Related papers: Cox's Theorem and the Jaynesian Interpretation of …

We review recent work that employs the framework of logical inference to establish a bridge between data gathered through experiments and their objective description in terms of human-made concepts. It is shown that logical inference…

This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…

Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this…

In recent years, there has been an increased need for the use of active systems - systems required to act automatically based on events, or changes in the environment. Such systems span many areas, from active databases to applications that…

Classical probability theory is formulated using sets. In this paper, we extend classical probability theory with propositional computability logic. Unlike other formalisms, computability logic is built on the notion of events/games, which…

Humans currently use arguments for explaining choices which are already made, or for evaluating potential choices. Each potential choice has usually pros and cons of various strengths. In spite of the usefulness of arguments in a decision…

We derive axiomatically the probability function that should be used to make decisions given any form of underlying uncertainty.

A primary motivation for reasoning under uncertainty is to derive decisions in the face of inconclusive evidence. However, Shafer's theory of belief functions, which explicitly represents the underconstrained nature of many reasoning…

Probability theory as extended logic is completed such that essentially any probability may be determined. This is done by considering propositional logic (as opposed to predicate logic) as syntactically suffcient and imposing a symmetry…

Bayesian networks provide an elegant formalism for representing and reasoning about uncertainty using probability theory. Theyare a probabilistic extension of propositional logic and, hence, inherit some of the limitations of propositional…

Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the…

A theory of measurement uncertainty is presented, which, since it is based exclusively on the Bayesian approach and on the subjective concept of conditional probability, is applicable in the most general cases. The recent International…

A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…

I show that probabilities in quantum mechanics are a measure of belief in the presence of human ignorance, just like all other probabilities. The Born interpretation of the square of modulus of the wave function arises from the interaction…

Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This…

A definition of a {\it Realistic} Physics Theory is proposed based on the idea that, at all time, the set of physical properties possessed (at that time) by a system should unequivocally determine the probabilities of outcomes of all…

The new interpretation of Quantum Mechanics is based on a complex probability theory. An interpretation postulate specifies events which can be observed and it follows that the complex probability of such event is, in fact, a real positive…

In this paper we deal with a new approach to probabilistic reasoning in a logical framework. Nearly almost all logics of probability that have been proposed in the literature are based on classical two-valued logic. After making clear the…

Richard Cox [1] set the axiomatic foundations of probable inference and the algebra of propositions. He showed that consistency within these axioms requires certain rules for updating belief. In this paper we use the analogy between…

Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive…