Neighborhood Contingency Logic

Fan, Jie; Ditmarsch, Hans van

doi:10.1007/978-3-662-45824-2_6

Cited by 18 publications

(28 citation statements)

References 13 publications

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“…We now use ∆-bisimulations to demonstrate that L ∆ is too weak to define some well-known frame classes. These results were already proved in [6,Prop. 7], but without the use of a bisimulation argument.…”

Section: Lemma 4 Every Neighbourhood Morphism Is a ∆-Morphismsupporting

confidence: 54%

“…From equation (2) it follows immediately that CL is sound and strongly complete with respect to the class of augmented neighbourhood frames. This question was left open in [6].…”

Section: Definition 8 (Neighbourhood Semantics Of Contingency Logic)mentioning

confidence: 99%

“…Non-normal logics are standardly interpreted on neighbourhood models [2,17,13]. Fan & Van Ditmarsch proposed in [6] to interpret the contingency operator on neighbourhood models. They left as an open question what a suitable notion of contingency bisimulation would be over neighbourhood models.…”

Section: Introductionmentioning

confidence: 99%

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Neighbourhood Contingency Bisimulation

Bakhtiari

Ditmarsch

Hansen

2016

Logic and Its Applications

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Section: Lemma 4 Every Neighbourhood Morphism Is a ∆-Morphismsupporting

confidence: 54%

“…From equation (2) it follows immediately that CL is sound and strongly complete with respect to the class of augmented neighbourhood frames. This question was left open in [6].…”

Section: Definition 8 (Neighbourhood Semantics Of Contingency Logic)mentioning

confidence: 99%

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Neighbourhood Contingency Bisimulation

Bakhtiari

Ditmarsch

Hansen

2016

Logic and Its Applications

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“…We say that M = S, N, V is a neighborhood model if S is a nonempty set of states, N : S → P(P(S)) is a neighborhood function, and V is a valuation assigning a set V (p) ⊆ S to each propositional variable p. A neighborhood frame is a neighborhood model without valuations. Given a neighborhood model M = S, N, V and a state s ∈ S, the semantics of ϕ ∈ L(∆) is defined recursively as follows [6],…”

Section: Preliminariesmentioning

confidence: 99%

“…To our knowledge, only the classical contingency logic, i.e. the minimal system of contingency logic under neighborhood semantics, is presented in the literature [6]. It is left as two open questions in [1] what the axiomatizations of monotone contingency logic and regular contingency logic are.…”

Section: Introductionmentioning

confidence: 99%

A Family of Neighborhood Contingency Logics

Fan¹

2019

Notre Dame J. Formal Logic

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This article proposes the axiomatizations of contingency logics of various natural classes of neighborhood frames. In particular, by defining a suitable canonical neighborhood function, we give sound and complete axiomatizations of monotone contingency logic and regular contingency logic, thereby answering two open questions raised by Bakhtiari, van Ditmarsch, and Hansen. The canonical function is inspired by a function proposed by Kuhn in 1995. We show that Kuhn's function is actually equal to a related function originally given by Humberstone.

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Beyond Knowing That: A New Generation of Epistemic Logics

Wang

2018

Jaakko Hintikka on Knowledge and Game-Theoretical Semantics

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Epistemic logic has become a major field of philosophical logic ever since the groundbreaking work by Hintikka (1962). Despite its various successful applications in theoretical computer science, AI, and game theory, the technical development of the field has been mainly focusing on the propositional part, i.e., the propositional modal logics of "knowing that". However, knowledge is expressed in everyday life by using various other locutions such as "knowing whether", "knowing what", "knowing how" and so on (knowing-wh hereafter). Such knowledge expressions are better captured in quantified epistemic logic, as was already discussed by Hintikka (1962) and his sequel works at length. This paper aims to draw the attention back again to such a fascinating but largely neglected topic. We first survey what Hintikka and others did in the literature of quantified epistemic logic, and then advocate a new quantifier-free approach to study the epistemic logics of knowing-wh, which we believe can balance expressivity and complexity, and capture the essential reasoning patterns about knowing-wh. We survey our recent line of work on the epistemic logics of 'knowing whether", "knowing what" and "knowing how" to demonstrate the use of this new approach.2 Hintikka was never happy with the term "possible worlds", since in his models there may be no "worlds" but only situations or states, which are partial descriptions of the worlds. However, in this paper we will still use the term "possible worlds" for convenience. 3 How is in general also considered as a wh-question word, besides what, when, where, who, whom, which, whose, and why. 4 The "knows X" search term can exclude the phrases such as "you know what" and count only the statements, while "know X" may appear in questions as well.

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Neighborhood Contingency Logic

Abstract: International audienceno abstrac

Cited by 18 publications

References 13 publications

Neighbourhood Contingency Bisimulation

Neighbourhood Contingency Bisimulation

A Family of Neighborhood Contingency Logics

Beyond Knowing That: A New Generation of Epistemic Logics

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