Search results for "If and only if"

showing 10 items of 36 documents

Reply from m. Heino, j.a.j. Metz and v. Kaitala.

1998

Eva Kisdi clarifies the relationships between frequency dependence, optimization and ESSs. We basically agree with all her comments. However, some further clarification may be useful.In the first paragraph of Kisdi's letter, ESSs and optimal strategies are seemingly opposed by saying that `finding an optimal strategy is a considerably stronger result than finding an ESS'. Although this statement is factually correct, it might engender a suggestion that is slightly wrong. Conceptually, ESSs are always primary: only ESSs matter from the viewpoint of long-term evolution. Optimization is secondary only, and must be justified by an ESS argument that explicitly accounts for the ecology in which t…

0106 biological sciences0303 health sciencesEcologyComputer scienceStatement (logic)media_common.quotation_subjectMonotonic functionFrequency dependence010603 evolutionary biology01 natural sciences03 medical and health sciencesIf and only ifArgumentFunction (engineering)Mathematical economicsValue (mathematics)Ecology Evolution Behavior and Systematics030304 developmental biologymedia_commonSimple (philosophy)Trends in ecologyevolution
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On Inductive Generalization in Monadic First-Order Logic With Identity

1966

Publisher Summary The chapter examines the results obtained by means of a system when the relation of identity is used in addition to monadic predicates. The chapter compares the new system of inductive logic sketched by Jaakko Hintikka with Carnap's system. The main advantage of Hintikka's system is that it gives natural degrees of confirmation to inductive generalizations, whereas Carnap's confirmation function c * enables one to deal satisfactorily with singular inductive inference only. According to Carnap's system, general sentences that are not logically true receive nonnegligible degrees of confirmation only if the evidence contains a large part of the individuals in the whole univer…

AlgebraGeneralizationIf and only ifIdentity (philosophy)media_common.quotation_subjectFunction (mathematics)Inductive reasoningFirst-order logicUniverse (mathematics)Mathematicsmedia_commonZero (linguistics)
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Values of games with probabilistic graphs

1999

Abstract In this paper we consider games with probabilistic graphs. The model we develop is an extension of the model of games with communication restrictions by Myerson (1977) . In the Myerson model each pair of players is joined by a link in the graph if and only if these two players can communicate directly. The current paper considers a more general setting in which each pair of players has some probability of direct communication. The value is defined and characterized in this context. It is a natural extension of the Myerson value and it turns out to be the Shapley value of a modified game.

Computer Science::Computer Science and Game TheorySociology and Political ScienceIf and only ifComputingMilieux_PERSONALCOMPUTINGProbabilistic logicGeneral Social SciencesStatistics Probability and UncertaintyDirect communicationShapley valueMathematical economicsGeneral PsychologyGraphMathematics
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Towards Advanced Visualisation Techniques in Case

1999

The complexity of information systems has resulted in more sophisticated CASE tools which integrate multifaceted design information using metamodeling and hypertext technologies. A designer can use this vast amount of tightly coupled information efficiently only if it is presented based on his needs and cognitive capabilities. In this paper we discuss how representations in CASE can be improved using advanced visualisation techniques.

Computer sciencebusiness.industryDesign informationlaw.inventionMetamodelingInformation visualizationIf and only iflawHuman–computer interactionVisualisation techniquesInformation systemHypertextComputer-aided software engineeringbusiness
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Knowledge and Mistakes

2015

This chapter is about how we attain knowledge, and how we fail to do so. I argue that a true thought counts as a piece of knowledge if and only if it has the right sort of causal history. I also argue that these so-called cognitive thoughts are the criteria of truth in the sense that they are guaranteed to be true and able to guarantee the truth of that which can be inferred from them. So I argue that there are three kinds of knowledge, namely the information conveyed by our senses, the information contained in our preconceptions and the conclusions that can be inferred from our sense-perceptions and our preconceptions. I then argue that we fail to attain knowledge if we assent to a thought…

Consistency testIf and only ifsortCognitionCriteria of truthPsychologyEpistemology
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Sturmian graphs and integer representations over numeration systems

