Propositional team logics

In recent years, the logic of questions and dependencies has been investigated in the closely related frameworks of inquisitive logic and dependence logic. These investigations have assumed classical logic as the background logic of statements, and added formulas expressing questions and dependencies to this classical core. In this paper, we broaden the scope of these investigations by studying questions and dependency in the context of intuitionistic logic. We propose an intuitionistic team semantics, where teams are embedded within intuitionistic Kripke models. The associated logic is a conservative extension of intuitionistic logic with questions and dependence formulas. We establish a number of results about this logic, including a normal form result, a completeness result, and translations to classical inquisitive logic and modal dependence logic.

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“…Notes 1. For dependence logic see, e.g., [26,27,18,16,17,14,28,31,32]; for inquisitive logic see, e.g., [12,13,5,7,8,9,22,15].…”

Section: Conclusion and Further Workmentioning

confidence: 99%

Questions and Dependency in Intuitionistic Logic

Ciardelli¹,

Iemhoff²,

Yang³

2020

Notre Dame J. Formal Logic

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“…. , p n , then they satisfy the same formulas over these variables (see also Yang and Väänänen [32]).…”

Section: Axioms Of Splittingmentioning

confidence: 84%

“…We extend QPL to quantified propositional team logic QPTL [11,12] and PL to propositional team logic PTL [32] as follows. For clarity, in the following we reserve the letters α, β, γ, .…”

Section: Propositional Team Logicmentioning

confidence: 99%

Axiomatizations of team logics

Lück

2018

Annals of Pure and Applied Logic

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In a modular approach, we lift Hilbert-style proof systems for propositional, modal and first-order logic to generalized systems for their respective team-based extensions. We obtain sound and complete axiomatizations for the dependence-free fragment FO(∼) of Väänänen's firstorder team logic TL, for propositional team logic PTL, quantified propositional team logic QPTL, modal team logic MTL, and for the corresponding logics of dependence, independence, inclusion and exclusion.As a crucial step in the completeness proof, we show that the above logics admit, in a particular sense, a semantics-preserving elimination of modalities and quantifiers from formulas.

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“…It has subsequently been used to extend first-order logic with database dependencies (e.g. Dependence logic [40], Independence logic [14], Inclusion logic [12]), and similar extensions have been proposed for propositional logics [47,48] and modal logics [41]. Generalizations of teams have been used as descriptive languages for probabilistic dependencies [10], for the expression of quantum phenomena [25], and for the modelisation of Bayesian networks [9].…”

Section: From Teams To Causal Teamsmentioning

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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Propositional team logics

Cited by 40 publications

References 32 publications

Questions and Dependency in Intuitionistic Logic

Questions and Dependency in Intuitionistic Logic

Axiomatizations of team logics

Team Semantics for Interventionist Counterfactuals: Observations vs. Interventions

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