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With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…

Machine Learning · Computer Science 2021-01-05 André Artelt , Barbara Hammer

Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…

Programming Languages · Computer Science 2021-11-29 Eytan Singher , Shachar Itzhaky

The aim of this note is to give a quick algebraic proof of (the combinatorial part of) the classification theorem for compact real surfaces, whose classical proofs (as in the Massey book and in the Conway ZIP proof) are based on surgery…

Algebraic Topology · Mathematics 2012-04-26 Maurizio Cailotto

Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…

Programming Languages · Computer Science 2020-09-22 Kazuhiko Sakaguchi

Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such…

Artificial Intelligence · Computer Science 2014-02-17 Cezary Kaliszyk , Josef Urban

Proof-theoretic methods are developed for subsystems of Johansson's logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems.…

Logic · Mathematics 2019-07-12 Marta Bílková , Almudena Colacito

Recently, computational modelling became a very important research tool that enables us to study problems that for decades evaded scientific analysis. Evolutionary systems are certainly examples of such problems: they are composed of many…

Populations and Evolution · Quantitative Biology 2009-07-04 Adam Lipowski , Dorota Lipowska

We introduce computational causal inference as an interdisciplinary field across causal inference, algorithms design and numerical computing. The field aims to develop software specializing in causal inference that can analyze massive…

Computation · Statistics 2020-07-22 Jeffrey C. Wong

The purpose of this paper is to explore the question "to what extent could we produce formal, machine-verifiable, proofs in real algebraic geometry?" The question has been asked before but as yet the leading algorithms for answering such…

Symbolic Computation · Computer Science 2021-06-17 Erika {Á}brahám , James Davenport , Matthew England , Gereon Kremer , Zak Tonks

The large language models (LLMs) might produce a persuasive argument within mathematical and logical fields, although such argument often includes some minor missteps, including the entire omission of side conditions, invalid inference…

Artificial Intelligence · Computer Science 2026-04-09 Kranthi Kommuru , Kunal Khanvilkar , Gaurav Parekh

In many virus families, tens to thousands of proteins assemble spontaneously into a capsid (protein shell) while packaging the genomic nucleic acid. This review summarizes recent advances in computational modeling of these dynamical…

Biomolecules · Quantitative Biology 2016-07-07 Michael F. Hagan , Roya Zandi

The past years have seen a drastic rise in studies devoted to the investigation of colexification patterns in individual languages families in particular and the languages of the world in specific. Specifically computational studies have…

Computation and Language · Computer Science 2023-02-03 Johann-Mattis List

Declarative modeling uses symbolic expressions to represent models. With such expressions one can formalize high-level mathematical computations on models that would be difficult or impossible to perform directly on a lower-level simulation…

Quantitative Methods · Quantitative Biology 2019-07-02 Eric Mjolsness

The ease and speed of spreading misinformation and propaganda on the Web motivate the need to develop trustworthy technology for detecting fallacies in natural language arguments. However, state-of-the-art language modeling methods exhibit…

Artificial Intelligence · Computer Science 2023-05-19 Zhivar Sourati , Filip Ilievski , Hông-Ân Sandlin , Alain Mermoud

Abstract argumentation frameworks (AFs) provide a formal setting to analyze many forms of reasoning with conflicting information. While the expressiveness of general infinite AFs make them a tempting tool for modeling many kinds of…

Artificial Intelligence · Computer Science 2025-08-26 Uri Andrews , Luca San Mauro

Recent advances in large language models (LLMs) have opened new avenues for accelerating scientific research. While models are increasingly capable of assisting with routine tasks, their ability to contribute to novel, expert-level…

Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…

Programming Languages · Computer Science 2018-05-21 Francisco Ferreira Ruiz

With the relentless rise of computer power, there is a widespread expectation that computers can solve the most pressing problems of science, and even more besides. We explore the limits of computational modelling and conclude that, in the…

Computers and Society · Computer Science 2021-04-28 Peter V. Coveney , Roger R. Highfield

A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…

Category Theory · Mathematics 2010-03-03 J. R. B. Cockett , C. A. Pastro

Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…

Information Theory · Computer Science 2017-08-01 Pat Morin , Wolfgang Mulzer , Tommy Reddad