Related papers: Comparing truth theories based on Weak and Strong …
We investigate the equational theory of Kleene algebra terms with variable complements -- (language) complement where it applies only to variables -- w.r.t. languages. While the equational theory w.r.t. languages coincides with the language…
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…
Counterfactual explanations provide actionable insights to achieve desired outcomes by suggesting minimal changes to input features. However, existing methods rely on fixed sets of mutable features, which makes counterfactual explanations…
We improve upon Huntington's affine geometry by showing that his independence proofs can be, in some cases, simplified. We carry out a systematic investigation of the strict notion of betweenness that Huntington employs (the three arguments…
In this paper, we study counterfactual fairness in text classification, which asks the question: How would the prediction change if the sensitive attribute referenced in the example were different? Toxicity classifiers demonstrate a…
TopKAT is the algebraic theory of Kleene algebra with tests (KAT) extended with a top element. Compared to KAT, one pleasant feature of TopKAT is that, in relational models, the top element allows us to express the domain and codomain of a…
The structure of a complete lattice formed by closed linear subspaces of a Hilbert space (i.e., a Hilbert lattice) entails some unreasonable consequences from the physical point of view. Specifically, this structure seems to contradict to…
Counterfactual explanations have become a mainstay of the XAI field. This particularly intuitive statement allows the user to understand what small but necessary changes would have to be made to a given situation in order to change a model…
We present a Kleene realizability semantics for the intensional level of the Minimalist Foundation, for short mtt, extended with inductively generated formal topologies, Church's thesis and axiom of choice. This semantics is an extension of…
In this paper we prove that no consistent finitely axiomatized theory one-dimensionally interprets its own extension with predicative comprehension. This constitutes a result with the flavor of the Second Incompleteness Theorem whose…
Continuity is one of the most central notions in mathematics, physics, and computer science. An interesting associated topic is decompositions of continuity, where continuity is shown to be equivalent to the combination of two or more weak…
We extend description logics (DLs) with non-monotonic reasoning features. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann and Magidor in the propositional…
Counterfactuals can explain classification decisions of neural networks in a human interpretable way. We propose a simple but effective method to generate such counterfactuals. More specifically, we perform a suitable diffeomorphic…
Feferman (1975) defines an impredicative system $\mathsf{T}_0$ of explicit mathematics, which is proof-theoretically equivalent to the subsystem $\Delta^1_2$-$\mathsf{CA} + \mathsf{BI}$ of second-order arithmetic. In this paper, we propose…
Kedem's Comment [arXiv:1402.1352] on our Letter [PRL 112, 040406 (2014)] contains only the criticism that we did not consider complex weak values. We point out follow-up work which uses the same analysis as in our Letter, includes any type…
This paper establishes a formal framework, grounded in mathematical logic and order theory, to analyze the inherent limitations of radical transparency. We demonstrate that self-referential disclosure policies inevitably encounter…
We develop a fully diagrammatic approach to the theory of finite-state automata, based on reinterpreting their usual state-transition graphical representation as a two-dimensional syntax of string diagrams. Moreover, we provide an…
In the field of Explainable AI, multiples evaluation metrics have been proposed in order to assess the quality of explanation methods w.r.t. a set of desired properties. In this work, we study the articulation between the stability,…
We show that one-way quantum one-counter automaton with zero-error is more powerful than its probabilistic counterpart on promise problems. Then, we obtain a similar separation result between Las Vegas one-way probabilistic one-counter…
We prove two completeness results for Kleene algebra with tests and a top element, with respect to guarded string languages and binary relations. While the equational theories of those two classes of models coincide over the signature of…