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Hilary Putnam once suggested that "the actual existence of sets as 'intangible objects' suffers... from a generalization of a problem first pointed out by Paul Benacerraf... are sets a kind of function or are functions a sort of set?"…
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
Classical probability theory is formulated using sets. In this paper, we extend classical probability theory with propositional computability logic. Unlike other formalisms, computability logic is built on the notion of events/games, which…
In this expository article we highlight the relevance of explanations for artificial intelligence, in general, and for the newer developments in {\em explainable AI}, referring to origins and connections of and among different approaches.…
Bipartite experiments are a recent object of study in causal inference, whereby treatment is applied to one set of units and outcomes of interest are measured on a different set of units. These experiments are particularly useful in…
We introduce a notion of quantum function, and develop a compositional framework for finite quantum set theory based on a 2-category of quantum sets and quantum functions. We use this framework to formulate a 2-categorical theory of quantum…
A choice of optimization objective is immensely pivotal in the design of a recommender system as it affects the general modeling process of a user's intent from previous interactions. Existing approaches mainly adhere to three categories of…
In Natural Language Understanding, the task of response generation is usually focused on responses to short texts, such as tweets or a turn in a dialog. Here we present a novel task of producing a critical response to a long argumentative…
The present paper deals with the perturbation analysis of set-valued inclusion problems, a problem format whose relevance has recently emerged in such contexts as robust and vector optimization as well as in vector equilibrium theory. The…
The paper studies complementary choice functions, i.e. monotonic and consistent choice functions. Such choice functions were introduced and used in the work \cite{RY} for investigation of matchings with complementary contracts. Three…
In graph theory and its practical networking applications, e.g., telecommunications and transportation, the problem of finding paths has particular importance. Selecting paths requires giving scores to the alternative solutions to drive a…
This paper develops a new approach to computational argumentation that is informed by philosophical and linguistic views. Namely, it takes into account two ideas that have received little attention in the literature on computational…
We introduce a concept called a collective: an interface with a protocol for aggregating contributions and distributing returns. Through such a protocol, many members may participate in a mutual endeavor. We present a variety of real-world…
Despite their ubiquitous use, Shapley value feature attributions can be misleading due to feature interaction in both model and data. We propose an alternative attribution approach, Shapley Sets, which awards value to sets of features.…
For argumentation mining, there are several sub-tasks such as argumentation component type classification, relation classification. Existing research tends to solve such sub-tasks separately, but ignore the close relation between them. In…
In a nutshell, submodular functions encode an intuitive notion of diminishing returns. As a result, submodularity appears in many important machine learning tasks such as feature selection and data summarization. Although there has been a…
In this paper, we present two methods to provide explanations for reasoning with belief functions in the valuation-based systems. One approach, inspired by Strat's method, is based on sensitivity analysis, but its computation is simpler…
We introduce a Gaussian process model of functions which are additive. An additive function is one which decomposes into a sum of low-dimensional functions, each depending on only a subset of the input variables. Additive GPs generalize…
This work explores the novel idea of learning a submodular scoring function to improve the specificity/selectivity of existing feature attribution methods. Submodular scores are natural for attribution as they are known to accurately model…
In this article, we define the Set Shaping Theory whose goal is the study of the bijection functions that transform a set of strings into a set of equal size made up of strings of greater length. The functions that meet this condition are…