Independence-Friendly Logic

Mann, Allen L.; Sandu, Gabriel; Sevenster, Merlijn

doi:10.1017/cbo9780511981418

Cited by 68 publications

(24 citation statements)

References 37 publications

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“…We conjecture that by attaching suitable operators to the atoms of L of the type k ∈ N, it should be possible to extend L such that resulting logics accomodate typical logics based on team semantics as fragments in a natural way. The game-theoretic approaches to team semantics developed in [4,8,15,18,21] provide some starting points for related investigations.…”

Section: Discussionmentioning

confidence: 99%

“…In this section we define a game-theoretic semantics for the language L (σ ). The semantics extends the well-known game-theoretic semantics of first-order logic (see, e.g., [18]). The semantic games are played by two players ∃ and ∀.…”

Section: A Semantics For L (σ )mentioning

confidence: 97%

“…Let f be an assignment function that interprets the free variables of ϕ in the domain A of A. The semantic game G(A, f , ϕ) is played between the two players ∃ and ∀ in the usual way (see, e.g., [11,18]). If the verifying player ∃ has a winning strategy in the game G(A, f , ϕ), we write A, f |= + ϕ and say that ϕ is true in (A, f ).…”

Section: Introductionmentioning

confidence: 99%

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Some Turing-Complete Extensions of First-Order Logic

Kuusisto¹

2014

Electron. Proc. Theor. Comput. Sci.

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We introduce a natural Turing-complete extension of first-order logic FO. The extension adds two novel features to FO. The first one of these is the capacity to add new points to models and new tuples to relations. The second one is the possibility of recursive looping when a formula is evaluated using a semantic game. We first define a game-theoretic semantics for the logic and then prove that the expressive power of the logic corresponds in a canonical way to the recognition capacity of Turing machines. Finally, we show how to incorporate generalized quantifiers into the logic and argue for a highly natural connection between oracles and generalized quantifiers.

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Section: Discussionmentioning

confidence: 99%

Section: A Semantics For L (σ )mentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Some Turing-Complete Extensions of First-Order Logic

Kuusisto¹

2014

Electron. Proc. Theor. Comput. Sci.

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“…Team Semantics [19,29] generalizes Tarski's Semantics for First Order Logic by letting formulas be satisfied or not satisfied by sets of assignments (called teams) rather than just by single assignments. This semantics was originally developed by Hodges in [19] in order to provide a compositional semantics for Independence-Friendly Logic [17,27], an extension of First Order Logic that generalizes its game-theoretic semantics by allowing agents to have imperfect information regarding the current game position; 1 but, as observed by Väänänen [29], as a logical framework it deserves study in its own right.…”

Section: Introductionmentioning

confidence: 99%

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

Galliani

2019

Electron. Proc. Theor. Comput. Sci.

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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.

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“…It was originally developed by Hodges, in [14], as a compositional alternative to the imperfect-information game theoretic semantics for independence friendly logic [13,18].…”

Section: Introductionmentioning

confidence: 99%

Upwards closed dependencies in team semantics

Galliani

2015

Information and Computation

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We prove that adding upwards closed first-order dependency atoms to first-order logic with team semantics does not increase its expressive power (with respect to sentences), and that the same remains true if we also add constancy atoms. As a consequence, the negations of functional dependence, conditional independence, inclusion and exclusion atoms can all be added to first-order logic without increasing its expressive power.Furthermore, we define a class of bounded upwards closed dependencies and we prove that unbounded dependencies cannot be defined in terms of bounded ones.

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Independence-Friendly Logic

Cited by 68 publications

References 37 publications

Some Turing-Complete Extensions of First-Order Logic

Some Turing-Complete Extensions of First-Order Logic

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

Upwards closed dependencies in team semantics

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