Determining Maximal Entropy Functions for Objective Bayesian Inductive Logic.
According to the objective Bayesian approach to inductive logic, premisses inductively entail a conclusion just when every probability function with maximal entropy, from all those that satisfy the premisses, satisfies the conclusion. When premisses and conclusion are constraints on probabilities of...
| Publicado en: | Journal of Philosophical Logic Vol. 52; no. 2; pp. 555 - 609 |
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| Autores principales: | , , |
| Formato: | Artículo |
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Springer Nature
Apr2023
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=162802440&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 162802440 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00223611 JPH jtl: Journal of Philosophical Logic issn: 00223611 maglogo: N pubinfo: dt: Apr2023 vid: 52 iid: 2 pid: 237 pub: Springer Nature artinfo: ui: 162802440 10.1007/s10992-022-09680-6 ppf: 555 ppct: 54 formats: fmt: @attributes: type: P size: 873KB tig: atl: Determining Maximal Entropy Functions for Objective Bayesian Inductive Logic. aug: au: Landes, Juergen Rafiee Rad, Soroush Williamson, Jon affil: Department of Philosophy "Piero Martinetti", University of Milan, Milan, Italy Dutch Institute for Emergent Phenomena (DIEP) and Institute for Logic, Language and Computation (ILLC), Amsterdam, The Netherlands Philosophy Department and Centre for Reasoning, University of Kent, Canterbury, UK su: Maximal functions Induction (Logic) Ergometry Predicate (Logic) Maximum entropy method Set functions sug: subj: Maximal functions Induction (Logic) Ergometry Predicate (Logic) Maximum entropy method Set functions keyword: Entropy First order logic Inductive logic Maximum entropy principle Probability logic ab: According to the objective Bayesian approach to inductive logic, premisses inductively entail a conclusion just when every probability function with maximal entropy, from all those that satisfy the premisses, satisfies the conclusion. When premisses and conclusion are constraints on probabilities of sentences of a first-order predicate language, however, it is by no means obvious how to determine these maximal entropy functions. This paper makes progress on the problem in the following ways. Firstly, we introduce the concept of a limit in entropy and show that, if the set of probability functions satisfying the premisses contains a limit in entropy, then this limit point is unique and is the maximal entropy probability function. Next, we turn to the special case in which the premisses are categorical sentences of the logical language. We show that if the uniform probability function gives the premisses positive probability, then the maximal entropy function can be found by simply conditionalising this uniform prior on the premisses. We generalise our results to demonstrate agreement between the maximal entropy approach and Jeffrey conditionalisation in the case in which there is a single premiss that specifies the probability of a sentence of the language. We show that, after learning such a premiss, certain inferences are preserved, namely inferences to inductive tautologies. Finally, we consider potential pathologies of the approach: we explore the extent to which the maximal entropy approach is invariant under permutations of the constants of the language, and we discuss some cases in which there is no maximal entropy probability function. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Journal of Philosophical Logic is a copyright of Springer, 2023. All Rights Reserved. item: Journal of Philosophical Logic holder: Springer Nature dt: @attributes: year: 2023 holdings: @attributes: islocal: N |
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