Showing papers on "Disjunctive normal form published in 2007"

Evolutionary Fuzzy Rule Induction Process for Subgroup Discovery: A Case Study in Marketing

Abstract: This paper presents a genetic fuzzy system for the data mining task of subgroup discovery, the subgroup discovery iterative genetic algorithm (SDIGA), which obtains fuzzy rules for subgroup discovery in disjunctive normal form. This kind of fuzzy rule allows us to represent knowledge about patterns of interest in an explanatory and understandable form that can be used by the expert. Experimental evaluation of the algorithm and a comparison with other subgroup discovery algorithms show the validity of the proposal. SDIGA is applied to a market problem studied in the University of Mondragon, Spain, in which it is necessary to extract automatically relevant and interesting information that helps to improve fair planning policies. The application of SDIGA to this problem allows us to obtain novel and valuable knowledge for experts.

Test conditions for fault classes in Boolean specifications

Abstract: Fault-based testing of software checks the software implementation for a set of faults. Two previous papers on fault-based testing [Kuhn 1999; Tsuchiya and Kikuno 2002] represent the required behavior of the software as a Boolean specification represented in Disjunctive Normal Form (DNF) and then show that faults may be organized in a hierarchy. This article extends these results by identifying necessary and sufficient conditions for fault-based testing. Unlike previous solutions, the formal analysis used to derive these conditions imposes no restrictions (such as DNF) on the form of the Boolean specification.

On Boolean Functions Encodable as a Single Linear Pseudo-Boolean Constraint

Abstract: A linear pseudo-Boolean constraint(LPB) is an expression of the form a 1 ·? 1 + ... + a m ·? m ? d, where each ? i is a literal(it assumes the value 1 or 0 depending on whether a propositional variable x i is true or false) and a 1 ,...,a m ,dare natural numbers. An LPB is a generalisation of a propositional clause, on the other hand it is a restriction of integer linear programming. LPBs can be used to represent Boolean functions more compactly than the well-known conjunctiveor disjunctivenormal forms. In this paper, we address the question: how muchmore compactly? We compare the expressiveness of a single LPB to that of related formalisms, and give an algorithm for computing an LPB representation of a given formula if this is possible.

Minimization of Boolean expressions using matrix algebra

Abstract: The more variables a logic expression contain, the more complicated is the interpretation of this expression. Since in a statistical sense prime implicants can be interpreted as interactions of binary variables, it is thus advantageous to convert such a logic expression into a disjunctive normal form consisting of prime implicants. In this paper, we present two algorithms based on matrix algebra for the identification of all prime implicants comprised in a logic expression and for the minimization of this set of prime implicants.

Subexponential time and fixed-parameter tractability: exploiting the miniaturization mapping

Abstract: Recently a mapping M, the so-called miniaturization mapping, has been introduced and it has been shown that M faithfully translates subexponential parameterized complexity into (unbounded) parameterized complexity [2]. We determine the preimages under M of various (classes of) problems and show that they coincide with natural reparameterizations which take into account the amount of nondeterminism needed to solve them.

Logic based pattern recognition - ontology content (1) 1

Abstract: Pattern recognition (classification) algorithmic models and related structures were considered and discussed since 70s: - one, which is formally related to the similarity treatment and so - to the discrete isoperimetric property, and the second, - logic based and introduced in terms of Reduced Disjunctive Normal Forms of Boolean Functions. A series of properties of structures appearing in Logical Models are listed and interpreted. This brings new knowledge on formalisms and ontology when a logic based hypothesis is the model base for Pattern Recognition (classification).

An inference control algorithm for RDF(S) repository

Abstract: Protecting RDF(S) repository is a topic in many Web applications. In RDF(S) repository, sensitive information can be inferred from nonsensitive data by iteratively applying the inference rules. Therefore, the problem of inference control is a crucial need for protecting RDF(S) repository. This paper presents an inference control algorithm that can prevent illegal inference effectively. In the algorithm, the inference dependence graph is defined to compute the logic expression of sensitive RDF(S) triples set, which is translated into the disjunctive normal form for obtaining the answers of the inference control problem.

Complexity of Subsumption in Extensions of EL

Abstract: During the last years, it has been shown that the description logic EL is well-suited for tractable reasoning In particular, reasoning is even tractable wrt general concept inclusion axioms, and various extensions of EL and their effects on the complexity of subsumption wrt general concept inclusion axioms have been studied In this thesis, we sharpen the border between tractability and intractability of subsumption in extensions of EL wrt cyclic TBoxes We provide two new extensions for which subsumption can be computed in polynomial time wrt cyclic TBoxes The first extends EL by role con- and disjunction in disjunctive normal form, primitive negation and p-admissible concrete domains, and the second by role con- and disjunction in disjunctive normal form and at-least restrictions Moreover, we show that a combination of the two extensions leads to intractability of subsumption wrt cyclic TBoxes, as well as EL extended by negation, disjunction, transitive closure over role names, functionality and concrete domains with abstract feature chains This justifies the fact that–except for inverse roles which remain an open problem–both extensions are maximal in the sense that they cannot be further extended without losing tractability of subsumption wrt cyclic TBoxes

Minimization of Boolean expressions using matrix algebra

Abstract: The more variables a logic expression contain, the more complicated is the interpretation of this expression. Since in a statistical sense prime implicants can be interpreted as interactions of binary variables, it is thus advantageous to convert such a logic expression into a disjunctive normal form consisting of prime implicants. In this paper, we present two algorithms based on matrix algebra for the identification of all prime implicants comprised in a logic expression and for the minimization of this set of prime implicants.

Towards an Epistemic Logic for Uncertain Agents

Abstract: In this paper, we propose a logic for reasoning about probabilistic belief, called PBL r Our language introduces formulas that express "agent ibelieves that the probability of φis at least p" We first provide an inference system of PBL r , and then introduce a probabilistic semantics for PBL r The soundness and finite model property of PBL r are proved, which ensure the weak completeness and decidability of PBL r

Over approximation of integrated circuit based clock gating logic

Abstract: A novel method for optimizing the implementation of clock gating logic in digital circuits utilizing clock gating. The method over-approximates the clock gating function by removing the variable with the least influence on the resulting approximation function. Approximations of clock gating functions expressed in normal form are performed by removing an appropriate component from the function. Approximations of clock gating functions expressed in conjunctive normal form are performed by removing a clause from the function. Approximations of clock gating functions expressed in disjunctive normal form are performed by removing a literal from a clause in the function.

Matrix Method for Principal Normal Form of Propositional Formula

Abstract: A matrix method for principal normal form of propositional formula is derived from disjunctive normal form and conjunctive normal form based on the extension principle and deletion principle of superscript vectors of simplified phrase and simplified clause. Calculation process of principal normal form with equivalent calculus or truth table is simplified by the method presented.

Model-Characterizing Formulas and Normal Forms in Godel Logics

Abstract: This paper focuses on three kinds of normal forms: the weak conjunctive normal form, the weak disjunctive normal form and the weak implicational normal form. The existence of these normal forms in Godel logics is investigated, and two kinds of reduction methods for them are presented, one of which is based on model-characterizing formulas and the other on rewriting systems. As byproducts of these investigations, three kinds of model-characterizing formulas are obtained. In the end, the complexities of reductions to these normal forms are also studied.