Game-Theoretical Semantics

Hintikka, Jaakko; Sandu, Gabriel

doi:10.1016/b978-0-444-53726-3.00008-6

Cited by 101 publications

(47 citation statements)

References 28 publications

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“…The (in)dependence-friendly logics of Hintikka (1973), Sandu (1993), Hintikka & Sandu (1996), Hodges (1997), andVäänänen (2007) seem particularly well-suited to express this kind of 'selective' covariation (a.k.a. imperfect information).…”

Section: Quantificational Dependencies Intra-sententially: Exceptionamentioning

confidence: 99%

The grammar of quantification and the fine structure of interpretation contexts

Brașoveanu

2012

Synthese

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Providing a compositional interpretation procedure for discourses in which descriptions of complex dependencies between interrelated objects are incrementally built is a key challenge for formal theories of natural language interpretation. This paper examines several quantificational phenomena and argues that we need richly structured contexts of interpretation that are passed on between different parts of the same sentence and also across sentential boundaries to account for these phenomena. The main contribution of the paper is showing how we can add structure to contexts in an incremental way, starting with the basic notion of context in classical first-order logic, i.e., interpretation contexts formalized as single total variable assignments.

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Section: Quantificational Dependencies Intra-sententially: Exceptionamentioning

confidence: 99%

The grammar of quantification and the fine structure of interpretation contexts

Brașoveanu

2012

Synthese

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“…[13] or [15]). In this extension of predicate logic it can be indicated that a quantifier is independent of some of the quantifiers with larger scope.…”

Section: The Representations Of the De Dicto -De Re Readingsmentioning

confidence: 99%

“…IF has been presented (e.g. in [13] and [15]) with a semantics that is not compositional. For instance, the interpretation of the sentence ∃x /z φ is not obtained from the interpretation of φ, but from the interpretation of φ[ c / x ], where constant c is found by application of a certain game strategy.…”

Section: The Principle Of Compositionalitymentioning

confidence: 99%

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Compositional Natural Language Semantics using Independence Friendly Logic or Dependence Logic

Janssen

2013

Stud Logica

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“…Since the expressive power of IF corresponds to that of existential secondorder logic (Σ 1 1 ) [4,5] and Σ 1 1 is not closed by (classical) negation, it is clear that classical negation cannot be defined in IF.…”

Section: Introductionmentioning

confidence: 99%

On the Expressive Power of IF-Logic with Classical Negation

Figueira

Gorín

Grimson

2011

Logic, Language, Information and Computation

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Abstract. It is well-known that Independence Friendly (IF) logic is equivalent to existential second-order logic (Σ 1 1 ) and, therefore, is not closed under classical negation. The boolean closure of IF sentences, called Extended IF-logic, on the other hand, corresponds to a proper fragment of ∆ 1 2 . In this paper we consider IF-logic extended with Hodges' flattening operator, which allows classical negation to occur also under the scope of IF quantifiers. We show that, nevertheless, the expressive power of this logic does not go beyond ∆ 1 2 . As part of the proof, we give a prenex normal form result and introduce a non-trivial syntactic fragment of full second-order logic that we show to be contained in ∆ 1 2 .

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Game-Theoretical Semantics

Cited by 101 publications

References 28 publications

The grammar of quantification and the fine structure of interpretation contexts

The grammar of quantification and the fine structure of interpretation contexts

Compositional Natural Language Semantics using Independence Friendly Logic or Dependence Logic

On the Expressive Power of IF-Logic with Classical Negation

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