Search results for " logic"

showing 10 items of 1720 documents

Error-Free Affine, Unitary, and Probabilistic OBDDs

2021

We introduce the affine OBDD model and show that zero-error affine OBDDs can be exponentially narrower than bounded-error unitary and probabilistic OBDDs on certain problems. Moreover, we show that Las-Vegas unitary and probabilistic OBDDs can be quadratically narrower than deterministic OBDDs. We also obtain the same results for the automata counterparts of these models.

Discrete mathematicsState complexityComputer Science::Logic in Computer ScienceComputer Science (miscellaneous)Probabilistic logicAffine transformationComputer Science::Computational ComplexityComputer Science::Artificial IntelligenceUnitary stateComputer Science::DatabasesMathematicsZero errorInternational Journal of Foundations of Computer Science
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Some dissenting views on the transitivity of individual preference

1990

(1) The transitivity property is not a necessary condition for the rationality of all individual preference relations. (2) A weakened definition of the transitivity is not necessarily relevant. (3) The non-transitivity of fuzzy preference relations is not inconsistent with a fuzzy total preorder structure on the set of alternatives.

Discrete mathematicsStructure (mathematical logic)Transitive relationProperty (philosophy)PreorderGeneral Decision SciencesRationalityManagement Science and Operations ResearchEuclidean relationMathematical economicsFuzzy logicPreferenceMathematicsAnnals of Operations Research
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Counting in the Two Variable Guarded Logic with Transitivity

2005

We show that the extension of the two-variable guarded fragment with transitive guards (GF+TG) by functionality statements is undecidable. This gives immediately undecidability of the extension of GF+TG by counting quantifiers. The result is optimal, since both the three-variable fragment of the guarded fragment with counting quantifiers and the two-variable guarded fragment with transitivity are undecidable. We also show that the extension of GF+TG with functionality, where functional predicate letters appear in guards only, is decidable and of the same complexity as GF+TG. This fragment captures many expressive modal and description logics.

Discrete mathematicsTransitive relationGuarded logicTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESFragment (logic)Description logicFunctional predicateTheoryofComputation_LOGICSANDMEANINGSOFPROGRAMSExtension (predicate logic)Undecidable problemMathematicsDecidability
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Ranking fuzzy interval numbers in the setting of random sets – further results

1999

Abstract We present some new properties of several fuzzy order relations, defined on the set of fuzzy numbers, from among those introduced in [S. Chanas, M. Delgado, J.L. Verdegay, M.A. Vila, Information Sciences 69 (1993) 201–217]. The main result is proving that four from among the relations considered in [S. Chanas, M. Delgado, J.L. Verdegay, M.A. Vila, Information Sciences 69 (1993) 201–217] are strongly transitive (s-transitive).

Discrete mathematicsTransitive relationInformation Systems and ManagementFuzzy classificationFuzzy setInterval (mathematics)Type-2 fuzzy sets and systemsFuzzy logicComputer Science ApplicationsTheoretical Computer ScienceArtificial IntelligenceControl and Systems EngineeringFuzzy mathematicsFuzzy numberSoftwareMathematicsInformation Sciences
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Transitive Reasoning with Imprecise Probabilities

2015

We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent \(\text{ p-consistent }\) sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Finally, we present the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases.

Discrete mathematicsTransitive relationSettore MAT/06 - Probabilita' E Statistica MatematicaSettore INF/01 - Informaticabusiness.industryProbabilistic logicSyllogismInferenceCoherence (philosophical gambling strategy)Settore M-FIL/02 - Logica E Filosofia Della ScienzaComputer Science::Artificial IntelligenceImprecise probabilityCoherence default imprecise probability knowledge base p-consistency p-entailment reasoning syllogism weak transitivityProbability propagationKnowledge basebusinessMathematics
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Common fixed point theorems for mappings satisfying common property (E.A.) in symmetric spaces

2011

In this paper, common fixed point theorems for mappings satisfying a generalized contractive condition are obtained in symmetric spaces by using the notion of common property (E.A.). In the process, a host of previously known results are improved and generalized. We also derive results on common fixed point in probabilistic symmetric spaces.

