Alena Vencovská

A note on the inevitability of maximum entropy

Abstract It is shown that, assuming natural principles of independence and consistency, the method of maximum entropy provides the only consistent model of inductive inference. This paper is related to earlier results of Shore and Johnson. The relation is briefly discussed in an appendix.

On the applicability of maximum entropy to inexact reasoning

Abstract It is shown that under a certain interpretation of belief maximum entropy arises naturally in inexact reasoning. Practical and theoretical consequences of this method are then discussed.

In defense of the maximum entropy inference process

Abstract This paper is a sequel to an earlier result of the authors that in making inferences from certain probabilistic knowledge bases the maximum entropy inference process, ME , is the only inference process respecting “common sense.” This result was criticized on the grounds that the probabilistic knowledge bases considered are unnatural and that ignorance of dependence should not be identified with statistical independence. We argue against these criticisms and also against the more general criticism that ME is representation dependent. In a final section, however, we provide a criticism of our own of ME , and of inference processes in general, namely that they fail to satisfy compactness.

A method for updating that justifies minimum cross entropy

Abstract Given a general knowledge base about a population of individuals, we consider the problem of applying, or updating, that general knowledge to reason about a particular individual from the population about whom we have only some partial and uncertain information. We show that given an inference process for reasoning about the general knowledge, this process yields a natural and justifiable method of updating to knowledge about a particular individual. In particular, we show that in the case of the maximum entropy inference process this yields minimum cross entropy updating. We also consider several other updating procedures arising in this way.

A natural prior probability distribution derived from the propositional calculus

Abstract A σ-additive probability measure on the real interval [0, 1] is defined by considering the expected values of “randomly chosen” large formulae of the propositional calculus, where the propositional variables are treated as independent random variables on {0, 1} with expected value 1 2 . Although arising naturally from logical and/or cognitive considerations, this measure is extremely complex and displays certain formally pathological features, including infinite density at all points of a certain dense subset of [0, 1]. Certain variantsof the construction are also considered. The introduction includes an account of motivation for the study of such measures arising from a fundamental problem in inexact reasoning.

Common Sense and Stochastic Independence

In this paper we shall extend the results in [Paris and Vencovska, 1990] and [Paris, 1999] on common sense belief formation from (finite) knowledge bases of linear probabilistic constraints to include also the case of polynomial non-linear constraints and in particular constraints expressing stochastic independence. Indeed our results will be seen to extend to entirely general sets of constraints provided their solution sets are closed.

Representation theorems for probability functions satisfying spectrum exchangeability in inductive logic

We prove de Finetti style representation theorems covering the class of all probability functions satisfying spectrum exchangeability in polyadic inductive logic and give an application by characterizing those probability functions satisfying spectrum exchangeability which can be extended to a language with equality whilst still satisfying that property.

Some Aspects of Polyadic Inductive Logic

We give a brief account of some de Finetti style representation theorems for probability functions satisfying Spectrum Exchangeability in Polyadic Inductive Logic, together with applications to Non-splitting, Language Invariance, extensions with Equality and Instantial Relevance.

A New Criterion for Comparing Fuzzy Logics for Uncertain Reasoning

A new criterion is introduced for judging the suitability of various “fuzzy logics” for practical uncertain reasoning in a probabilistic world and the relationship of this criterion to several established criteria, and its consequences for truth functional belief, are investigated.

A characterization of the language invariant families satisfying spectrum exchangeability in polyadic inductive logic

A necessary and sufficient condition in terms of a de Finetti style representation is given for a probability function in Polyadic Inductive Logic to satisfy being part of a Language Invariant family satisfying Spectrum Exchangeability. This theorem is then considered in relation to the unary Carnap and Nix–Paris Continua.