Enumeration Complexity of Poor Man’s Propositional Dependence Logic

AbstractA logical approach to Bell’s Inequalities of quantum mechanics has been introduced by Abramsky and Hardy (Abramsky & Hardy, 2012). We point out that the logical Bell’s Inequalities of Abramsky & Hardy (2012) are provable in the probability logic of Fagin, Halpern and Megiddo (Fagin et al., 1990). Since it is now considered empirically established that quantum mechanics violates Bell’s Inequalities, we introduce a modified probability logic, that we call quantum team logic, in which Bell’s Inequalities are not provable, and prove a Completeness theorem for this logic. For this end we generalise the team semantics of dependence logic (Väänänen, 2007) first to probabilistic team semantics, and then to what we call quantum team semantics.

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On Definability in Dependence Logic

Journal of Logic Language and Information ◽

10.1007/s10849-009-9082-0 ◽

2009 ◽

Vol 18 (3) ◽

pp. 317-332 ◽

Cited By ~ 34

Author(s):

Juha Kontinen ◽

Jouko Väänänen

Keyword(s):

Dependence Logic

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Recipient Dependence - Logic and Determinants

10.4324/9781003176091-12 ◽

2021 ◽

pp. 167-175

Author(s):

Christian Catrina

Keyword(s):

Dependence Logic

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Expressivity and Complexity of Dependence Logic

Dependence Logic ◽

10.1007/978-3-319-31803-5_2 ◽

2016 ◽

pp. 5-32 ◽

Cited By ~ 10

Author(s):

Arnaud Durand ◽

Juha Kontinen ◽

Heribert Vollmer

Keyword(s):

Dependence Logic

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Dependence logic with generalized quantifiers: Axiomatizations

Journal of Computer and System Sciences ◽

10.1016/j.jcss.2017.03.010 ◽

2017 ◽

Vol 88 ◽

pp. 90-102 ◽

Cited By ~ 2

Author(s):

Fredrik Engström ◽

Juha Kontinen ◽

Jouko Väänänen

Keyword(s):

Generalized Quantifiers ◽

Dependence Logic

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LOGICS FOR PROPOSITIONAL DETERMINACY AND INDEPENDENCE

The Review of Symbolic Logic ◽

10.1017/s1755020317000272 ◽

2018 ◽

Vol 11 (3) ◽

pp. 470-506 ◽

Cited By ~ 1

Author(s):

VALENTIN GORANKO ◽

ANTTI KUUSISTO

Keyword(s):

Natural Language ◽

Kripke Semantics ◽

Dependence Logic ◽

Team Semantics ◽

Reasoning Tasks ◽

Image Position ◽

The Way

AbstractThis paper investigates formal logics for reasoning about determinacy and independence. Propositional Dependence Logic${\cal D}$and Propositional Independence Logic${\cal I}$are recently developed logical systems, based on team semantics, that provide a framework for such reasoning tasks. We introduce two new logics${{\cal L}_D}$and${{\cal L}_{\,I\,}}$, based on Kripke semantics, and propose them as alternatives for${\cal D}$and${\cal I}$, respectively. We analyse the relative expressive powers of these four logics and discuss the way these systems relate to natural language. We argue that${{\cal L}_D}$and${{\cal L}_{\,I\,}}$naturally resolve a range of interpretational problems that arise in${\cal D}$and${\cal I}$. We also obtain sound and complete axiomatizations for${{\cal L}_D}$and${{\cal L}_{\,I\,}}$.

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Complexity of Two-Variable Dependence Logic and IF-Logic

2011 IEEE 26th Annual Symposium on Logic in Computer Science ◽

10.1109/lics.2011.14 ◽

2011 ◽

Cited By ~ 4

Author(s):

Juha Kontinen ◽

Antti Kuusisto ◽

Peter Lohmann ◽

Jonni Virtema

Keyword(s):

Dependence Logic ◽

If Logic

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DEPENDENCE LOGIC IN PREGEOMETRIES AND ω-STABLE THEORIES

Journal of Symbolic Logic ◽

10.1017/jsl.2015.16 ◽

2016 ◽

Vol 81 (1) ◽

pp. 32-55 ◽

Cited By ~ 6

Author(s):

GIANLUCA PAOLINI ◽

JOUKO VÄÄNÄNEN

Keyword(s):

Model Theory ◽

General Context ◽

Dependence Logic ◽

Database Theory ◽

Special Cases

AbstractWe present a framework for studying the concept of independence in a general context covering database theory, algebra and model theory as special cases. We show that well-known axioms and rules of independence for making inferences concerning basic atomic independence statements are complete with respect to a variety of semantics. Our results show that the uses of independence concepts in as different areas as database theory, algebra, and model theory, can be completely characterized by the same axioms. We also consider concepts related to independence, such as dependence.

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