunctive logic programs and disjunctive-free logic programs. We present certain criteria under which a disjunctive program is semantically equivalent with its disjunctive-free (shifted) version.

Implementation of a class of Boolean functions with a small number of zeros by irredundant disjunctive normal forms

Abstract: Irredundant disjunctive normal forms (DNFs) are obtained for Boolean functions defined by a matrix of zeros of order k x n, k ≥ 4 that contains an identity submatrix (disregarding the duality and permutation of columns) of order k x k. Special attention is paid to the construction of irredundant DNFs for full Boolean functions.

Normal forms and truth tables for interval-valued fuzzy logic

Abstract: In this paper, we provide normal forms and truth tables for interval-valued fuzzy logic which are analogous to those for classical logic, i.e. analogous to the disjunctive and conjunctive normal forms and truth tables for Boolean algebras. We give an algorithm for rewriting an expression to obtain its disjunctive normal form. We also give an algorithm for obtaining the disjunctive normal form of an expression from its table of truth values.

Domain-specific language design requires feature descriptions

Abstract: A domain-specific language (DSL) provides a notation tailored towards an application domain and is based on the relevant concepts and features of that domain. As such, a DSL is a means to describe and generate members of a family of programs in the domain. A prerequisite for the design of a DSL is a detailed analysis and structuring of the application domain.Graphical feature diagrams have been proposed to organize the dependencies between such features, and to indicate which ones are common to all family members and which ones vary. In this paper, we study feature diagrams in more details, as well as their relationship to domain-specific languages. We propose the Feature Description Language (FDL), a textual language to describe features.We explore automated manipulation of feature descriptions such as normalization, expansion to disjunctive normal form, variability computation and constraint satisfaction. Feature descriptions can be directly mapped to UML diagrams which in their turn can be used for Java code generation. The value of FDL is assessed via a case study in the use and expressiveness of feature descriptions for the area of documentation generators.

An artificial neural network satisfiability tester

Abstract: An artificial neural network tester for the satisfiability problem of propositional calculus is presented. Satisfiability is treated as a constraint satisfaction optimization problem and, contrary to most of the existing satisfiability testers, the expressions are converted into disjunctive normal form before testing. The artificial neural network is based on the principles of harmony theory. Its basic characteristics are the simulated annealing procedure and the harmony function; the latter constitutes a measure of the satisfiability of the expression under the current truth assignment to its variables. The tester is such that: (a) the satisfiability of any expression is determined; (b) a truth assignment to the variables of the expression is output which renders true the greatest possible number of clauses; (c) all the truth assignments which render true the maximum number of clauses can be produced. © 2001 John Wiley & Sons, Inc.