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We describe a graph-theoretic syntax for self-referential formulas as well as a four-valued logic to include contradictory and independent formulas. We then explore the degree to which generalized truth tables can be realized in our theory,…

Logic · Mathematics 2007-05-23 Dan Seabold , Stefan Waner , Steve Warner

In the paper, the question whether truth values can be assigned to the propositions before their verification is discussed. To answer this question, a notion of a propositionally noncontextual theory is introduced that in order to explain…

Quantum Physics · Physics 2017-09-27 Arkady Bolotin

There are some recent approaches and results about the use of answer-set programming for specifying counterfactual interventions on entities under classification, and reasoning about them. These approaches are flexible and modular in that…

Artificial Intelligence · Computer Science 2021-08-26 Leopoldo Bertossi

Machine learning plays a role in many deployed decision systems, often in ways that are difficult or impossible to understand by human stakeholders. Explaining, in a human-understandable way, the relationship between the input and output of…

Machine Learning · Computer Science 2022-11-17 Sahil Verma , Varich Boonsanong , Minh Hoang , Keegan E. Hines , John P. Dickerson , Chirag Shah

Recent work by Chatzi et al. and Ravfogel et al. has developed, for the first time, a method for generating counterfactuals of probabilistic Large Language Models. Such counterfactuals tell us what would - or might - have been the output of…

Artificial Intelligence · Computer Science 2026-04-21 Sander Beckers

Machine learning can impact people with legal or ethical consequences when it is used to automate decisions in areas such as insurance, lending, hiring, and predictive policing. In many of these scenarios, previous decisions have been made…

Machine Learning · Statistics 2018-03-09 Matt J. Kusner , Joshua R. Loftus , Chris Russell , Ricardo Silva

Counterfactual thinking is a crucial yet challenging topic for artificial intelligence to learn knowledge from data and ultimately improve performance for new scenarios. Many research works, including the Potential Outcome Model (POM) and…

Artificial Intelligence · Computer Science 2026-02-24 Mingyu Kang , Duxin Chen , Ziyuan Pu , Jianxi Gao , Wenwu Yu

We consider counterfactual explanations, the problem of minimally adjusting features in a source input instance so that it is classified as a target class under a given classifier. This has become a topic of recent interest as a way to…

Machine Learning · Computer Science 2021-03-02 Miguel Á. Carreira-Perpiñán , Suryabhan Singh Hada

Transparency is an essential requirement of machine learning based decision making systems that are deployed in real world. Often, transparency of a given system is achieved by providing explanations of the behavior and predictions of the…

Machine Learning · Computer Science 2021-05-18 André Artelt , Barbara Hammer

We propose an architecture for training generative models of counterfactual conditionals of the form, 'can we modify event A to cause B instead of C?', motivated by applications in robot control. Using an 'adversarial training' paradigm, an…

Robotics · Computer Science 2020-09-23 Simón C. Smith , Subramanian Ramamoorthy

Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…

Programming Languages · Computer Science 2015-02-05 Mauro Jaskelioff , Russell O'Connor

Probabilistic logic programs are logic programs where some facts hold with a specified probability. Here, we investigate these programs with a causal framework that allows counterfactual queries. Learning the program structure from…

Logic in Computer Science · Computer Science 2023-08-31 Kilian Rückschloß , Felix Weitkämper

The concept of imaginary logical values was introduced by Spencer-Brown in Laws of Form, in analogy to the square root of -1 in the complex numbers. In this paper, we develop a new approach to representing imaginary values. The resulting…

Logic · Mathematics 2020-04-28 Louis H. Kauffman , Arthur M. Collings

Being able to provide counterfactual interventions - sequences of actions we would have had to take for a desirable outcome to happen - is essential to explain how to change an unfavourable decision by a black-box machine learning model…

Machine Learning · Computer Science 2023-02-08 Giovanni De Toni , Bruno Lepri , Andrea Passerini

Causality is vital for understanding true cause-and-effect relationships between variables within predictive models, rather than relying on mere correlations, making it highly relevant in the field of Explainable AI. In an automated…

Machine Learning · Computer Science 2024-08-28 Arturo Fredes , Jordi Vitria

Due to the significant advancement of Natural Language Processing and Computer Vision-based models, Visual Question Answering (VQA) systems are becoming more intelligent and advanced. However, they are still error-prone when dealing with…

Computer Vision and Pattern Recognition · Computer Science 2022-01-11 Zeyd Boukhers , Timo Hartmann , Jan Jürjens

We give a detailed exposition of the "vectorized" notation for dealing with quantum operations. This notation is used to highlight the relationships between representations of completely-positive dynamics. Vectorization considerably…

Quantum Physics · Physics 2011-08-19 Alexei Gilchrist , Daniel R. Terno , Christopher J. Wood

While machine learning models are usually assumed to always output a prediction, there also exist extensions in the form of reject options which allow the model to reject inputs where only a prediction with an unacceptably low certainty…

Machine Learning · Computer Science 2022-02-16 André Artelt , Johannes Brinkrolf , Roel Visser , Barbara Hammer

Counterfactual reasoning, a fundamental aspect of human cognition, involves contemplating alternatives to established facts or past events, significantly enhancing our abilities in planning and decision-making. In light of the advancements…

Computation and Language · Computer Science 2024-04-17 Letian Zhang , Xiaotong Zhai , Zhongkai Zhao , Yongshuo Zong , Xin Wen , Bingchen Zhao

We introduce a formalism for the evaluation of counterfactual queries in the framework of quantum causal models, generalising Pearl's semantics for counterfactuals in classical causal models, thus completing the last rung in the quantum…

Quantum Physics · Physics 2024-09-18 Ardra Kooderi Suresh , Markus Frembs , Eric G. Cavalcanti