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A set is introreducible if it can be computed by every infinite subset of itself. Such a set can be thought of as coding information very robustly. We investigate introreducible sets and related notions. Our two main results are that the…
A logic for specification and verification is derived from the axioms of Zermelo-Fraenkel set theory. The proofs are performed using the proof assistant Isabelle. Isabelle is generic, supporting several different logics. Isabelle has the…
Vast amounts of text on the Web are unstructured and ungrammatical, such as classified ads, auction listings, forum postings, etc. We call such text "posts." Despite their inconsistent structure and lack of grammar, posts are full of useful…
We study codes with a single check element derived from group rings, namely, checkable codes. The notion of a code-checkable group ring is introduced. Necessary and sufficient conditions for a group ring to be code-checkable are given in…
As machine learning is increasingly used to help make decisions, there is a demand for these decisions to be explainable. Arguably, the most explainable machine learning models use decision rules. This paper focuses on decision sets, a type…
Definition bias is a negative phenomenon that can mislead models. Definition bias in information extraction appears not only across datasets from different domains but also within datasets sharing the same domain. We identify two types of…
Conditions are essential in the statements of biological literature. Without the conditions (e.g., environment, equipment) that were precisely specified, the facts (e.g., observations) in the statements may no longer be valid. One…
Algebraic systems are constructed from which series of maximum distance separable (mds) codes are derived. The methods use unit and idempotent schemes.
The use of Bayesian information criterion (BIC) in the model selection procedure is under the assumption that the observations are independent and identically distributed (i.i.d.). However, in practice, we do not always have i.i.d. samples.…
Credal sets are sets of probability distributions that are considered as candidates for an imprecisely known ground-truth distribution. In machine learning, they have recently attracted attention as an appealing formalism for uncertainty…
We propose a method for generating explainable rule sets from tree-ensemble learners using Answer Set Programming (ASP). To this end, we adopt a decompositional approach where the split structures of the base decision trees are exploited in…
We give a new proof of quantifier elimination in the theory of all ordered abelian groups in a suitable language. More precisely, this is only "quantifier elimination relative to ordered sets" in the following sense. Each definable set in…
One of the key concepts in testing is that of adequate test sets. A test selection criterion decides which test sets are adequate. In this paper, a language schema for specifying a large class of test selection criteria is developed; the…
A scoring system is a simple decision model that checks a set of features, adds a certain number of points to a total score for each feature that is satisfied, and finally makes a decision by comparing the total score to a threshold.…
The safe integration of machine learning modules in decision-making processes hinges on their ability to quantify uncertainty. A popular technique to achieve this goal is conformal prediction (CP), which transforms an arbitrary base…
For any finite totally ordered set, the multisets of intervals form an abelian category. Various classes of subcategories admit natural combinatorial descriptions, and counting them yields familiar integer sequences. Surprisingly, in some…
A prevailing assumption in machine learning is that model correctness must be enforced after the fact. We observe that the properties determining whether an AI model is numerically stable, computationally correct, or consistent with a…
We apply the foundational proof certificate (FPC) framework to the problem of designing high-level outlines of proofs. The FPC framework provides a means to formally define and check a wide range of proof evidence. A focused proof system is…
This work presents a systematic study of objective evaluations of abstaining classifications using Information-Theoretic Measures (ITMs). First, we define objective measures for which they do not depend on any free parameter. This…
International Classification of Diseases (ICD) are the de facto codes used globally for clinical coding. These codes enable healthcare providers to claim reimbursement and facilitate efficient storage and retrieval of diagnostic…