A Triple Uniqueness of the Maximum Entropy Approach

Landes, Jürgen; Vejnarová, Jiřina; Wilson, Nic

doi:10.1007/978-3-030-86772-0_46

Cited by 5 publications

(1 citation statement)

References 43 publications

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“…One, due to Jeff Paris and his co-workers, takes limits of maximum entropy functions on finite sublanguages [2,29,35,37,38]. The second explication considers maximal entropy probability functions defined on the infinite language as a whole [18,20,36,42,44]. The limit approach provides a constructive means to determine the probabilities for MaxEnt inference.…”

Section: Introductionmentioning

confidence: 99%

Determining Maximal Entropy Functions for Objective Bayesian Inductive Logic

Landes

Rad²,

Williamson³

2022

J Philos Logic

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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.

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Section: Introductionmentioning

confidence: 99%

Determining Maximal Entropy Functions for Objective Bayesian Inductive Logic

Landes

Rad²,

Williamson³

2022

J Philos Logic

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Discovering Maximum Entropy Knowledge

Landes

2024

Erkenn

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This paper seeks to determine a rational agent’s evidential constraints given her beliefs. Rationality is here construed as adherence to a principle of entropy maximisation. I determine the rational agent’s set of probability efunctions compatible with the evidence, $${\mathbb {E}}$$ E , given the maximum entropy function and given some constraints on the shape of $${\mathbb {E}}$$ E . I also consider agents employing a centre of mass approach to form their beliefs rather than entropy maximisation.

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Formal Epistemology Meets Mechanism Design

Landes

2023

J Gen Philos Sci

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This article connects recent work in formal epistemology to work in economics and computer science. Analysing the Dutch Book Arguments, Epistemic Utility Theory and Objective Bayesian Epistemology we discover that formal epistemologists employ the same argument structure as economists and computer scientists. Since similar approaches often have similar problems and have shared solutions, opportunities for cross-fertilisation abound.

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A Triple Uniqueness of the Maximum Entropy Approach

Cited by 5 publications

References 43 publications

Determining Maximal Entropy Functions for Objective Bayesian Inductive Logic

Determining Maximal Entropy Functions for Objective Bayesian Inductive Logic

Discovering Maximum Entropy Knowledge

Formal Epistemology Meets Mechanism Design

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