Tractability frontiers in probabilistic team semantics and existential second-order logic over the reals

Hannula, Miika; Virtema, Jonni

doi:10.1016/j.apal.2022.103108

Cited by 6 publications

(3 citation statements)

References 34 publications

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“…Due to the use of identities, constrained polynomials are terms over the expansion of (K, +, ⋅, 0, 1) by suitable χ-functions giving access to identity between terms. Our approach can be used to reduce satisfaction in K-team semantics to the existential first-order theory of K. Similar reductions have been utilised in the case of Boolean and probabilistic team semantics to analyse the complexity of model checking and satisfiability (Hannula et al 2019;Hannula and Virtema 2022;Durand, Kontinen, and Väänänen 2022) Let A be a finite model with universe A. Let V be a finite set of variables and ⃗ a ∈ A V .…”

Section: Algebraic K-team Semanticsmentioning

confidence: 99%

Unified Foundations of Team Semantics via Semirings

Barlag

Hannula

Kontinen

et al. 2023

Proceedings of the Twentieth International Conference on Principles of Knowledge Representation and Reasoning

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Semiring semantics for first-order logic provides a way to trace how facts represented by a model are used to deduce satisfaction of a formula. Team semantics is a framework for studying logics of dependence and independence in diverse contexts such as databases, quantum mechanics, and statistics by extending first-order logic with atoms that describe dependencies between variables. Combining these two, we propose a unifying approach for analysing the concepts of dependence and independence via a novel semiring team semantics, which subsumes all the previously considered variants for first-order team semantics. In particular, we study the preservation of satisfaction of dependencies and formulae between different semirings. In addition we create links to reasoning tasks such as provenance, counting, and repairs.

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Section: Algebraic K-team Semanticsmentioning

confidence: 99%

Unified Foundations of Team Semantics via Semirings

Barlag

Hannula

Kontinen

et al. 2023

Proceedings of the Twentieth International Conference on Principles of Knowledge Representation and Reasoning

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“…), we leave it as an open issue whether the specific atom Pr(β | α ∧ γ) = Pr(β | γ) needed here is expressible, and whether the conditional independence atoms are. The results in [16] point towards inexpressibility of these atoms, but the methods that are used in that paper rely on quantifiers.…”

Section: While Conditional Comparison Atoms Of the General Formmentioning

confidence: 99%

Team Semantics for Interventionist Counterfactuals: Observations vs. Interventions

Barbero

Sandu

2020

J Philos Logic

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Team semantics is a highly general framework for logics which describe dependencies and independencies among variables. Typically, the (in)dependencies considered in this context are properties of sets of configurations or data records. We show how team semantics can be further generalized to support languages for the discussion of interventionist counterfactuals and causal dependencies, such as those that arise in manipulationist theories of causation (Pearl, Hitchcock, Woodward, among others). We show that the “causal teams” we introduce in the present paper can be used for modelling some classical counterfactual scenarios which are not captured by the usual causal models. We then analyse the basic properties of our counterfactual languages and discuss extensively the differences with respect to the Lewisian tradition.

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“…This paper is an extended version of [27]. Here we include all the proofs that were previously omitted.…”

Section: Introductionmentioning

confidence: 99%