Related papers: Invariance under permutations as a semantic motiva…
We study the complexity of invariant inference and its connections to exact concept learning. We define a condition on invariants and their geometry, called the fence condition, which permits applying theoretical results from exact concept…
The invariant is one of central topics in science, technology and engineering. The differential invariant is essential in understanding or describing some important phenomena or procedures in mathematics, physics, chemistry, biology or…
Justification theory is a unifying semantic framework. While it has its roots in non-monotonic logics, it can be applied to various areas in computer science, especially in explainable reasoning; its most central concept is a justification:…
Reasoning about unpredicted change consists in explaining observations by events; we propose here an approach for explaining time-stamped observations by surprises, which are simple events consisting in the change of the truth value of a…
We look at intensionality from the perspective of computation. In particular, we review how game semantics has been used to characterize the sequential functional processes, leading to powerful and flexible methods for constructing fully…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
Let $A$ be a finite or countable alphabet and let $\theta$ be literal (anti)morphism onto $A^*$ (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under…
It is generally believed that a full-fledged theory of quantum gravity should exhibit background independence and diffeomorphism invariance. In its most general form, the latter comprises field redefinitions, which are diffeomorphisms in…
We discuss recent work for causal inference and predictive robustness in a unifying way. The key idea relies on a notion of probabilistic invariance or stability: it opens up new insights for formulating causality as a certain risk…
This paper is primarily concerned with assessing a set-theoretical system, $S^*$, for the foundations of category theory suggested by Solomon Feferman. $S^*$ is an extension of NFU, and may be seen as an attempt to accommodate unrestricted…
Twenty years ago, in an article titled "Covariance and contravariance: conflict without a cause", I argued that covariant and contravariant specialization of method parameters in object-oriented programming had different purposes and…
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…
The affine group of a tree is the group of the isometries of a homogeneous tree that fix an end of its boundary. Consider a probability measure on this group and the associated random walk. The main goal of this paper is to determine the…
Majorisation, also called rearrangement inequalities, yields a type of stochastic ordering in which two or more distributions can be compared. In this paper we argue that majorisation is a good candidate as a theory for uncertainty. We…
Promoting a theory with a finite number of terms into an effective field theory with an infinite number of terms worsens simplicity, predictability, falsifiability, and other attributes often favored in theory choice. However, the…
This paper presents a novel possible worlds semantics, designed to elucidate the underpinnings of ultrafinitism. By constructing a careful modification of the well-known Kripke models for inuitionistic logic, we seek to extend our…
Inferential relations govern our concept use. In order to understand a concept it has to be located in a space of implications. There are different kinds of conditions for statements, i.e. that the conditions represent different kinds of…
Qubits have been designed in the framework of quantum mechanics. Attempts to formulate the problem in the language of quantum field theory have been proposed already. In this short note we refine the meaning of qubits within the framework…
The paper studies the notion of supposition encoded in non-Archimedean conditional probability (and revealed in the acceptance of the so-called indicative conditionals). The notion of qualitative change of view that thus arises is…
This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argumentative-consequence relation taking into account the existence of consistent arguments in favor of a conclusion and the…