Recipient Dependence - Logic and Determinants

2021 ◽  
pp. 167-175
Author(s):  
Christian Catrina
Keyword(s):  
Dependence Logic

scholarly journals QUANTUM TEAM LOGIC AND BELL’S INEQUALITIES

2015 ◽  
Vol 8 (4) ◽  
pp. 722-742 ◽  
Author(s):  
TAPANI HYTTINEN ◽  
GIANLUCA PAOLINI ◽  
JOUKO VÄÄNÄNEN
Keyword(s):  
Quantum Mechanics ◽  
Completeness Theorem ◽  
Probability Logic ◽  
Bell’S Inequalities ◽  
Dependence Logic ◽  
Logical Approach ◽  
Team Semantics ◽  
Bell's Inequalities

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.

On Definability in Dependence Logic

2009 ◽  
Vol 18 (3) ◽  
pp. 317-332 ◽  
Author(s):  
Juha Kontinen ◽  
Jouko Väänänen
Keyword(s):  
Dependence Logic

Expressivity and Complexity of Dependence Logic

2016 ◽  
pp. 5-32 ◽  
Author(s):  
Arnaud Durand ◽  
Juha Kontinen ◽  
Heribert Vollmer
Keyword(s):  
Dependence Logic

scholarly journals Dependence logic with generalized quantifiers: Axiomatizations

2017 ◽  
Vol 88 ◽  
pp. 90-102 ◽  
Author(s):  
Fredrik Engström ◽  
Juha Kontinen ◽  
Jouko Väänänen
Keyword(s):  
Generalized Quantifiers ◽  
Dependence Logic

scholarly journals LOGICS FOR PROPOSITIONAL DETERMINACY AND INDEPENDENCE

2018 ◽  
Vol 11 (3) ◽  
pp. 470-506 ◽  
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${{\cal L}_{\,I\,}}$.

scholarly journals Complexity of Two-Variable Dependence Logic and IF-Logic

2011 ◽  
Author(s):  
Juha Kontinen ◽  
Antti Kuusisto ◽  
Peter Lohmann ◽  
Jonni Virtema
Keyword(s):  
Dependence Logic ◽  
If Logic

scholarly journals DEPENDENCE LOGIC IN PREGEOMETRIES AND ω-STABLE THEORIES

2016 ◽  
Vol 81 (1) ◽  
pp. 32-55 ◽  
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.

scholarly journals Boolean dependence logic and partially-ordered connectives

2017 ◽  
Vol 88 ◽  
pp. 103-125 ◽  
Author(s):  
Johannes Ebbing ◽  
Lauri Hella ◽  
Peter Lohmann ◽  
Jonni Virtema
Keyword(s):  
Dependence Logic ◽  
Partially Ordered

scholarly journals Polyteam semantics

2020 ◽  
Vol 30 (8) ◽  
pp. 1541-1566
Author(s):  
Miika Hannula ◽  
Juha Kontinen ◽  
Jonni Virtema
Keyword(s):  
Analogous Result ◽  
Expressive Power ◽  
Order Logic ◽  
Mathematical Framework ◽  
Dependency Theory ◽  
Dependence Logic ◽  
First Order ◽  
Team Semantics ◽  
Implication Problem ◽  
Second Order Logic

Abstract Team semantics is the mathematical framework of modern logics of dependence and independence in which formulae are interpreted by sets of assignments (teams) instead of single assignments as in first-order logic. In order to deepen the fruitful interplay between team semantics and database dependency theory, we define Polyteam Semantics in which formulae are evaluated over a family of teams. We begin by defining a novel polyteam variant of dependence atoms and give a finite axiomatization for the associated implication problem. We relate polyteam semantics to team semantics and investigate in which cases logics over the former can be simulated by logics over the latter. We also characterize the expressive power of poly-dependence logic by properties of polyteams that are downwards closed and definable in existential second-order logic ($\textsf{ESO}$). The analogous result is shown to hold for poly-independence logic and all $\textsf{ESO}$-definable properties. We also relate poly-inclusion logic to greatest fixed point logic.

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