Related papers: Constructive Analysis in the Agda Proof Assistant
While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…
In structural proof theory, designing and working on large calculi make it difficult to get intuitions about each rule individually and as part of a whole system. We introduce two novel tools to help working on calculi using the approach of…
An invaluable feature of computer algebra systems is their ability to plot the graph of functions. Unfortunately, when one is trying to design a library of mathematical functions, this feature often falls short, producing incorrect and…
This study provides some results about two-level type-theoretic notions in a way that the proofs are fully formalizable in a proof assistant implementing two-level type theory such as Agda. The difference from prior works is that these…
The algebraic properties of the combination of probabilistic choice and nondeterministic choice have long been a research topic in program semantics. This paper explains a formalization in the Coq proof assistant of a monad equipped with…
Electronic exams (e-exams) have the potential to substantially reduce the effort required for conducting an exam through automation. Yet, care must be taken to sacrifice neither task complexity nor constructive alignment nor grading…
Proof assistants are software-based tools that are used in the mechanization of proof construction and validation in mathematics and computer science, and also in certified program development. Different tools are being increasingly used in…
Evaluating the abilities of learners is a fundamental objective in the field of education. In particular, there is an increasing need to assess higher-order abilities such as expressive skills and logical thinking. Constructed-response…
AuDaLa is a recently introduced programming language that follows the new data autonomous paradigm. In this paradigm, small pieces of data execute functions autonomously. Considering the paradigm and the design choices of AuDaLa, it is…
Explainable Artificial Intelligence and Formal Argumentation have received significant attention in recent years. Argumentation-based systems often lack explainability while supporting decision-making processes. Counterfactual and…
Teaching college students how to write rigorous proofs is a critical objective in courses that introduce formal reasoning. Over the course of several years, we have developed a mechanically-checkable style of calculational reasoning that we…
Principal Component Analysis and biplots are so well-established and readily implemented that it is just too tempting to give for granted their internal workings. In this note I get back to basics in comparing how PCA and biplots are…
For typical first-order logical theories, satisfying assignments have a straightforward finite representation that can directly serve as a certificate that a given assignment satisfies the given formula. For non-linear real arithmetic…
Recent trends in AI verification and Explainable AI have raised the question of whether AI planning techniques can be verified. In this paper, we present a novel resource logic, the Proof Carrying Plans (PCP) logic that can be used to…
Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…
This paper presents the Soda language for verifying multi-agent systems. Soda is a high-level functional and object-oriented language that supports the compilation of its code not only to Scala, a strongly statically typed high-level…
Bias in AI systems can lead to unfair and discriminatory outcomes, especially when left untested before deployment. Although fairness testing aims to identify and mitigate such bias, existing tools are often difficult to use, requiring…
Legal expert systems routinely rely on date computations to determine the eligibility of a citizen to social benefits or whether an application has been filed on time. Unfortunately, date arithmetic exhibits many corner cases, which are…
The rapid advancements in large language models and generative artificial intelligence (AI) capabilities are making their broad application in the high-stakes testing context more likely. Use of generative AI in the scoring of constructed…
Principal component analysis (PCA) is by far the most widespread tool for unsupervised learning with high-dimensional data sets. Its application is popularly studied for the purpose of exploratory data analysis and online process…