A Continuum of Inductive Methods Arising from a Generalized Principle of Instantial Relevance

Abstract

In this paper we consider a natural generalization of the Principle of Instantial Relevance and give a complete characterization of the probabilistic belief functions satisfying this principle as a family of discrete probability functions parameterized by a single real δ ∈ [0, 1).

The Counterpart Principle of Analogical Support by Structural Similarity

“…The following is a stronger symmetry based principle which is also frequently seen in Inductive Logic; for example, it is satisfied by both Carnap's Continuum of Inductive Methods and the Nix-Paris Continuum, [20].…”

“…2 The usual method of thinning down towards such rational choices is to impose 'rationality principles' which these probability functions should arguably satisfy. Of course there can be considerable disagreement about which principles are rational (to the extent of different candidates being mutually inconsistent, see for example [20]) but one such widely accepted principle is that the inherent symmetry between the constants should be respected by any rational probability function w on L. Precisely w should satisfy:…”

“…, γ, γ , the δ occurring in the jth coordinate, γ = 2 −q (1 − δ) and 0 ≤ δ ≤ 1. Indeed they both satisfy the stronger condition of ULi with Ax, the language invariant families being given by fixing λ, respectively δ, and varying L, see [20], [21], or for a more technical account [14] or [23].…”

A rigorous and customizable framework for privacy

“…Our efforts at axiomatizing privacy and utility are motivated by corresponding efforts in mathematical philosophy and probabilistic inductive logic (e.g., [8,33]) where the goal is to model the reasoning of a rational agent.…”

The Twin Continua of Inductive Methods

“…In the early 2000's however C. J. Nix and the rst author, [14], made a somewhat unexpected discovery.…”