2012

AbstractIn this paper we consider a numeration system, originally due to Ostrowski, based on the continued fraction expansion of a real number α. We prove that this system has deep connections with the Sturmian graph associated with α. We provide several properties of the representations of the natural integers in this system. In particular, we prove that the set of lazy representations of the natural integers in this numeration system is regular if and only if the continued fraction expansion of α is eventually periodic. The main result of the paper is that for any number i the unique path weighted i in the Sturmian graph associated with α represents the lazy representation of i in the Ost…

Discrete mathematicsContinued fractionsApplied MathematicsNumeration systemsSturmian graphsGraphCombinatoricsOstrowski numerationIntegerIf and only ifnumeration systems Sturmian graphs continued fractions.Numeration systems; SUBWORD GRAPHS; WORDSDiscrete Mathematics and CombinatoricsSUBWORD GRAPHSContinued fractionWORDSMathematicsReal number
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ON THE STAR HEIGHT OF RATIONAL LANGUAGES

1994

Two problems concerning the star height of a rational language are investigated: the star height one problem and the relationships between the unambiguity of an expression and its star height. For this purpose we consider the class of factorial, transitive and rational (FTR) languages. From the algebraic point of view a FTR language is the set of factors of a rational submonoid M. Two subclasses of FTR languages are introduced: renewal languages, corresponding to the case of M finitely generated, and unambiguous renewal languages, corresponding to the case of M finitely generated and free. We prove that a FTR language has star height one if and only if it is renewal. This gives a simple de…

Discrete mathematicsFactorialTransitive relationStar heightGeneral Mathematicsmedia_common.quotation_subjectComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)AmbiguityRegular languageIf and only ifComputer Science::Programming LanguagesEntropy (information theory)Algebraic numberMathematicsmedia_commonInternational Journal of Algebra and Computation
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A decomposition theorem for compact-valued Henstock integral

2006

We prove that if X is a separable Banach space, then a measurable multifunction Γ : [0, 1] → ck(X) is Henstock integrable if and only if Γ can be represented as Γ = G + f, where G : [0, 1] → ck(X) is McShane integrable and f is a Henstock integrable selection of Γ.

Discrete mathematicsIntegrable systemSelection (relational algebra)MultifunctionHenstock integralIf and only ifGeneral MathematicsBanach spacePettis integralKurzweil–Henstock–Pettis integral selectionSeparable spaceMathematicsDecomposition theorem
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Marked systems and circular splicing

2007

Splicing systems are generative devices of formal languages, introduced by Head in 1987 to model biological phenomena on linear and circular DNA molecules. In this paper we introduce a special class of finite circular splicing systems named marked systems. We prove that a marked system S generates a regular circular language if and only if S satisfies a special (decidable) property. As a consequence, we show that we can decide whether a regular circular language is generated by a marked system and we characterize the structure of these regular circular languages.

Discrete mathematicsProperty (programming)Structure (category theory)Molecular computingCircular wordDecidabilityRegular languageIf and only ifRNA splicingFormal languageSplicing systemFormal languageGenerative grammarAutomata theoryMathematics
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A Decomposition Theorem for the Fuzzy Henstock Integral

2012

We study the fuzzy Henstock and the fuzzy McShane integrals for fuzzy-number valued functions. The main purpose of this paper is to establish the following decomposition theorem: a fuzzy-number valued function is fuzzy Henstock integrable if and only if it can be represented as a sum of a fuzzy McShane integrable fuzzy-number valued function and of a fuzzy Henstock integrable fuzzy number valued function generated by a Henstock integrable function.

Discrete mathematicsPure mathematicsIntegrable systemMathematics::General MathematicsLogicMathematics::Classical Analysis and ODEsFunction (mathematics)Fuzzy logicComputingMethodologies_PATTERNRECOGNITIONArtificial IntelligenceIf and only ifSettore MAT/05 - Analisi MatematicaFuzzy Henstock integral fuzzy McShane integral Henstock-Kurzweil and McShane equiintegrabilityFuzzy numberLocally integrable functionComputingMethodologies_GENERALMathematicsDecomposition theorem
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