The Countable Henkin Principle

Goldblatt, Robert

doi:10.1007/978-3-319-09719-0_13

Cited by 3 publications

(2 citation statements)

References 17 publications

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“…for each ϕ(x) either there is some k with ¬ϕ(k) ∈ or ∀xϕ(x) ∈ . For details on this construction Goldblatt (2014) can be consulted. 37 I.e.…”

Section: Lemma 510 If Is ωmentioning

confidence: 99%

How to Express Self-Referential Probability. A Kripkean Proposal

Campbell-Moore

2015

The Review of Symbolic Logic

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We present a semantics for a language that includes sentences that can talk about their own probabilities. This semantics applies a fixed point construction to possible world style structures. One feature of the construction is that some sentences only have their probability given as a range of values. We develop a corresponding axiomatic theory and show by a canonical model construction that it is complete in the presence of the ω-rule. By considering this semantics we argue that principles such as introspection, which lead to paradoxical contradictions if naively formulated, should be expressed by using a truth predicate to do the job of quotation and disquotation and observe that in the case of introspection the principle is then consistent.

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“…for each ϕ(x) either there is some k with ¬ϕ(k) ∈ or ∀xϕ(x) ∈ . For details on this construction Goldblatt (2014) can be consulted. 37 I.e.…”

Section: Lemma 510 If Is ωmentioning

confidence: 99%

How to Express Self-Referential Probability. A Kripkean Proposal

Campbell-Moore

2015

The Review of Symbolic Logic

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“…Although not a perfect duality due to these restrictions, the groundwork laid in that paper nevertheless led to significant advances in the completeness of Markovian logics [21], [22]. Previously, strong completeness theorems had used a powerful infinitary axiom scheme called the countable additivity rule, which has uncountably many instances.…”

Section: Introductionmentioning

confidence: 99%

Unrestricted stone duality for Markov processes

Furber¹,

Kozen²,

Larsen³

et al. 2017

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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Abstract-Stone duality relates logic, in the form of Boolean algebra, to spaces. Stone-type dualities abound in computer science and have been of great use in understanding the relationship between computational models and the languages used to reason about them. Recent work on probabilistic processes has established a Stone-type duality for a restricted class of Markov processes. The dual category was a new notion-Aumann algebras-which are Boolean algebras equipped with countable family of modalities indexed by rational probabilities. In this article we consider an alternative definition of Aumann algebra that leads to dual adjunction for Markov processes that is a duality for many measurable spaces occurring in practice. This extends a duality for measurable spaces due to Sikorski. In particular, we do not require that the probabilistic modalities preserve a distinguished base of clopen sets, nor that morphisms of Markov processes do so. The extra generality allows us to give a perspicuous definition of event bisimulation on Aumann algebras.

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