Quantifiers for reasoning with imperfect information and Σ¹₁-logic

Caicedo, Xavier; Krynicki, Michał

doi:10.1090/conm/235/03463

Cited by 17 publications

(46 citation statements)

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“…The last two are given in this article (for the first one, cf. [3]); the prenex normal form uses ideas from [1]. The question of which of the containments are strict remains open.…”

Section: Discussionmentioning

confidence: 99%

“…Normal forms in the context of SL were initially investigated in [1]. Later, Janssen [7] observed some anomalies which cast doubt on the correctness of these results.…”

Section: Normal Forms For Sl(↓)mentioning

confidence: 99%

“…Later, Janssen [7] observed some anomalies which cast doubt on the correctness of these results. However, it was shown in [3] that only the formal apparatus employed in [1] was defective, and not the results per se.…”

Section: Normal Forms For Sl(↓)mentioning

confidence: 99%

“…In this section we revisit the prenex normal form results of [1] and extend them to account for ↓ and ↑. For this, bound variables will be tacitly renamed when necessary 4 and the following formula manipulation tools will be employed.…”

Section: Normal Forms For Sl(↓)mentioning

confidence: 99%

“…Formula (7) in the above proof was taken from [1], with the proviso that independences on y 1 and y 2 are added to ψ 1 and ψ 2 in order to avoid unwanted signaling [7,8,3]. This was most probably an involuntary omission in [1].…”

Section: Normal Forms For Sl(↓)mentioning

confidence: 99%

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On the Expressive Power of IF-Logic with Classical Negation

Figueira

Gorín

Grimson

2011

Logic, Language, Information and Computation

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Abstract. It is well-known that Independence Friendly (IF) logic is equivalent to existential second-order logic (Σ 1 1 ) and, therefore, is not closed under classical negation. The boolean closure of IF sentences, called Extended IF-logic, on the other hand, corresponds to a proper fragment of ∆ 1 2 . In this paper we consider IF-logic extended with Hodges' flattening operator, which allows classical negation to occur also under the scope of IF quantifiers. We show that, nevertheless, the expressive power of this logic does not go beyond ∆ 1 2 . As part of the proof, we give a prenex normal form result and introduce a non-trivial syntactic fragment of full second-order logic that we show to be contained in ∆ 1 2 .

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“…The last two are given in this article (for the first one, cf. [3]); the prenex normal form uses ideas from [1]. The question of which of the containments are strict remains open.…”

Section: Discussionmentioning

confidence: 99%

“…Normal forms in the context of SL were initially investigated in [1]. Later, Janssen [7] observed some anomalies which cast doubt on the correctness of these results.…”

Section: Normal Forms For Sl(↓)mentioning

confidence: 99%

Section: Normal Forms For Sl(↓)mentioning

confidence: 99%

Section: Normal Forms For Sl(↓)mentioning

confidence: 99%

Section: Normal Forms For Sl(↓)mentioning

confidence: 99%

See 3 more Smart Citations

On the Expressive Power of IF-Logic with Classical Negation

Figueira

Gorín

Grimson

2011

Logic, Language, Information and Computation

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On the Formal Semantics of IF-Like Logics

Figueira

Gorín

Grimson

2008

Logic, Language, Information and Computation

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In classical logics, the meaning of a formula is invariant with respect to the renaming of bound variables. This property, normally taken for granted, has been shown not to hold in the case of Independence Friendly (IF) logics. In this paper we argue that this is not an inherent characteristic of these logics but a defect in the way in which the compositional semantics given by Hodges for the regular fragment was generalized to arbitrary formulas. We fix this by proposing an alternative formalization, based on a variation of the classical notion of valuation. Basic metatheoretical results are proven. We present these results for Hodges' slash logic (from which these can be easily transferred to other IF-like logics) and we also consider the flattening operator, for which we give novel game-theoretical semantics.

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Independence-Friendly Logic Without Henkin Quantification

Barbero

Hella

Rönnholm

2017

Logic, Language, Information, and Computation

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We analyze from a global point of view the expressive resources of IF logic that do not stem from Henkin (partially-ordered) quantification. When one restricts attention to regular IF sentences, this amounts to the study of the fragment of IF logic which is individuated by the game-theoretical property of Action Recall. We prove that the fragment of Action Recall can express all existential second-order (ESO) properties. This can be accomplished already by the prenex fragment of Action Recall, whose only second-order source of expressiveness are the so-called signalling patterns. The proof shows that a complete set of Henkin prefixes is explicitly definable in the fragment of Action Recall. In the more general case, in which also irregular IF sentences are allowed, we show that full ESO expressive power can be achieved using neither Henkin nor signalling patterns.

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Quantifiers for reasoning with imperfect information and Σ¹₁-logic

Cited by 17 publications

References 0 publications

On the Expressive Power of IF-Logic with Classical Negation

On the Expressive Power of IF-Logic with Classical Negation

On the Formal Semantics of IF-Like Logics

Independence-Friendly Logic Without Henkin Quantification

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