Related papers: Taming Differentiable Logics with Coq Formalisatio…
As large language models (LLMs) are increasing integrated into fact-checking pipelines, formal logic is often proposed as a rigorous means by which to mitigate bias, errors and hallucinations in these models' outputs. For example, some…
Ensuring that safety-critical applications behave as intended is an important yet challenging task. Modeling languages like differential dynamic logic (dL) have proof calculi capable of proving guarantees for such applications. However, dL…
We introduce a logical approach to formalizing statistical properties of machine learning. Specifically, we propose a formal model for statistical classification based on a Kripke model, and formalize various notions of classification…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
Natural language explanations play a fundamental role in Natural Language Inference (NLI) by revealing how premises logically entail hypotheses. Recent work has shown that the interaction of large language models (LLMs) with theorem provers…
What provides the highest level of assurance for correctness of execution within a programming language? One answer, and our solution in particular, to this problem is to provide a formalization for, if it exists, the denotational semantics…
Applying dynamic logics to program verifications is a challenge, because their axiomatic rules for regular expressions can be difficult to be adapted to different program models. We present a novel dynamic logic, called DLp, which supports…
We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called…
This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
Verifying the functional correctness of programs with both classical and quantum constructs is a challenging task. The presence of probabilistic behaviour entailed by quantum measurements and unbounded while loops complicate the…
The use of formal language for deductive logical reasoning aligns well with language models (LMs), where translating natural language (NL) into first-order logic (FOL) and employing an external solver results in a verifiable and therefore…
We describe a formalization of higher-order rewriting theory and formally prove that an AFS is strongly normalizing if it can be interpreted in a well-founded domain. To do so, we use Coq, which is a proof assistant based on dependent type…
We present three projects concerned with applications of proof assistants in the area of programming language theory and mathematics. The first project is about a certified compilation technique for a domain-specific programming language…
Defeasible rules are used in providing computable representations of legal documents and, more recently, have been suggested as a basis for explainable AI. Such applications draw attention to the scalability of implementations. The…
Prior research has demonstrated noticeable performance gains through the use of probabilistic tokenizations, an approach that involves employing multiple tokenizations of the same input string during the training phase of a language model.…
Current trends in Machine Learning prefer explainability even when it comes at the cost of performance. Therefore, explainable AI methods are particularly important in the field of Fraud Detection. This work investigates the applicability…
Large Language Models (LLMs) show remarkable capabilities, yet their stochastic next-token prediction creates logical inconsistencies and reward hacking that formal symbolic systems avoid. To bridge this gap, we introduce a formal logic…
We present a way to apply quantum logic to the study of quantum programs. This is made possible by using an extension of the usual propositional language in order to make transformations performed on the system appear explicitly. This way,…
Compiler correctness proofs for higher-order concurrent languages are difficult: they involve establishing a termination-preserving refinement between a concurrent high-level source language and an implementation that uses low-level shared…