The application of the maximum entropy principle to determine probabilities on finite domains is well-understood. Its application to infinite domains still lacks a well-studied comprehensive approach. There are two different strategies for applying the maximum entropy principle on first-order predicate languages: (i) applying it to finite sublanguages and taking a limit; (ii) comparing finite entropies of probability functions defined on the language as a whole. The entropy-limit conjecture roughly says that these two strategies result in the same probabilities. While the conjecture is known to hold for monadic languages as well as for premiss sentences containing only existential or only universal quantifiers, its status for premiss sentences of greater quantifier complexity is, in general, unknown. I here show that the first approach fails to provide a sensible answer for some Sigma(2)-premiss sentences. I discuss implications of this failure for the first strategy and consequences for the entropy-limit conjecture.

The Entropy-Limit (Conjecture) for Σ₂-Premisses [The Entropy-Limit (Conjecture) for Sigma(2)-Premisses] / J. Landes. - In: STUDIA LOGICA. - ISSN 0039-3215. - 109:2(2021 Apr), pp. 423-442. [10.1007/s11225-020-09912-3]

The Entropy-Limit (Conjecture) for Σ₂-Premisses [The Entropy-Limit (Conjecture) for Sigma(2)-Premisses]

J. Landes
2021

Abstract

The application of the maximum entropy principle to determine probabilities on finite domains is well-understood. Its application to infinite domains still lacks a well-studied comprehensive approach. There are two different strategies for applying the maximum entropy principle on first-order predicate languages: (i) applying it to finite sublanguages and taking a limit; (ii) comparing finite entropies of probability functions defined on the language as a whole. The entropy-limit conjecture roughly says that these two strategies result in the same probabilities. While the conjecture is known to hold for monadic languages as well as for premiss sentences containing only existential or only universal quantifiers, its status for premiss sentences of greater quantifier complexity is, in general, unknown. I here show that the first approach fails to provide a sensible answer for some Sigma(2)-premiss sentences. I discuss implications of this failure for the first strategy and consequences for the entropy-limit conjecture.
Inductive logic; Maximum entropy; Objective Bayesianism;
Settore M-FIL/02 - Logica e Filosofia della Scienza
30-giu-2020
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/938991
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