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A Double Team Semantics for Generalized Quantifiers

We investigate extensions of dependence logic with generalized quantifiers. We also introduce and investigate the notion of a generalized atom. We define a system of semantics that can accommodate variants of dependence logic, possibly extended with generalized quantifiers and generalized atoms, und...

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Detalles Bibliográficos
Autor principal: Kuusisto, Antti
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Netherlands 2015
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4587362/
https://www.ncbi.nlm.nih.gov/pubmed/26435580
http://dx.doi.org/10.1007/s10849-015-9217-4
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author Kuusisto, Antti
author_facet Kuusisto, Antti
author_sort Kuusisto, Antti
collection PubMed
description We investigate extensions of dependence logic with generalized quantifiers. We also introduce and investigate the notion of a generalized atom. We define a system of semantics that can accommodate variants of dependence logic, possibly extended with generalized quantifiers and generalized atoms, under the same umbrella framework. The semantics is based on pairs of teams, or double teams. We also devise a game-theoretic semantics equivalent to the double team semantics. We make use of the double team semantics by defining a logic [Formula: see text] which canonically fuses together two-variable dependence logic[Formula: see text] and two-variable logic with counting quantifiers[Formula: see text] . We establish that the satisfiability and finite satisfiability problems of [Formula: see text] are complete for [Formula: see text] .
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spelling pubmed-45873622015-10-02 A Double Team Semantics for Generalized Quantifiers Kuusisto, Antti J Logic Lang Inf Article We investigate extensions of dependence logic with generalized quantifiers. We also introduce and investigate the notion of a generalized atom. We define a system of semantics that can accommodate variants of dependence logic, possibly extended with generalized quantifiers and generalized atoms, under the same umbrella framework. The semantics is based on pairs of teams, or double teams. We also devise a game-theoretic semantics equivalent to the double team semantics. We make use of the double team semantics by defining a logic [Formula: see text] which canonically fuses together two-variable dependence logic[Formula: see text] and two-variable logic with counting quantifiers[Formula: see text] . We establish that the satisfiability and finite satisfiability problems of [Formula: see text] are complete for [Formula: see text] . Springer Netherlands 2015-04-28 2015 /pmc/articles/PMC4587362/ /pubmed/26435580 http://dx.doi.org/10.1007/s10849-015-9217-4 Text en © The Author(s) 2015 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Kuusisto, Antti
A Double Team Semantics for Generalized Quantifiers
title A Double Team Semantics for Generalized Quantifiers
title_full A Double Team Semantics for Generalized Quantifiers
title_fullStr A Double Team Semantics for Generalized Quantifiers
title_full_unstemmed A Double Team Semantics for Generalized Quantifiers
title_short A Double Team Semantics for Generalized Quantifiers
title_sort double team semantics for generalized quantifiers
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4587362/
https://www.ncbi.nlm.nih.gov/pubmed/26435580
http://dx.doi.org/10.1007/s10849-015-9217-4
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