March 16, 2018

Analogies and Theories: Formal Models of Reasoning - download pdf or read online

By Itzhak Gilboa, Larry Samuelson, David Schmeidler

ISBN-10: 0198738021

ISBN-13: 9780198738022

The booklet describes formal types of reasoning which are geared toward taking pictures the way in which that financial brokers, and determination makers mostly take into consideration their surroundings and make predictions in accordance with their prior adventure. the focal point is on analogies (case-based reasoning) and basic theories (rule-based reasoning), and at the interplay among them, in addition to among them and Bayesian reasoning. A unified strategy permits one to review the dynamics of inductive reasoning when it comes to the mode of reasoning that's used to generate predictions.

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Example text

Second, our combination axiom also has a flavor of independence. In particular, it rules out situations in which past occurrences of a case make future occurrences of the same case less likely. 4 Discussion of the Axioms The rule we axiomatize generalizes rankings by empirical frequencies. Moreover, the previous section shows that it also generalizes several well-known statistical techniques. It follows that there is a wide range of applications for which this rule, and the axioms it satisfies, are plausible.

Since 1 − λ ≥ 0 and 1 − λ − μ = θ ≥ 0, dividing by the sum of the coefficients yields a contradiction to the convex hull condition. Proof of Theorem 2: We present the proof for the case |X| ≥ 4. The proofs for the cases |X| = 2 and |X| = 3 will be described as by-products along the way. Part 1: (i) implies (ii). 1 For every I ∈ ZT + and every k ∈ N, I= kI . Proof: Follows from consecutive application of the combination axiom. In view of this claim, we extend the definition of I to functions I whose T values are non-negative rationals.

First, we have defined M M∈M where each M is a set. This implicitly assumes that only the number of repetitions of cases, and not their order, matters. This structural assumption is reminiscent of de Finetti’s exchangeability condition (though the latter is defined in a more elaborate probabilistic model). Second, our combination axiom also has a flavor of independence. In particular, it rules out situations in which past occurrences of a case make future occurrences of the same case less likely.

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Analogies and Theories: Formal Models of Reasoning by Itzhak Gilboa, Larry Samuelson, David Schmeidler


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