Related papers: Why Extension-Based Proofs Fail
Given a sound first-order p-time theory $T$ capable of formalizing syntax of first-order logic we define a p-time function $g_T$ that stretches all inputs by one bit and we use its properties to show that $T$ must be incomplete. We leave it…
Mathematical models of the real world are simplified representations of complex systems. A caveat to using mathematical models is that predicted causal effects and conditional independences may not be robust under model extensions, limiting…
Machine learning algorithms enable advanced decision making in contemporary intelligent systems. Research indicates that there is a tradeoff between their model performance and explainability. Machine learning models with higher performance…
We provide a complete characterization of both uniform and non-uniform deterministic consensus solvability in distributed systems with benign process and communication faults using point-set topology. More specifically, we non-trivially…
In existing simulation proof techniques, a single step in a lower-level specification may be simulated by an extended execution fragment in a higher-level one. As a result, it is cumbersome to mechanize these techniques using general…
While the very first consensus protocols for the synchronous model were designed to match the worst-case lower bound, deciding in exactly t+1 rounds in all runs, it was soon realized that they could be strictly improved upon by early…
We employ the combinatorial atlas technology to prove new correlation inequalities for the number of linear extensions of finite posets. These include the approximate independence of probabilities and expectations of values of random linear…
In this work, we study progress conditions for commutativity-aware, linearizable implementations of shared objects. Motivated by the observation that commuting operations can be executed in parallel, we introduce…
In the present paper, the existence and multiplicity problems of extensions are addressed. The focus is on extension of the stable type. The main result of the paper is an elegant characterization of the existence and multiplicity of…
In this paper a new mathematical procedure is presented for combining different pieces of evidence which are represented in the interval form to reflect our knowledge about the truth of a hypothesis. Evidences may be correlated to each…
Given an argumentation framework AF, we introduce a mapping function that constructs a disjunctive logic program P, such that the preferred extensions of AF correspond to the stable models of P, after intersecting each stable model with the…
The nature and scope of various impossibility proofs as they relate to real-world situations are discussed. In particular, it is shown in words without technical symbols how secure quantum bit commitment protocols may be obtained with…
We introduce a framework of layered subsets, and give a sufficient condition for when a set system supports an agreement test. Agreement testing is a certain type of property testing that generalizes PCP tests such as the plane vs. plane…
It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…
For AI systems to garner widespread public acceptance, we must develop methods capable of explaining the decisions of black-box models such as neural networks. In this work, we identify two issues of current explanatory methods. First, we…
In recent years, explainable machine learning methods have been very successful. Despite their success, most explainable machine learning methods are applied to black-box models without any domain knowledge. By incorporating domain…
Many proof assistants allow the use of features and axioms that increase their expressive power. However, these extensions must be used with care, as some combinations are known to lead to logical inconsistencies. Therefore, proof…
We study the complexity of reachability problems on branching extensions of vector addition systems, which allows us to derive new non-elementary complexity bounds for fragments and variants of propositional linear logic. We show that…
Hidden-variable models aim to reproduce the results of quantum theory and to satisfy our classical intuition. Their refutation is usually based on deriving predictions that are different from those of quantum mechanics. Here instead we…
The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so…