Related papers: Logically-consistent hypothesis testing in the hex…
Tremendous research effort has been dedicated over the years to thoroughly investigate non-monotonic reasoning. With the abundance of non-monotonic logical formalisms, a unified theory that enables comparing the different approaches is much…
We present a family of paraconsistent counterparts of the constructive modal logic CK. These logics aim to formalise reasoning about contradictory but non-trivial propositional attitudes like beliefs or obligations. We define their…
Coherence with respect to Kelly-Mac Lane graphs is proved for categories that correspond to the multiplicative fragment without constant propositions of classical linear first-order predicate logic without or with mix. To obtain this…
The computational properties of modal and propositional dependence logics have been extensively studied over the past few years, starting from a result by Sevenster showing NEXPTIME-completeness of the satisfiability problem for modal…
We consider the problems of hypothesis testing on a probability measure of independent sample, on solution of ill-posed problem, on deconvolution problem and on Poisson mean measure. For all these setups necessary conditions and sufficient…
Three-way logical question answering (QA) assigns one of $\text{True}$, $\text{False}$, or $\text{Unknown}$ to a hypothesis $H$ given a premise set $S$. We study this task as a compact compositional inference problem: predictions for $H$…
We review and test twelve different approaches to the detection of finite-time coherent material structures in two-dimensional, temporally aperiodic flows. We consider both mathematical methods and diagnostic scalar fields, comparing their…
Belief systems are often treated as globally consistent sets of propositions or as scalar-valued probability distributions. Such representations tend to obscure the internal structure of belief, conflate external credibility with internal…
We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set…
We present a propositional logic %which can be used to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and…
The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric.…
We present a brief history of quasicrystals and a short introduction to classical lattice-gas models of interacting particles. We discuss stability of non-periodic tilings and one-dimensional sequences of symbols seen as ground states of…
Large Language Models (LLMs) are expected to be predictable and trustworthy to support reliable decision-making systems. Yet current LLMs often show inconsistencies in their judgments. In this work, we examine logical preference consistency…
In Bayesian statistics the precise point-null hypothesis $\theta=\theta_0$ can be tested by checking whether $\theta_0$ is contained in a credible set. This permits testing of $\theta=\theta_0$ without having to put prior probabilities on…
The cosmic distance duality relation is a milestone of cosmology involving the luminosity and angular diameter distances. Any departure of the relation points to new physics or systematic errors in the observations, therefore tests of the…
In this work we present a generalization of the recently developed Hardy-like logical proof of contextuality and of the so-called KCBS contextuality inequality for any qudit of dimension greater than three. Our approach uses compatibility…
Large language models (LLMs) have achieved remarkable successes on various tasks. However, recent studies have found that there are still significant challenges to the logical reasoning abilities of LLMs, which can be categorized into the…
Logical bilateralism challenges traditional concepts of logic by treating assertion and denial as independent yet opposed acts. While initially devised to justify classical logic, its constructive variants show that both acts admit…
Epistemic and doxastic logics are modal logics for knowledge and belief, and serve as foundational models for rational agents in game theory, philosophy, and computer science. We examine the consequences of modeling agents capable of a…
In the interpretation of experimental data, one is actually looking for plausible explanations. We look for a measure of plausibility, with which we can compare different possible explanations, and which can be combined when there are…