On Existential Declarations of Independence in if Logic

Barbero, Fausto

doi:10.1017/s175502031200038x

Cited by 10 publications

(9 citation statements)

References 16 publications

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“…In particular, in the literature ( [13], [16], [15] sect. 6.4, [1]) there has been some interest in properties that limit the ability of players to forget. Considering for example the role of Eloise:…”

Section: Preliminariesmentioning

confidence: 99%

“…Under the assumption of regularity, each of these properties has been given a syntactical characterization in the literature (see e.g., [15], [1]). For action recall the characterization is as follows: Assume that ϕ is a regular IF sentence.…”

Section: Preliminariesmentioning

confidence: 99%

“…In IF logic, the same is achieved by means of a linear prefix, together with a slashing device. For example, the Henkin quantifier H 1 2 is expressed in IF logic by the sequence of quantifiers ∀x 1 1 ∃y 1 ∀x 1 2 (∃y 2 /{x 1 1 , y 1 }). The slashed quantifier (∃y 2 /{x 1 1 , y 1 }) expresses the fact that y 2 is independent from x 1 1 and y 1 .…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Independence-Friendly Logic Without Henkin Quantification

Barbero

Hella

Rönnholm

2017

Logic, Language, Information, and Computation

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“…The common underlying idea will be that of requiring, for truth, not only the existence of a winning strategy for the Verifiers; rather, the existence will be required of a winning strategy which is, in some sense, really playable when the players are forbidden to cooperate, or limited therein. A more general guiding principle for devising and testing these kinds of semantics could be given by the notion of relevance that was introduced in Barbero (2013). Call an occurrence of a variable x in the slash set Y of (∃y/Y ) a declaration of independence of y from x; given an IF quantifier prefix Q which contains exactly one declaration of independence of y from x, call Q y←x the quantifier prefix which differs from Q in that (∃y/Y ) is replaced by (∃y/(Y \ {x})).…”

Section: Standard Versus Epistemic Semanticsmentioning

confidence: 99%

“…The seemingly counterintuitive truth value assigned by GTS comes from the assumption (implicit in the usual modelization of game theory) that players can coordinate their strategies, and so for example decide a priori that they will both choose a fixed element a. In Barbero (2013), the author considered more examples of these kinds of discrepancies and attempted a classification of them.…”

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confidence: 99%

Cooperation in Games and Epistemic Readings of Independence-Friendly Sentences

Barbero

2017

J of Log Lang and Inf

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In the literature on logics of imperfect information it is often stated, incorrectly, that the Game-Theoretical Semantics of Independence-Friendly (IF) quantifiers captures the idea that the players of semantical games are forced to make some moves without knowledge of the moves of other players. We survey here the alternative semantics for IF logic that have been suggested in order to enforce this "epistemic reading" of sentences. We introduce some new proposals, and a more general logical language which distinguishes between "independence from actions" and "independence from strategies". New semantics for IF logic can be obtained by choosing embeddings of the set of IF sentences into this larger language. We compare all the semantics proposed and their purported game-theoretical justifications, and disprove a few claims that have been made in the literature.

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Modeling Monty Hall in If Logic

Sandu¹,

Velica²

2017

Outstanding Contributions to Logic

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Let us start by considering two formulations of the Monty Hall problem (Grinstead and Snell, Introduction to Probabilities). The rst formulation is: Suppose you are on a Monty Hall's Let's Make a Deal!You are given the choice of three doors, behind one door is a car, the others goats. You pick up a door, say 1, Monty Hall opens another door, say 3, which has a goat. Monty says to you Do you want to pick door 2? Is it to your advantage to switch your choice of doors? (Grinstead and Snell, Introduction to Probabilities, Example 4.6, p. 136) The second formulation is more general: We say that C is using the stay strategy if she picks a door, and, if oered a chance to switch to another door, declines to do so (i.e., he stays with his original choice). Similarly, we say that C is using the switch strategy if he picks a door, and, if oered a chance to switch to another door, takes the oer. Now suppose that C decides in advance to play the stay strategy. Her only action in this case is to pick a door (and decline an invitation to switch, if one is oered). What is the probability that she wins a car? The same question can be asked about the switch strategy. (Idem, p. 137) Grinstead and Snell remark that the rst formulation of the problem asks for the conditional probability that C wins if she switches doors, given that she has chosen door 1 and that Monty Hall has chosen door 3 whereas the second formulation is about the comparative probabilities of two kinds of strategies for C, the switch strategy and the stay strategy. They point out that using the stay strategy, the contestant C will win the car with probability 1/3, since 1/3 of the time the door he picks will have the car behind it. But if C plays the switch strategy, then he will win whenever the door he originally picked does not have the car behind it, which happens 2/3 of the time. (Idem, p. 13). Grinstead and Snell give a solution to the rst problem using conditional probabilities. van Benthem (2003) gives a solution to the same problem in terms of product updates and probabilites.

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On Existential Declarations of Independence in if Logic

Cited by 10 publications

References 16 publications

Independence-Friendly Logic Without Henkin Quantification

Independence-Friendly Logic Without Henkin Quantification

Cooperation in Games and Epistemic Readings of Independence-Friendly Sentences

Modeling Monty Hall in If Logic

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