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The objet language

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The objet language

Common knowledge

and

the object language

Ehud Lehrer, Dov Samet

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The objet language

 

 

 

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Models of knowledge

 

 

 

 

 

 

- initial assignment

 

.

 

 

 

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There are partitions that are coarser than both the red and the blue partitions.

 

 

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The size of a model

The size of a formula

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The metric

 

 

 

 

𝝎

 

 

 

 

 

 

 

 

 

 

 

 

The size of a model

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The size of a formula

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Gluing

 

 

 

We unite the two elements.

 

 

 

 

 

 

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∙

 

 

 

 

 

connected

connected

 

∙

 

 

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The truth of 𝒇 at 𝝎 in a model 𝑴 depends only on the restriction of 𝑴 to the ball of radius Dep(𝒇), centered at 𝝎.

 

∙

 

 

∙

 

 

 

 

connected

connected

 

 

 

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Halpern J.Y., D. Samet and E. Segev�Defining knowledge in terms of belief: The modal logic perspective.�Review of Symbolic Logic 2 (3), (2009)

Halpern J.Y., D. Samet and E. Segev�On definability in multimodal logic.�Review of Symbolic Logic 2 (3), (2009)

 

 

 

NOT

When algebraic semantics is used.

S5-knowledge is not syntactically reducible to KD45-belief.

S5-knowledge is semantically reducible to KD45-belief.