Probabilistic Team Semantics

Durand, Arnaud; Hannula, Miika; Kontinen, Juha; Meier, Arne; Virtema, Jonni

doi:10.1007/978-3-319-90050-6_11

Cited by 34 publications

(68 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In conclusion, from the assumption that {m} ⊥ {m} does not follow from Σ according to the rules we were able to find a relational diversity rank-function that satisfies Σ but not {m} ⊥ {m}. Thus (2) implies (3), and this concludes the proof. Now we can generalize the completeness result to arbirary independence statements:…”

Section: From Diversity To Independencementioning

confidence: 51%

“…Trivially (1) implies (2) and (3) implies (1). So we prove only that (2) implies (3). Suppose x ⊥ y follows semantically from Σ but does not follow by the above rules.…”

Section: From Diversity To Independencementioning

confidence: 82%

“…Suppose X is a nonempty, finite set of variable assignments s from a finite set V of variables to a set A of elements (in the language of Dependence and Independence Logic, such a X is said to be a team over A with domain V ). 3 Given some…”

Section: Examplesmentioning

confidence: 99%

“…Independence Logic [5], likewise, extends First Order Logic by an atom x ⊥ y that states that the tuples of quantified variables x and y are chosen independently, in the sense that every possible choice of x and of y may occur together. These logics -and the generalization of Tarski's Semantics used for their analysis, commonly called Team Semantics -have lead in the last decade to a considerable amount of research regarding logics augmented by various notions of dependence and independence, in the first order case but also in the propositional case [16], in the modal case [13,7], in the temporal case [9], and recently even in probabilistic cases [8,3,6].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Diversity, Dependence and Independence

Galliani

Väänánen

2020

Lecture Notes in Computer Science

View full text Add to dashboard Cite

We introduce the concepts of dependence and independence in a very general framework. We use a concept of rank to study dependence and independence. By means of the rank we identify (total) dependence with inability to create more diversity, and (total) independence with the presence of maximum diversity. We show that our theory of dependence and independence covers a variety of dependence concepts, for example the seemingly unrelated concepts of linear dependence in algebra and dependence of variables in logic.

show abstract

Section: From Diversity To Independencementioning

confidence: 51%

“…Trivially (1) implies (2) and (3) implies (1). So we prove only that (2) implies (3). Suppose x ⊥ y follows semantically from Σ but does not follow by the above rules.…”

Section: From Diversity To Independencementioning

confidence: 82%

Section: Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Diversity, Dependence and Independence

Galliani

Väänánen

2020

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…It is also of more direct practical interest, because of the connections between Team Semantics and Database Theory (see for instance [16,24]). Probabilistic variants of Team Semantics have recently gathered attention (see for instance [3,4,15]).…”

Section: Introductionmentioning

confidence: 99%

Characterizing Strongly First Order Dependencies: The Non-Jumping Relativizable Case

Galliani

2019

Electron. Proc. Theor. Comput. Sci.

View full text Add to dashboard Cite

Team Semantics generalizes Tarski's Semantics for First Order Logic by allowing formulas to be satisfied or not satisfied by sets of assignments rather than by single assignments. Because of this, in Team Semantics it is possible to extend the language of First Order Logic via new types of atomic formulas that express dependencies between different assignments.Some of these extensions are much more expressive than First Order Logic proper; but the problem of which atoms can instead be added to First Order Logic without increasing its expressive power is still unsolved.In this work, I provide an answer to this question under the additional assumptions (true of most atoms studied so far) that the dependency atoms are relativizable and non-jumping. Furthermore, I show that the global (or Boolean) disjunction connective can be added to any strongly first order family of dependencies without increasing the expressive power, but that the same is not true in general for non strongly first order dependencies.

show abstract

Facets of Distribution Identities in Probabilistic Team Semantics

Hannula

Hirvonen

Kontinen

et al. 2019

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

We study probabilistic team semantics which is a semantical framework allowing the study of logical and probabilistic dependencies simultaneously. We examine and classify the expressive power of logical formalisms arising by different probabilistic atoms such as conditional independence and different variants of marginal distribution equivalences. We also relate the framework to the first-order theory of the reals and apply our methods to the open question on the complexity of the implication problem of conditional independence.

show abstract

Probabilistic Team Semantics

Cited by 34 publications

References 21 publications

Diversity, Dependence and Independence

Diversity, Dependence and Independence

Characterizing Strongly First Order Dependencies: The Non-Jumping Relativizable Case

Facets of Distribution Identities in Probabilistic Team Semantics

Contact Info

Product

Resources

About