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Towards the entropy-limit conjecture

Landes, Jürgen, Rafiee Rad, Soroush, Williamson, Jon (2020) Towards the entropy-limit conjecture. Annals of Pure and Applied Logic, 172 (2). Article Number 102870. ISSN 0168-0072. (doi:10.1016/j.apal.2020.102870) (KAR id:82911)

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The maximum entropy principle is widely used to determine non-committal probabilities on a finite domain, subject to a set of constraints, but its application to continuous domains is notoriously problematic. This paper concerns an intermediate case, where the domain is a first-order predicate language. Two strategies have been put forward for applying the maximum entropy principle on such a domain: (i) applying it to finite sublanguages and taking the pointwise limit of the resulting probabilities as the size n of the sublanguage increases; (ii) selecting a probability function on the language as a whole whose entropy on finite sublanguages of size n is not dominated by that of any other probability function for sufficiently large n. The entropy-limit conjecture says that, where these two approaches yield determinate probabilities, the two methods yield the same probabilities. If this conjecture is found to be true, it would provide a boost to the project of seeking a single canonical inductive logic—a project which faltered when Carnap's attempts in this direction succeeded only in determining a continuum of inductive methods. The truth of the conjecture would also boost the project of providing a canonical characterisation of normal or default models of first-order theories. Hitherto, the entropy-limit conjecture has been verified for languages which contain only unary predicate symbols and also for the case in which the constraints can be captured by a categorical statement of quantifier complexity. This paper shows that the entropy-limit conjecture also holds for categorical statements of complexity, for various non-categorical constraints, and in certain other general situations.

Item Type: Article
DOI/Identification number: 10.1016/j.apal.2020.102870
Uncontrolled keywords: Maximum entropy, Objective Bayesianism, Probabilistic constraints on predicate languages, Inductive logic, Normal models, Default models
Subjects: B Philosophy. Psychology. Religion > B Philosophy (General)
Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Arts and Humanities > School of European Culture and Languages
Depositing User: Matthias Werner
Date Deposited: 14 Sep 2020 15:19 UTC
Last Modified: 25 Sep 2020 13:25 UTC
Resource URI: (The current URI for this page, for reference purposes)
Williamson, Jon:
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