Related papers: Quantifying Rational Belief
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from…
The theory of belief functions manages uncertainty and also proposes a set of combination rules to aggregate opinions of several sources. Some combination rules mix evidential information where sources are independent; other rules are…
We investigate whether quantum history theories can be consistent with Bayesian reasoning and whether such an analysis helps clarify the interpretation of such theories. First, we summarise and extend recent work categorising two different…
In this paper we attempt to analyze the concept of quantum probability within quantum computation and quantum computational logic. While the subjectivist interpretation of quantum probability explains it as a reliable predictive tool for an…
We introduce a logic for reasoning about evidence that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…
Do norms of rationality apply to machine learning models, in particular language models? In this paper we investigate this question by focusing on a special subset of rational norms: coherence norms. We consider both logical coherence norms…
Making a decision is often a matter of listing and comparing positive and negative arguments. In such cases, the evaluation scale for decisions should be considered bipolar, that is, negative and positive values should be explicitly…
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…
Plausible reasoning concerns situations whose inherent lack of precision is not quantified; that is, there are no degrees or levels of precision, and hence no use of numbers like probabilities. A hopefully comprehensive set of principles…
Topos theory has been suggested by D\"oring and Isham as an alternative mathematical structure with which to formulate physical theories. In particular, the topos approach suggests a radical new way of thinking about what a theory of…
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…
An analysis using classical stochastic processes is used to construct a consistent system of quantum counterfactual reasoning. When applied to a counterfactual version of Hardy's paradox, it shows that the probabilistic character of quantum…
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…
We present a logical framework that enables us to define a formal theory of computational trust in which this notion is analysed in terms of epistemic attitudes towards the possible objects of trust and in relation to existing evidence in…
Advances in the general capabilities of large language models (LLMs) have led to their use for information retrieval, and as components in automated decision systems. A faithful representation of probabilistic reasoning in these models may…
It is argued that the usual postulates of quantum mechanics are too strong. It is conjectured that it is possible to interpret all experiments if we maintain the formalism of quantum theory without modification, but weaken the postulates…
Given conflicting probability estimates for a set of events, how can we quantify how much they conflict? How can we find a single probability distribution that best encapsulates the given estimates? One approach is to minimize a loss…
The problem of combining beliefs in the Dempster-Shafer belief theory has attracted considerable attention over the last two decades. The classical Dempster's Rule has often been criticised, and many alternative rules for belief combination…
The usual formulation of quantum theory is rather abstract. In recent work I have shown that we can, nevertheless, obtain quantum theory from five reasonable axioms. Four of these axioms are obviously consistent with both classical…
The choice of priors may become an insoluble problem if priors and Bayes' rule are not seen and accepted in the framework of subjectivism. Therefore, the meaning and the role of subjectivity in science is considered and defended from the…