Related papers: Logically-consistent hypothesis testing in the hex…
Epistemic logic programs constitute an extension of the stable models semantics to deal with new constructs called subjective literals. Informally speaking, a subjective literal allows checking whether some regular literal is true in all…
We present a propositional logic 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 complete axiomatization…
Despite great performance on Olympiad-level reasoning problems, frontier large language models can still struggle on high school math when presented with novel problems outside standard benchmarks. Going beyond final accuracy, we propose a…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
Evidential reasoning is cast as the problem of simplifying the evidence-hypothesis relation and constructing combination formulas that possess certain testable properties. Important classes of evidence as identifiers, annihilators, and…
Propositional and modal inclusion logic are formalisms that belong to the family of logics based on team semantics. This article investigates the model checking and validity problems of these logics. We identify complexity bounds for both…
Statistical hypothesis testing is the central method to demarcate scientific theories in both exploratory and inferential analyses. However, whether this method befits such purpose remains a matter of debate. Established approaches to…
We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second G\"odel incompleteness theorem to stably…
In many mathematical models for pattern formation, a regular hexagonal pattern is stable in an infinite region. However, laboratory and numerical experiments are carried out in finite domains, and this imposes certain constraints on the…
Explaining autonomous and intelligent systems is critical in order to improve trust in their decisions. Counterfactuals have emerged as one of the most compelling forms of explanation. They address ``why not'' questions by revealing how…
This article examines two approaches to verification, one based on using a logic for expressing properties of a system, and one based on showing the system equivalent to a simpler system that obviously has whatever property is of interest.…
For $\chi^2-$tests with increasing number of cells, Cramer-von Mises tests, tests generated $\mathbb{L}_2$- norms of kernel estimators and tests generated quadratic forms of estimators of Fourier coefficients, we find necessary and…
The introduction of explicit notions of rejection, or disbelief, into logics for knowledge representation can be justified in a number of ways. Motivations range from the need for versions of negation weaker than classical negation, to the…
In this paper, we propose a comprehensive benchmark to investigate models' logical reasoning capabilities in complex real-life scenarios. Current explanation datasets often employ synthetic data with simple reasoning structures. Therefore,…
While Large language models (LLMs) have proved able to address some complex reasoning tasks, we also know that they are highly sensitive to input variation, which can lead to different solution paths and final answers. Answer consistency…
This paper develops a consistent heteroskedasticity robust Lagrange Multiplier (LM) type specification test for semiparametric conditional mean models. Consistency is achieved by turning a conditional moment restriction into a growing…
A number of biomedical problems require performing many hypothesis tests, with an attendant need to apply stringent thresholds. Often the data take the form of a series of predictor vectors, each of which must be compared with a single…
As large language models (LLMs) are increasing integrated into fact-checking pipelines, formal logic is often proposed as a rigorous means by which to mitigate bias, errors and hallucinations in these models' outputs. For example, some…
In two earlier papers we derived congruence formats with regard to transition system specifications for weak semantics on the basis of a decomposition method for modal formulas. The idea is that a congruence format for a semantics must…
In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation…