Related papers: Some Extensions of Probabilistic Logic

Ehrhard, Pagani and Tasson proposed a model of probabilistic functional programming in a category of normed positive cones and stable measurable cone maps, which can be seen as a coordinate-free generalization of probabilistic coherence…

The concept of Logical Entropy, $S_L = 1- \sum_{i=1}^n p_i^2$, where the $p_i$ are normalized probabilities, was introduced by David Ellerman in a series of recent papers. Although the mathematical formula itself is not new, Ellerman…

Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…

Statistical Relational Models and, more recently, Probabilistic Programming, have been making strides towards an integration of logic and probabilistic reasoning. A natural expectation for this project is that a probabilistic logic…

We present probabilistic approaches to check the validity of selected connexive principles within the setting of coherence. Connexive logics emerged from the intuition that conditionals of the form "If $\sim A$, then $A$", should not hold,…

The probability axioms by R. T. Cox can be regarded as the modern foundations of Bayesian inference, the idea of assigning degrees of belief to logical propositions in a manner consistent with Boolean logic. In this work it is shown that…

Abstract argumentation offers an appealing way of representing and evaluating arguments and counterarguments. This approach can be enhanced by a probability assignment to each argument. There are various interpretations that can be ascribed…

This paper investigates the possibility of performing automated reasoning in probabilistic logic when probabilities are expressed by means of linguistic quantifiers. Each linguistic term is expressed as a prescribed interval of proportions.…

Physicists have, hitherto, mostly adopted a frequentist conception of probability, according to which probability statements apply only to ensembles. It is argued that we should, instead, adopt an epistemic, or Bayesian conception, in which…

There are two main approach to probability, one of set-theoretic character where probability is the measure of a set, and another one of linguistic character where probability is the degree of confidence in a proposition. In this work we…

An inductive logic can be formulated in which the elements are not propositions or probability distributions, but information systems. The logic is complete for information systems with binary hypotheses, i.e., it applies to all such…

A method for computing probabilistic propositions is presented. It assumes the availability of a single external routine for computing the probability of one instantiated variable, given a conjunction of other instantiated variables. In…

Qualitative and quantitative approaches to reasoning about uncertainty can lead to different logical systems for formalizing such reasoning, even when the language for expressing uncertainty is the same. In the case of reasoning about…

In the modern Bayesian view classical probability theory is simply an extension of conventional logic, i.e., a quantitative tool that allows for consistent reasoning in the presence of uncertainty. Classical theory presupposes, however,…

We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of…

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…

By considering probability distributions over the set of assignments the expected truth values assignment to propositional variables are extended through linear operators, and the expected truth values of the clauses at any given…

In this talk - based on the results of a forthcoming paper (Coletti, Scozzafava and Vantaggi 2002), presented also by one of us at the Conference on "Non Classical Logic, Approximate Reasoning and Soft-Computing" (Anacapri, Italy, 2001) -…

For many standard models of random structure, first-order logic sentences exhibit a convergence phenomenon on random inputs. The most well-known example is for random graphs with constant edge probability, where the probabilities of…

I defend an analog of probabilism that characterizes rationally coherent estimates for chances. Specifically, I demonstrate the following accuracy-dominance result for stochastic theories in the C*-algebraic framework: supposing an…