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We present Ax-Prover, a multi-agent system for automated theorem proving in Lean that can solve problems across diverse scientific domains and operate either autonomously or collaboratively with human experts. To achieve this, Ax-Prover…
Most of the engineering and physical systems are generally characterized by differential and difference equations based on their continuous-time and discrete-time dynamics, respectively. Moreover, these dynamical models are analyzed using…
This document describes how to use the XML static analyzer in practice. It provides informal documentation for using the XML reasoning solver implementation. The solver allows automated verification of properties that are expressed as…
This paper presents a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier $I$. $I$ forms a formula from two…
Artificial Intelligence (AI) models increasingly drive high-stakes consumer interactions, yet their decision logic often remains opaque. Prevailing explainable AI techniques rely on post hoc numerical feature attributions, which fail to…
Formal theorem proving with TLA+ provides rigorous guarantees for system specifications, but constructing proofs requires substantial expertise and effort. While large language models have shown promise in automating proofs for tactic-based…
Solving partial differential equations (PDEs) on complex domains can present significant computational challenges. The Diffuse Domain Method (DDM) is an alternative that reformulates the partial differential equations on a larger, simpler…
We fine-tuned and compared several encoder-based Transformer large language models (LLM) to predict differential item functioning (DIF) from the item text. We then applied explainable artificial intelligence (XAI) methods to these models to…
In-context learning (ICL) enables multimodal large language models (MLLMs) to classify images from a few labelled examples. Yet, how these models use the provided context remains opaque. While Chain-of-Thought prompting is widely used,…
Logic-based approaches to AI have the advantage that their behavior can in principle be explained to a user. If, for instance, a Description Logic reasoner derives a consequence that triggers some action of the overall system, then one can…
This paper introduces robust differential dynamic logic (a fragment of differential dynamic logic) to specify and reason about robust hybrid systems. Practically meaningful syntactic restrictions naturally ensure that definable properties…
Formalisms for specifying statistical models, such as probabilistic-programming languages, typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the…
This paper presents the DLV system, which is widely considered the state-of-the-art implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel…
Recent advancements in Large Language Models (LLMs) have demonstrated exceptional capabilities in complex tasks like machine translation, commonsense reasoning, and language understanding. One of the primary reasons for the adaptability of…
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…
Programs must be correct with respect to their application domain. Yet, the program specification and verification approaches so far only consider correctness in terms of computations. In this work, we present a two-tier Hoare Logic that…
In mission-critical domains such as law enforcement and medical diagnosis, the ability to explain and interpret the outputs of deep learning models is crucial for ensuring user trust and supporting informed decision-making. Despite…
The latest Deep Learning (DL) models for detection and classification have achieved an unprecedented performance over classical machine learning algorithms. However, DL models are black-box methods hard to debug, interpret, and certify. DL…
We investigate the automatic differentiation of hybrid models, viz. models that may contain delays, logical tests and discontinuities or loops. We consider differentiation with respect to parameters, initial conditions or the time. We…
This paper proposes new semantics for nondeterministic program execution, replacing the standard relational semantics for propositional dynamic logic (PDL). Under these new semantics, program execution is represented as fundamentally…