scholarly journals Safe dependency atoms and possibility operators in team semantics

2020 ◽  
pp. 104593
Author(s):  
Pietro Galliani
Keyword(s):  
Team Semantics

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.

scholarly journals Tractability Frontier of Data Complexity in Team Semantics

2015 ◽  
Vol 193 ◽  
pp. 73-85 ◽  
Author(s):  
Arnaud Durand ◽  
Juha Kontinen ◽  
Nicolas de Rugy-Altherre ◽  
Jouko Väänänen
Keyword(s):  
Data Complexity ◽  
Team Semantics

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 Logics with Multiteam Semantics

2022 ◽  
Vol 23 (2) ◽  
pp. 1-30
Author(s):  
Erich Grädel ◽  
Richard Wilke
Keyword(s):  
Wide Spectrum ◽  
Expressive Power ◽  
Second Order ◽  
Order Logic ◽  
Specific Class ◽  
Mathematical Basis ◽  
Logical Operators ◽  
Team Semantics ◽  
Independence Properties ◽  
Second Order Logic

Team semantics is the mathematical basis of modern logics of dependence and independence. In contrast to classical Tarski semantics, a formula is evaluated not for a single assignment of values to the free variables, but on a set of such assignments, called a team. Team semantics is appropriate for a purely logical understanding of dependency notions, where only the presence or absence of data matters, but being based on sets, it does not take into account multiple occurrences of data values. It is therefore insufficient in scenarios where such multiplicities matter, in particular for reasoning about probabilities and statistical independencies. Therefore, an extension from teams to multiteams (i.e. multisets of assignments) has been proposed by several authors. In this paper we aim at a systematic development of logics of dependence and independence based on multiteam semantics. We study atomic dependency properties of finite multiteams and discuss the appropriate meaning of logical operators to extend the atomic dependencies to full-fledged logics for reasoning about dependence properties in a multiteam setting. We explore properties and expressive power of a wide spectrum of different multiteam logics and compare them to second-order logic and to logics with team semantics. In many cases the results resemble what is known in team semantics, but there are also interesting differences. While in team semantics, the combination of inclusion and exclusion dependencies leads to a logic with the full power of both independence logic and existential second-order logic, independence properties of multiteams are not definable by any combination of properties that are downwards closed or union closed and thus are strictly more powerful than inclusion-exclusion logic. We also study the relationship of logics with multiteam semantics with existential second-order logic for a specific class of metafinite structures. It turns out that inclusion-exclusion logic can be characterised in a precise sense by the Presburger fragment of this logic, but for capturing independence, we need to go beyond it and add some form of multiplication. Finally, we also consider multiteams with weights in the reals and study the expressive power of formulae by means of topological properties.

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.

Separation logic and logics with team semantics

2021 ◽  
pp. 103063
Author(s):  
Darion Haase ◽  
Erich Grädel ◽  
Richard Wilke
Keyword(s):  
Separation Logic ◽  
Team Semantics

scholarly journals SOME OBSERVATIONS ABOUT GENERALIZED QUANTIFIERS IN LOGICS OF IMPERFECT INFORMATION

2019 ◽  
Vol 12 (3) ◽  
pp. 456-486 ◽  
Author(s):  
FAUSTO BARBERO
Keyword(s):  
Imperfect Information ◽  
Proof Theory ◽  
Higher Order ◽  
Generalized Quantifiers ◽  
First Order ◽  
Generalized Quantifier ◽  
Team Semantics ◽  
Special Cases ◽  
Qualitative Component ◽  
Definition Of

AbstractWe analyse the two definitions of generalized quantifiers for logics of dependence and independence that have been proposed by F. Engström, comparing them with a more general, higher order definition of team quantifier. We show that Engström’s definitions (and other quantifiers from the literature) can be identified, by means of appropriate lifts, with special classes of team quantifiers. We point out that the new team quantifiers express a quantitative and a qualitative component, while Engström’s quantifiers only range over the latter. We further argue that Engström’s definitions are just embeddings of the first-order generalized quantifiers into team semantics, and fail to capture an adequate notion of team-theoretical generalized quantifier, save for the special cases in which the quantifiers are applied to flat formulas. We also raise several doubts concerning the meaningfulness of the monotone/nonmonotone distinction in this context. In the appendix we develop some proof theory for Engström’s quantifiers.

Sign in / Sign up

Export Citation Format

Share Document