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For certain problems involving vector fields, it is possible to find an associated imaginary field that, in conjunction with the first, forms a complex field for which the equation can be solved. This result is generalized to arbitrary…

Differential Geometry · Mathematics 2007-05-23 Dennis Hou

LLMs can be unpredictable, as even slight alterations to the prompt can cause the output to change in unexpected ways. Thus, the ability of models to accurately explain their behavior is critical, especially in high-stakes settings. One…

Computation and Language · Computer Science 2025-11-26 Marvin Limpijankit , Yanda Chen , Melanie Subbiah , Nicholas Deas , Kathleen McKeown

Counterfactual reasoning, a cornerstone of human cognition and decision-making, is often seen as the 'holy grail' of causal learning, with applications ranging from interpreting machine learning models to promoting algorithmic fairness.…

Machine Learning · Computer Science 2025-04-11 Yahya Aalaila , Gerrit Großmann , Sumantrak Mukherjee , Jonas Wahl , Sebastian Vollmer

In this article we propose an approach that models the truth behavior of cognitive entities (i.e. sets of connected propositions) by taking into account in a very explicit way the possible influence of the cognitive person (the one that…

Quantum Physics · Physics 2007-05-23 Diederik Aerts , Jan Broekaert , Sonja Smets

Estimating an individual's potential outcomes under counterfactual treatments is a challenging task for traditional causal inference and supervised learning approaches when the outcome is high-dimensional (e.g. gene expressions, impulse…

Machine Learning · Statistics 2025-02-13 Yulun Wu , Layne C. Price , Zichen Wang , Vassilis N. Ioannidis , Robert A. Barton , George Karypis

The purpose of this paper is to introduce justification logics based on conditional logics. We introduce a new family of logics, called conditional justification logics, which incorporates a counterfactual conditional in its language. For…

Logic · Mathematics 2025-01-17 Meghdad Ghari

One well motivated explanation method for classifiers leverages counterfactuals which are hypothetical events identical to real observations in all aspects except for one feature. Constructing such counterfactual poses specific challenges…

Machine Learning · Computer Science 2024-09-12 Pirmin Lemberger , Antoine Saillenfest

In the wake of responsible AI, interpretability methods, which attempt to provide an explanation for the predictions of neural models have seen rapid progress. In this work, we are concerned with explanations that are applicable to natural…

Computation and Language · Computer Science 2023-05-29 Giorgos Filandrianos , Edmund Dervakos , Orfeas Menis-Mastromichalakis , Chrysoula Zerva , Giorgos Stamou

In eXplainable Artificial Intelligence (XAI), counterfactual explanations are known to give simple, short, and comprehensible justifications for complex model decisions. However, we are yet to see more applied studies in which they are…

Artificial Intelligence · Computer Science 2023-05-18 Raphael Mazzine Barbosa de Oliveira , Sofie Goethals , Dieter Brughmans , David Martens

Counterfactual reasoning and contextuality is defined and critically evaluated with regard to its nonempirical content. To this end, a uniqueness property of states, explosion views and link observables are introduced. If only a single…

Quantum Physics · Physics 2009-11-10 Karl Svozil

Verifying the correctness of a textual statement requires not only semantic reasoning about the meaning of words, but also symbolic reasoning about logical operations like count, superlative, aggregation, etc. In this work, we propose…

Computation and Language · Computer Science 2020-04-29 Wanjun Zhong , Duyu Tang , Zhangyin Feng , Nan Duan , Ming Zhou , Ming Gong , Linjun Shou , Daxin Jiang , Jiahai Wang , Jian Yin

Counterfactuals operationalised through algorithmic recourse have become a powerful tool to make artificial intelligence systems explainable. Conceptually, given an individual classified as y -- the factual -- we seek actions such that…

We study decision-making problems where data comprises points from a collection of binary polytopes, capturing aggregate information stemming from various combinatorial selection environments. We propose a nonparametric approach for…

Optimization and Control · Mathematics 2026-02-24 Yanqiu Ruan , Karthyek Murthy , Karthik Natarajan

Recently, eXplainable AI (XAI) research has focused on counterfactual explanations as post-hoc justifications for AI-system decisions (e.g. a customer refused a loan might be told: If you asked for a loan with a shorter term, it would have…

Artificial Intelligence · Computer Science 2023-05-10 Saugat Aryal , Mark T Keane

In many applications, it is important to be able to explain the decisions of machine learning systems. An increasingly popular approach has been to seek to provide \emph{counterfactual instance explanations}. These specify close possible…

Artificial Intelligence · Computer Science 2021-09-22 Adam White , Artur d'Avila Garcez

Providing clear explanations to the choices of machine learning models is essential for these models to be deployed in crucial applications. Counterfactual and semi-factual explanations have emerged as two mechanisms for providing users…

Machine Learning · Computer Science 2026-01-15 André Artelt , Martin Olsen , Kevin Tierney

Complex vector analysis is widely used to analyze continuous systems in many disciplines, including physics and engineering. In this paper, we present a higher-order-logic formalization of the complex vector space to facilitate conducting…

Logic in Computer Science · Computer Science 2014-05-19 Sanaz Khan-Afshar , Vincent Aravantinos , Osman Hasan , Sofiene Tahar

Recommender system practitioners are facing increasing pressure to explain recommendations. We explore how to explain recommendations using counterfactual logic, i.e. "Had you not interacted with the following items, we would not recommend…

Artificial Intelligence · Computer Science 2023-02-10 Yuanshun Yao , Chong Wang , Hang Li

Natural language explanations of deep neural network decisions provide an intuitive way for a AI agent to articulate a reasoning process. Current textual explanations learn to discuss class discriminative features in an image. However, it…

Computer Vision and Pattern Recognition · Computer Science 2018-06-27 Lisa Anne Hendricks , Ronghang Hu , Trevor Darrell , Zeynep Akata

Counterfactual explanations shed light on the decisions of black-box models by explaining how an input can be altered to obtain a favourable decision from the model (e.g., when a loan application has been rejected). However, as noted…

Machine Learning · Computer Science 2023-12-13 Francesco Leofante , Nico Potyka