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Abramsky, Samson; Väänánen, Jouko

doi:10.1007/s11229-008-9415-6

Cited by 74 publications

(124 citation statements)

References 25 publications

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“…In the past decade, both areas of research have grown rapidly. 1 With the exception of Punčochář's work [20,23], discussed in Section 5, the research has focused on enriching existing systems of classical logic (propositional, modal, or first-order) with questions and dependence formulas. However, there is no a priori reason why investigating the logic of questions and dependency would require a commitment to an underlying classical logic of statements.…”

Section: Introductionmentioning

confidence: 99%

Questions and Dependency in Intuitionistic Logic

Ciardelli¹,

Iemhoff²,

Yang³

2020

Notre Dame J. Formal Logic

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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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Section: Introductionmentioning

confidence: 99%

Questions and Dependency in Intuitionistic Logic

Ciardelli¹,

Iemhoff²,

Yang³

2020

Notre Dame J. Formal Logic

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“…This yields a decomposition of these atoms into more basic and better-behaved operationswhich allows for a natural proof-theory. While the possibility of such a decomposition was noted by Abramsky and Väänänen (2009), the present work casts new light on this connection in several ways. First, we can now see that this decomposition reflects a fundamental connection between dependencies and questions: a dependency is a case of entailment having questions as its protagonists; since entailments can be internalized as implications, dependencies can be expressed as implications between questions.…”

Section: Dependence Logicmentioning

confidence: 63%

Questions as information types

Ciardelli

2016

Synthese

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This paper argues that questions have an important role to to play in logic, both semantically and proof-theoretically. Semantically, we show that by generalizing the classical notion of entailment to questions, we can capture not only the standard relation of logical consequence, which holds between pieces of information, but also the relation of logical dependency, which holds between information types. Prooftheoretically, we show that questions may be used in inferences as placeholders for arbitrary information of a given type; by manipulating such placeholders, we may construct formal proofs of dependencies. Finally, we show that such proofs have a specific kind of constructive content: they do not just witness the existence of a certain dependency, but actually encode a method for transforming information of the types described by the assumptions into information of the type described by the conclusion.

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“…. ., S T x (α k ), S T x (β)) and the intuitionistic disjunction ∨ can both be defined in first-order dependence logic in terms of the other atoms and connectives 1…”

Section: Proofmentioning

confidence: 99%

Modal dependence logics: axiomatizations and model-theoretic properties

Yang

2017

Logic Journal of the IGPL

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Modal dependence logics are modal logics defined on the basis of team semantics and have the downward closure property. In this paper, we introduce sound and complete deduction systems for the major modal dependence logics, especially those with intuitionistic connectives in their languages. We also establish a concrete connection between team semantics and single-world semantics, and show that modal dependence logics can be interpreted as variants of intuitionistic modal logics.2010 Mathematics Subject Classification: 03B45, 03B60, 03B55 Keywords: dependence logic, team semantics, modal logic, intuitionistic modal logic, intermediate logics Dependence logic is a logical formalism, introduced by Väänänen [28], that captures the notion of dependence in social and natural sciences. The modal version of the logic is called modal dependence logic and was introduced in [29]. Modal dependence logic extends the usual modal logic by adding a new type of atomic formulas =(p 1 , . . . , p 1 , q), called dependence atoms, to express dependencies between propositions, and by lifting the usual single-world semantics to the so-called team semantics, introduced by Hodges [13,14]. Formulas of modal dependence logic are evaluated on sets of possible worlds of Kripke models, called teams. Intuitively, a dependence atom =(p 1 , . . . , p 1 , q) is true if within a team the truth value of the proposition q is functionally determined by the truth values of the propositions p 1 , . . ., p n .Research on modal dependence logic and its variants has been active in recent years. Basic model-theoretic properties of the logics were studied in e.g., [26], a van Benthem Theorem for the logics was proved in [16], and the frame definability of the logics was studied in [24,25]. The expressive power and the relevant computation complexity problems of the logics were investigated extensively in e.g., [7,8,9,12,19,20,26]. In this paper, we study two problems that received less attention in the literature, namely the axiomatization problem and the comparison between team semantics and the single-world semantics.

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From IF to BI

Cited by 74 publications

References 25 publications

Questions and Dependency in Intuitionistic Logic

Questions and Dependency in Intuitionistic Logic

Questions as information types

Modal dependence logics: axiomatizations and model-theoretic properties

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