Related papers: Remarks on Fixed Point Assertions in Digital Topol…

We look at characterizing which formulas are expressible in rich decidable logics such as guarded fixpoint logic, unary negation fixpoint logic, and guarded negation fixpoint logic. We consider semantic characterizations of definability, as…

We prove that compact topological 4-manifolds can be effectively presented by a finite amount of data.

This note corrects conditions in Proposition 3.4 and Theorem 5.2(ii) and comments on imprecisions in Propositions 4.2 and 4.4 in Fissler and Ziegel (2016).

I reply to the four points raised by S. A. Hayward, R. Di Criscienzo, M. Nadalini, L. Vanzo, S. Zerbini (arXiv:0909.2956v1) against my comment (arXiv:0907.2020v1) to their previous article. I maintain my position on the wrongness of their…

The present paper focuses on the notions of covering spaces, pseudo-covering spaces, and their equivalences. We discuss something incorrectly mentioned in Boxer's papers and correct them. Indeed, Sections 4-6 (or 4-6) of \cite{B3} are…

Improvements in large language models have led to increasing optimism that they can serve as reliable evaluators of natural language generation outputs. In this paper, we challenge this optimism by thoroughly re-evaluating five…

The definition of the weighted version of difficulty in "Termination of 4-fold canonical flips" contains some errors. In this paper, we describe these errors and how to correct them. Anyway, any sequence of 4-fold canonical flips…

Counterfactual explanations are emerging as an attractive option for providing recourse to individuals adversely impacted by algorithmic decisions. As they are deployed in critical applications (e.g. law enforcement, financial lending), it…

In this note the authors have raised the question regarding the validity of the main result in [1] by setting an example.

We present a new and compelling approach to the efficient solution of important computational problems that arise in the context of abstract argumentation. Our approach makes known algorithms defined for restricted fragments generally…

The purpose of this erratum and addendum is to correct the errors in [1]. It consists of five components: 1. Lemma 7.1 and Proposition 7.2 are wrong and discarded; 2. A new proof of existence $\lambda(\xi)$ in (7.1) without Proposition 7.2;…

This work concludes a series of four papers on the foundational theory of orbifolds and stacks. We apply the abstract theory, developed in its predecessors, to orbifolds derived from manifolds. Specifically, we show how the very concrete…

In this note we correct two errors in our paper "On the Homology of Completion and Torsion", arXiv:1010.4386, that appeared in Algebras and Representation Theory (2014).

This position paper provides a critical but constructive discussion of current practices in benchmarking and evaluative practices in the field of formal reasoning and automated theorem proving. We take the position that open code, open…

In this note we document a gap in an argument in the above paper, and point to new work in the literature giving a complete proof of the main result.

We correct some oversights in the paper "A spectral sequence for stratified spaces and configuration spaces of points" by the second named author. In particular we explain that an additional hypothesis should be added to Theorem 4.15 in…

On [3, p. 199] one says "We mention parenthetically that the proof of [99, Lemma 41.3] is incorrect, and we do not know whether it, [99, Theorem 41.5] and [99, Theorem 41.6] are true". The previously cited reference [99] is our reference…

Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…

Abstract argumentation offers an appealing way of representing and evaluating arguments and counterarguments. This approach can be enhanced by a probability assignment to each argument. There are various interpretations that can be ascribed…

Here we give a reformulation of a key lemma in the paper [2], "Spaces of Topological Complexity One", which is necessary due to an oversight.