Some Observations on Induction in Predicate Probabilistic Reasoning

A Note on Binary Inductive Logic

“…the vector of non-zero values |{ i : h i = j }| arranged in non-increasing order 11 . [For more details see for example [16].] This observation seems to us to point to the significance of this property and justifies us giving a name to it Clearly the principles Px and SN (for this binary language) follow from Sx.…”

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

“…To emphasize the incompatibility of these two principles note, as shown in [14], that, away from the extreme cases, JSP implies Reichenbach's Axiom, and that Reichenbach's Axiom contradicts GPIR.…”

“…Finally, by the asymptotic consistency of Bayes posteriors (see for example Theorem 7.78 of [16] or page 25 of [14]) we see that the RHS of (15) converges to…”

“…For more on this, in particular the conditions under which equality can hold here, see [6], [9], [14]. The Generalized Principle of Instantial Relevance, GPIR, proposed in [8], [14] takes the intuition behind PIR a step further.…”

“…The Generalized Principle of Instantial Relevance, GPIR, proposed in [8], [14] takes the intuition behind PIR a step further. In words, GPIR says that the observation of an object satisfying a set of properties should not decrease the belief in further objects satisfying a superset of those properties.…”