Related papers: Arrow-Sen theory simplified
Subatomic systems were recently introduced to identify the structural principles underpinning the normalization of proofs. "Subatomic" means that we can reformulate logical systems in accordance with two principles. Their atomic formulas…
We study finite first-order satisfiability (FSAT) in the constructive setting of dependent type theory. Employing synthetic accounts of enumerability and decidability, we give a full classification of FSAT depending on the first-order…
To the best of our knowledge, a complete characterization of the domains that escape the famous Arrow's impossibility theorem remains an open question. We believe that different ways of proving Arrovian theorems illuminate this problem.…
We consider a family of binary triangular arrays, called approval ballot triangles (ABTs), that are in bijection with totally symmetric self-complementary plane partitions (TSSCPPs). These triangles correspond to a ballot process in which…
This paper contributes to a development of randomized methods for neural networks. The proposed learner model is generated incrementally by stochastic configuration (SC) algorithms, termed as Stochastic Configuration Networks (SCNs). In…
Users of OCR systems, from different institutions and scientific disciplines, prefer and produce different transcription styles. This presents a problem for training of consistent text recognition neural networks on real-world data. We…
One of the ultimate goals of representation learning is to achieve compactness within a class and well-separability between classes. Many outstanding metric-based and prototype-based methods following the Expectation-Maximization paradigm,…
Interpretable machine learning is essential in high-stakes domains where decision-making requires accountability, transparency, and trust. While rule-based models offer global and exact interpretability, learning rule sets that…
Selecting input features of top relevance has become a popular method for building self-explaining models. In this work, we extend this selective rationalization approach to text matching, where the goal is to jointly select and align text…
The field of fair AI aims to counter biased algorithms through computational modelling. However, it faces increasing criticism for perpetuating the use of overly technical and reductionist methods. As a result, novel approaches appear in…
In this paper, we describe the formalization of the axiom of choice and several of its famous equivalent theorems in Morse-Kelley set theory. These theorems include Tukey's lemma, the Hausdorff maximal principle, the maximal principle,…
Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take…
Let X be a finite set of alternatives. A choice function c is a mapping which assigns to nonempty subsets S of X an element c(S) of S. A rational choice function is one for which there is a linear ordering on the alternatives such that c(S)…
Abstractive text summarization is a highly difficult problem, and the sequence-to-sequence model has shown success in improving the performance on the task. However, the generated summaries are often inconsistent with the source content in…
We investigate the domain of satisfiable formulas in satisfiability modulo theories (SMT), in particular, automatic generation of a multitude of satisfying assignments to such formulas. Despite the long and successful history of SMT in…
We introduce a top-down approach to discourse parsing that is conceptually simpler than its predecessors (Kobayashi et al., 2020; Zhang et al., 2020). By framing the task as a sequence labelling problem where the goal is to iteratively…
Feature selection identifies subsets of informative features and reduces dimensions in the original feature space, helping provide insights into data generation or a variety of domain problems. Existing methods mainly depend on feature…
The paper is the second of two and shows that (assuming large cardinals) set theory is a tractable (and we dare to say tame) first order theory when formalized in a first order signature with natural predicate symbols for the basic…
TMs are a pattern recognition approach that uses finite state machines for learning and propositional logic to represent patterns. In addition to being natively interpretable, they have provided competitive accuracy for various tasks. In…
In social choice theory, Sen's value restriction and Pattanaik's not-strict value restriction are both attractive conditions for testing social preference transitivity and/or non-empty social choice set existence. This article introduces a…