Related papers: Interactive Realizability, Monads and Witness Extr…

Existing human motion Q\&A methods rely on explicit program execution, where the requirement for manually defined functional modules may limit the scalability and adaptability. To overcome this, we propose an implicit program-guided motion…

Mechanistic interpretability aims to understand model behaviors in terms of specific, interpretable features, often hypothesized to manifest as low-dimensional subspaces of activations. Specifically, recent studies have explored subspace…

In this work, we consider the fundamental problem of reachability analysis over imperative programs with real variables. The reachability property requires that a program can reach certain target states during its execution. Previous works…

This is the author's Ph.D. Thesis. It contains results from four years of research into realizability and categorical logic. The main subjects are the axiomatisation of realizable propositions, and a characterization of realizability…

How difficult are interactive theorem provers to use? We respond by reviewing the formalization of Hilbert's tenth problem in Isabelle/HOL carried out by an undergraduate research group at Jacobs University Bremen. We argue that, as…

The recently initiated approach called computability logic is a formal theory of interactive computation. See a comprehensive online source on the subject at http://www.cis.upenn.edu/~giorgi/cl.html . The present paper contains a soundness…

We propose a monotonic logic of internalised non-monotonic or instant interactive proofs (LiiP) and reconstruct an existing monotonic logic of internalised monotonic or persistent interactive proofs (LiP) as a minimal conservative extension…

Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform…

The abductive natural language inference task ($\alpha$NLI) is proposed to infer the most plausible explanation between the cause and the event. In the $\alpha$NLI task, two observations are given, and the most plausible hypothesis is asked…

Realizable online regression can behave very differently from online classification. Even without any margin or stochastic assumptions, realizability may enforce horizon-free (finite) cumulative loss under metric-like losses, even when the…

Explanations for AI models in high-stakes domains like medicine often lack verifiability, which can hinder trust. To address this, we propose an interactive agent that produces explanations through an auditable sequence of actions. The…

The theory of classical realizability is a framework in which we can develop the proof-program correspondence. Using this framework, we show how to transform into programs the proofs in classical analysis with dependent choice and the…

For machine learning models to be most useful in numerous sociotechnical systems, many have argued that they must be human-interpretable. However, despite increasing interest in interpretability, there remains no firm consensus on how to…

To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…

The paper gives a soundness and completeness proof for the implicative fragment of intuitionistic calculus with respect to the semantics of computability logic, which understands intuitionistic implication as interactive algorithmic…

We present a new type system with support for proofs of programs in a call-by-value language with control operators. The proof mechanism relies on observational equivalence of (untyped) programs. It appears in two type constructors, which…

Abductive reasoning is a popular non-monotonic paradigm that aims to explain observed symptoms and manifestations. It has many applications, such as diagnosis and planning in artificial intelligence and database updates. In propositional…

We introduce a notion of realizability with ordinal Turing machines based on recognizability rather than computability, i.e., the ability to uniquely identify an object. We show that the arising concept of $r$-realizabilty has the property…

OnlineProver is an interactive proof assistant tailored for the educational setting. Its main features include a user-friendly interface for editing and checking proofs. The user interface provides feedback directly within the derivation,…

While intelligent tutoring systems (ITSs) can use information from past students to personalize instruction, each new student is unique. Moreover, the education problem is inherently difficult because the learning process is only partially…