Probability logic, logical probability, and inductive support

Levi, Isaac

doi:10.1007/s11229-009-9474-3

Cited by 5 publications

(2 citation statements)

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“…For a taste of diverse but comparably forceful critical voices, see[29,35,39]. Of course, there are cases which tend to defy the distinction between representatives and critics: Isaac Levi's work (e.g.,[33]) is a major example.…”

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Confirmation as partial entailment: A representation theorem in inductive logic

Crupi

Tentori

2013

Journal of Applied Logic

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The most prominent research program in inductive logic -here just labeled The Program, for simplicity -relies on probability theory as its main building block and aims at a proper generalization of deductive-logical relations by a theory of partial entailment. We prove a representation theorem by which a class of ordinally equivalent measures of inductive support or confirmation is singled out as providing a uniquely coherent way to work out these two major sources of inspiration of The Program.The current state of inductive logic may appear puzzling. Some highly sophisticated observers in philosophy, for instance, have come to see the very term as "slightly antiquated" (see [32, p. 291]). Yet the central issue of inductive logic -i.e., the evaluation of how given premises or data affect the credibility of conclusions or hypotheses of interest -never ceased to play a significant role in a wide range of research domains. Up to recent times, striking examples arise from fields such as cognitive psychology, computer science and the law (by way of illustration, see [19], [2], and [1], respectively). Thus, the problem of inductive logic seems not to have lost its relevance, which provides motivation to stick to the label after all, whatever its fate in certain philosophical quarters.Survey presentations usually agree on one account, i.e., that much contemporary work in inductive logic has consistently relied on two pillars. First, probability (in its modern mathematical meaning) is viewed as the main "building block" for inductive-logical theorizing. And second, inductive logic is meant to provide an analogue of classical deductive logic in some suitable sense (see [12] and [21]). For the sake of convenience, we will simply use The Program to denote the combination of these two guidelines in inductive logic research.In this contribution, we do not mean to defend The Program as such. We will rather enrich it through a novel formal result, i.e., a representation theorem by which a class of ordinally equivalent measures of inductive support or confirmation is singled out as capturing a small number of axioms. These axioms, we will argue, provide an unusually neat instantiation of the spirit of The Program itself.

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Confirmation as partial entailment: A representation theorem in inductive logic

Crupi

Tentori

2013

Journal of Applied Logic

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“…Part II starts out by sketching the theory of credal networks (Chapter 8). This theory, a generalization of the theory of Bayesian networks (Pearl 1988;Neapolitan 1990), is a particularly powerful and efficient way of finding a probability interval Y such that FQPL is answered. The focus in this part of the book is on constructing appropriate networks for specific inference problems and on applying this machinery to those problems.…”

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A unifying framework of probabilistic reasoning

Sprenger

2011

Metascience

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There is a German proverb that among four lawyers, there are five different opinions. This is, in some sense, also true of probabilistic reasoning: there is a plurality of competing approaches which the outsider finds hard to oversee. Subjective Bayesianism, interval-valued probabilities, Dempster-Shafer theory, classical statistics, the Principle of Maximum Entropy, Evidential Probability and so on. To the untrained eye, they all appear disparate and sometimes idiosyncratic. While it is hard to judge the degree to which they conflict and cohere, it is even harder to come up with a unifying perspective. Perhaps, it is for that reason that relatively few researchers devote their time to investigating parallels, differences and conflicts between these frameworks-among the notable exceptions, there are Teddy Seidenfeld (1979, 1987) and Isaac Levi (2007). Since these researchers are not any more in the bloom of their youth, it is nice to see that the baton is passed on to the next generation. On not more than 155 pages, Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler and Jon Williamson make a heroic tour de force through these theories of probabilistic reasoning, with the aim of identifying a unifying overarching framework. The core idea of their book is derived from an analogy with classical first-order logic. There, the central question is the validity of an entailment relation between propositions / 1 ,…,/ N (the premises) and proposition w (the conclusion): / 1 ;. . .; / N w: ð1Þ Probabilistic logics differ from classical logics in that the valuation function maps these propositions not to the binary values ''true'' and ''false'', but to sets X , [0, 1]. The sentence / X is standardly interpreted as ''the probability of / lies in the

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An Objective Bayesian Account of Confirmation

Williamson

2011

Explanation, Prediction, and Confirmation

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Probability logic, logical probability, and inductive support

Cited by 5 publications

References 42 publications

Confirmation as partial entailment: A representation theorem in inductive logic

Confirmation as partial entailment: A representation theorem in inductive logic

A unifying framework of probabilistic reasoning

An Objective Bayesian Account of Confirmation

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