Related papers: Predicative well-ordering
We investigate predicative aspects of order theory in constructive univalent foundations. By predicative and constructive, we respectively mean that we do not assume Voevodsky's propositional resizing axioms or excluded middle. Our work…
Sources of predictability in the basic laws of physics are described in the most general theoretical context -- the quantum theory of the universe as a whole. (To appear in the Proceedings of the conference on Fundamental Sources of…
From an inconsistent database non-trivial arguments may be constructed both for a proposition, and for the contrary of that proposition. Therefore, inconsistency in a logical database causes uncertainty about which conclusions to accept.…
Logics of limited belief aim at enabling computationally feasible reasoning in highly expressive representation languages. These languages are often dialects of first-order logic with a weaker form of logical entailment that keeps reasoning…
In this position paper we discuss three main shortcomings of existing approaches to counterfactual causality from the computer science perspective, and sketch lines of work to try and overcome these issues: (1) causality definitions should…
One of quantum theory's salient features is its apparent indeterminism, i.e. measurement outcomes are typically probabilistic. We formally define and address whether this uncertainty is unavoidable or whether post-quantum theories can offer…
Machine learning models that predict the feasibility of chemical reactions have become central to automated synthesis planning. Despite their predictive success, these models often lack transparency and interpretability. We introduce a…
Solomonoff unified Occam's razor and Epicurus' principle of multiple explanations to one elegant, formal, universal theory of inductive inference, which initiated the field of algorithmic information theory. His central result is that the…
The capability of making explainable inferences regarding physical processes has long been desired. One fundamental physical process is object motion. Inferring what causes the motion of a group of objects can even be a challenging task for…
The minimization of the length of syntactic dependencies is a well-established principle of word order and the basis of a mathematical theory of word order. Here we complete that theory from the perspective of information theory, adding a…
Practicing mathematicians often assume that mathematical claims, when they are true, have good reasons to be true. Such a state of affairs is "unreasonable", in Wigner's sense, because basic results in computational complexity suggest that…
There are three principle paradigms of statistical inference: (i) Bayesian, (ii) information-based and (iii) frequentist inference. We describe an objective prior (the weighting or $w$-prior) which unifies objective Bayes and…
Word order is an important concept in natural language, and in this work, we study how word order affects the induction of world knowledge from raw text using language models. We use word analogies to probe for such knowledge. Specifically,…
In many prediction problems, the predictive model affects the distribution of the prediction target. This phenomenon is known as performativity and is often caused by the behavior of individuals with vested interests in the outcome of the…
A model of knowledge representation is described in which propositional facts and the relationships among them can be supported by other facts. The set of knowledge which can be supported is called the set of cognitive units, each having…
In this paper some initial work towards a new approach to qualitative reasoning under uncertainty is presented. This method is not only applicable to qualitative probabilistic reasoning, as is the case with other methods, but also allows…
Nonmonotonic logics are usually characterized by the presence of some notion of 'conditional' that fails monotonicity. Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the…
What is the best way to define algorithmic fairness? While many definitions of fairness have been proposed in the computer science literature, there is no clear agreement over a particular definition. In this work, we investigate ordinary…
The main result presented in this article is that probability can fundamentally be characterized as a subset of conditional expectation induced by a plausible preorder on random quantities. This is justified by the fact that probability is…
Rational inference relations were introduced by Lehmann and Magidor as the ideal systems for drawing conclusions from a conditional base. However, there has been no simple characterization of these relations, other than its original…