Discrete mathematicsTriple systemSettore MAT/05 - Analisi MatematicaGeneral MathematicsSymmetric spaceProbabilistic logicCommon fixed pointSymmetric space common property (E.A.) common fixed point.Common propertyPoint (geometry)Mathematics
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Probabilistic Interpretations of Predicates

2016

In classical logic, any m-ary predicate is interpreted as an m-argument two-valued relation defined on a non-empty universe. In probability theory, m-ary predicates are interpreted as probability measures on the mth power of a probability space. m-ary probabilistic predicates are equivalently semantically characterized as m-dimensional cumulative distribution functions defined on \(\mathbb {R}^m\). The paper is mainly concerned with probabilistic interpretations of unary predicates in the algebra of cumulative distribution functions defined on \(\mathbb {R}\). This algebra, enriched with two constants, forms a bounded De Morgan algebra. Two logical systems based on the algebra of cumulative…

Discrete mathematicsUnary operationComputer Science::Logic in Computer ScienceCumulative distribution functionClassical logicProbabilistic logicRandom variableŁukasiewicz logicDe Morgan algebraMathematicsProbability measure
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Uncountable Realtime Probabilistic Classes

2018

We investigate the minimal cases for realtime probabilistic machines that can define uncountably many languages with bounded error. We show that logarithmic space is enough for realtime PTMs on unary languages. On non-unary case, we obtain the same result for double logarithmic space, which is also tight. When replacing the work tape with a few counters, we can still achieve similar results for unary linear-space two-counter automata, unary sublinear-space three-counter automata, and non-unary sublinear-space two-counter automata. We also show how to slightly improve the sublinear-space constructions by using more counters.

Discrete mathematicsUnary operationComputer scienceProbabilistic logic020206 networking & telecommunicationsComputerApplications_COMPUTERSINOTHERSYSTEMS0102 computer and information sciences02 engineering and technology01 natural sciencesLogarithmic spaceBounded error010201 computation theory & mathematics0202 electrical engineering electronic engineering information engineeringComputer Science (miscellaneous)020201 artificial intelligence & image processingUncountable setBinary caseInternational Journal of Foundations of Computer Science
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On Branciari’s theorem for weakly compatible mappings

2010

AbstractIn a recent paper B. Samet and H. Yazidi [B. Samet, H. Yazidi, An extension of Banach fixed point theorem for mappings satisfying a contractive condition of integral type, Ital. J. Pure Appl. Math. (in press)] have obtained an interesting theorem for mappings satisfying a contractive condition of integral type. The aim of this note is to present a generalization of their main result.

Discrete mathematicsWeakly compatibleGeneralizationBanach fixed-point theoremApplied MathematicsFixed-point theoremWeakly compatible mappingsExtension (predicate logic)Type (model theory)Common fixed pointContractive condition of integral typeCommon fixed point Weakly compatible mappings Contractive condition of integral typeSettore MAT/05 - Analisi MatematicaCommon fixed pointMathematicsApplied Mathematics Letters
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Common fixed point theorems for families of occasionally weakly compatible mappings

2011

We prove some common fixed point theorems in probabilistic semi-metric spaces for families of occasionally weakly compatible mappings. We also give a common fixed point theorem for mappings satisfying an integral-type implicit relation.

Discrete mathematicsWeakly compatibleRelation (database)010102 general mathematicsProbabilistic logicOccasionally weakly compatible mappingProbabilistic metric spaceCommon fixed point01 natural sciencesProbabilistic metric spaceComputer Science Applications010101 applied mathematicsLeast fixed pointSettore MAT/05 - Analisi MatematicaModelling and SimulationModeling and SimulationCommon fixed point0101 mathematicsCoincidence pointCommon fixed point theoremMathematicsMathematical and Computer Modelling
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