A Double Team Semantics for Generalized Quantifiers

Kuusisto, Antti

doi:10.1007/s10849-015-9217-4

Cited by 37 publications

(58 citation statements)

References 20 publications

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“…Exceptions to this are given for instance by the study of logics which add to Team Semantics generalised quantifiers[1,4], or a contradictory negation[23] 3. This is a special case of the more general -and not necessarily first order -notion of dependency used in[7], which comes from[19].…”

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confidence: 99%

Safe Dependency Atoms and Possibility Operators in Team Semantics

Galliani

2018

Electron. Proc. Theor. Comput. Sci.

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I consider the question of which dependencies are safe for a Team Semantics-based logic FO(D), in the sense that they do not increase its expressive power over sentences when added to it. I show that some dependencies, like totality, non-constancy and non-emptiness, are safe for all logics FO(D), and that other dependencies, like constancy, are not safe for FO(D) for some choices of D despite being strongly first order (that is, safe for FO( / 0)). I furthermore show that the possibility operator ⋄φ , which holds in a team if and only if φ holds in some nonempty subteam, can be added to any logic FO(D) without increasing its expressive power over sentences.

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confidence: 99%

Safe Dependency Atoms and Possibility Operators in Team Semantics

Galliani

2018

Electron. Proc. Theor. Comput. Sci.

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“…The agenda and main idea of the current paper, i.e., investigating dependence logic with a Kripke-style semantics instead of team semantics, has been first mentioned and briefly motivated in [Kuu14] and its later incarnations such as, e.g., [Kuu15]. Similar ideas have subsequently been developed in [Cia16b].…”

Section: The Content and Contributions Of This Papermentioning

confidence: 99%

“…We next combine disjunctions and determinacy statements and show that this leads to problematic interpretations from the point of view of natural language (cf. [Kuu14]).…”

Section: Natural Language and Logics Of Determinacy And Independencementioning

confidence: 99%

Logics for Propositional Determinacy and Independence

Goranko

Kuusisto

2018

The Review of Symbolic Logic

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This paper investigates formal logics for reasoning about determinacy and independence. Propositional Dependence Logic D and Propositional Independence Logic I are recently developed logical systems, based on team semantics, that provide a framework for such reasoning tasks. We introduce two new logics L D and L I , based on Kripke semantics, and propose them as alternatives for D and I, respectively. We analyse the relative expressive powers of these four logics and discuss the way these systems relate to natural language. We argue that L D and L I naturally resolve a range of interpretational problems that arise in D and I. We also obtain sound and complete axiomatizations for L D and L I . * Visiting professorship 1 Also available as a reprint in [SvE88].

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“…But what is a dependency condition, in a general sense? The following definition is based on the generalized atoms of [17]: …”

Section: Upwards Closed Dependenciesmentioning

confidence: 99%

Upwards closed dependencies in team semantics

Galliani

2015

Information and Computation

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We prove that adding upwards closed first-order dependency atoms to first-order logic with team semantics does not increase its expressive power (with respect to sentences), and that the same remains true if we also add constancy atoms. As a consequence, the negations of functional dependence, conditional independence, inclusion and exclusion atoms can all be added to first-order logic without increasing its expressive power.Furthermore, we define a class of bounded upwards closed dependencies and we prove that unbounded dependencies cannot be defined in terms of bounded ones.

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A Double Team Semantics for Generalized Quantifiers

Cited by 37 publications

References 20 publications

Safe Dependency Atoms and Possibility Operators in Team Semantics

Safe Dependency Atoms and Possibility Operators in Team Semantics

Logics for Propositional Determinacy and Independence

Upwards closed dependencies in team semantics

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