Singular Terms, Truth-Value Gaps, and Free Logic

Fraassen, Bas C. van

doi:10.2307/2024549

Cited by 433 publications

(88 citation statements)

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“…10 8 Some further details are given later. For supervaluations, see inter alia (van Fraassen, 1966;Fine, 1975;Keefe, 2000). 9 Compare (Field, 2000).…”

Section: The Classical Frameworkmentioning

confidence: 99%

Probability and Nonclassical Logic

Williams

2017

Oxford Handbooks Online

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This chapter presents axioms for comparative conditional probability relations. The axioms presented here are more general than usual. Each comparative relation is a weak partial order on pairs of sentences but need not be a complete order relation. The axioms for these comparative relations are probabilistically sound for the broad class of conditional probability functions known as Popper functions. Furthermore, these axioms are probabilistically complete. Arguably, the notion of comparative conditional probability provides a foundation for Bayesian confirmation theory. Bayesian confirmation functions are overly precise probabilistic representations of the more fundamental logic of comparative support. The most important features of evidential support are captured by comparative relationships among argument strengths, realized by the comparative support relations and their logic.

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“…10 8 Some further details are given later. For supervaluations, see inter alia (van Fraassen, 1966;Fine, 1975;Keefe, 2000). 9 Compare (Field, 2000).…”

Section: The Classical Frameworkmentioning

confidence: 99%

Probability and Nonclassical Logic

Williams

2017

Oxford Handbooks Online

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“…Intuitively, a set of possible worlds supports the claim that p might be the case just in case it contains at least one possible world at which p is true, and we may then capture the difference between what is compatible with the common ground and what is explicitly recognized in discourse in a supervaluationist fashion (following Willer 2013a, though see Franke & de Jager 2011, de Jager 2009, Swanson 2006, and Yalcin 2011 for alternative awareness models). 12 If p is compatible with the common ground, ¬p fails to be common ground and so there is at least one set of possible worlds satisfying everything that is 12 Applications of supervaluationist techniques to various philosophical topics can be found, for instance, in Fine 1975, van Fraassen 1966, Kamp 1975, and Thomason 1970. Beaver (2001, recognizes the importance of supervaluationist techniques in modeling the common ground, though his motivation is different from mine: his interest is to account for the possibility that participants in a discourse may sometimes not know what the common ground is.…”

Section: Basicsmentioning

confidence: 99%

Lessons from Sobel sequences

Willer

2017

Semantics and Pragmatics

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“…In case of FO and its truth assignment υ, υ was introduced in (van Fraassen 1966) where it was called the supervaluation s. s is not truth functional, for if p I = q I = u, then (p ∨ ¬p) s:I = t = (p ∨ q) s:I = u while the components of the two disjunctions have the same supervaluation. A truth-functional definition of a three-valued truth assignment is obtained by using the ultimate approximations of the boolean functions associated to connectives and quantifiers.…”

Section: Approximating Boolean Functionsmentioning

confidence: 99%

Semantics of templates in a compositional framework for building logics

Dasseville¹,

Hallen²,

Janssens³

et al. 2015

Theory and Practice of Logic Programming

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There is a growing need for abstractions in logic specification languages such as FO(·) and ASP. One technique to achieve these abstractions are templates (sometimes called macros). While the semantics of templates are virtually always described through a syntactical rewriting scheme, we present an alternative view on templates as second order definitions. To extend the existing definition construct of FO(·) to second order, we introduce a powerful compositional framework for defining logics by modular integration of logic constructs specified as pairs of one syntactical and one semantical inductive rule. We use the framework to build a logic of nested second order definitions suitable to express templates. We show that under suitable restrictions, the view of templates as macros is semantically correct and that adding them does not extend the descriptive complexity of the base logic, which is in line with results of existing approaches.

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Singular Terms, Truth-Value Gaps, and Free Logic

Cited by 433 publications

References 0 publications

Probability and Nonclassical Logic

Probability and Nonclassical Logic

Lessons from Sobel sequences

Semantics of templates in a compositional framework for building logics

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