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Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
This paper offers a comprehensive introduction to Bayesian inference, combining historical context, theoretical foundations, and core analytical examples. Beginning with Bayes' theorem and the philosophical distinctions between Bayesian and…
In this paper, we propose a model for building natural language explanations for Bayesian Network Reasoning in terms of factor arguments, which are argumentation graphs of flowing evidence, relating the observed evidence to a target…
The conventional postulate for the probabilistic interpretation of quantum mechanics is asymmetric in preparation and measurement, making retrodiction reliant on inference by use of Bayes' theorem. Here, a more fundamental symmetric…
A framework is presented for a computational theory of probabilistic argument. The Probabilistic Reasoning Environment encodes knowledge at three levels. At the deepest level are a set of schemata encoding the system's domain knowledge.…
We construct a model of type theory enjoying parametricity from an arbitrary one. A type in the new model is a semi-cubical type in the old one, illustrating the correspondence between parametricity and cubes. Our construction works not…
It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that standard approaches…
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.…
Probabilistic argumentation is an alternative to causal modeling with Bayesian networks. Probabilistic argumentation structures (PAS) are defined on families of compatible frames (f.c.f). This is a generalization of the usual multivariate…
In an earlier paper, a new theory of measurefree "conditional" objects was presented. In this paper, emphasis is placed upon the motivation of the theory. The central part of this motivation is established through an example involving a…
We present a general logical framework for reasoning about agents' cognitive attitudes of both epistemic type and motivational type. We show that it allows us to express a variety of relevant concepts for qualitative decision theory…
It is suggested that an AI inference system should reflect an inference policy that is tailored to the domain of problems to which it is applied -- and furthermore that an inference policy need not conform to any general theory of rational…
A theory of quantitative inference about the parameters of sampling distributions is constructed deductively by following very general rules, referred to as the Cox-Polya-Jaynes Desiderata. The inferences are made in terms of probability…
Many formal languages of contemporary mathematical music theory -- particularly those employing category theory -- are powerful but cumbersome: ideas that are conceptually simple frequently require expression through elaborate categorical…
Bayesian inference as applied in a legal setting is about belief transfer and involves a plurality of agents and communication protocols. A forensic expert (FE) may communicate to a trier of fact (TOF) first its value of a certain…
The probabilistic predictions of quantum theory are conventionally obtained from a special probabilistic axiom. But that is unnecessary because all the practical consequences of such predictions follow from the remaining, non-probabilistic,…
Although conventional logical systems based on logical calculi have been successfully used in mathematics and beyond, they have definite limitations that restrict their application in many cases. For instance, the principal condition for…
We define a context-sensitive temporal probability logic for representing classes of discrete-time temporal Bayesian networks. Context constraints allow inference to be focused on only the relevant portions of the probabilistic knowledge.…
Conditioning is a key feature in probabilistic programming to enable modeling the influence of data (also known as observations) to the probability distribution described by such programs. Determining the posterior distribution is also…
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…