Related papers: Linear Realisability over nets: multiplicatives (l…
Neural networks offer good approximation to many tasks but consistently fail to reach perfect generalization, even when theoretical work shows that such perfect solutions can be expressed by certain architectures. Using the task of formal…
Reproducibility has become an intensely debated topic in NLP and ML over recent years, but no commonly accepted way of assessing reproducibility, let alone quantifying it, has so far emerged. The assumption has been that wider scientific…
Enhancing the mathematical reasoning of large language models (LLMs) demands high-quality training data, yet conventional methods face critical challenges in scalability, cost, and data reliability. To address these limitations, we propose…
We revisit a fundamental result in real-time verification, namely that the binary reachability relation between configurations of a given timed automaton is definable in linear arithmetic over the integers and reals. In this paper we give a…
A modified realisability interpretation of infinitary logic is formalised and proved sound in constructive type theory (CTT). The logic considered subsumes first order logic. The interpretation makes it possible to extract programs with…
Max-Plus Linear (MPL) systems are an algebraic formalism with practical applications in transportation networks, manufacturing and biological systems. In this paper, we investigate the problem of automatically analyzing the properties of…
We introduce the notion of coherent graphs, and show how those can be used to define dynamic semantics for Multiplicative Linear Logic (MLL) extended with non-determinism. Thanks to the use of a coherence relation rather than mere formal…
Syntactic NL or succinctly SNL was first introduced in 2017, analogously to SNP, as a ``syntactically''-defined natural subclass of NL (nondeterministic logarithmic-space complexity class) using a restricted form of logical sentences,…
We obtain modal completeness of the interpretability logics ILP_0 and ILR w.r.t. generalized Veltman semantics. Our proofs are based on the notion of smart (full) labels. We also give shorter proofs of completeness w.r.t. generalized…
By using a combination of algebraic, geometric, and dynamical techniques, together with input from higher dimensional Diophantine approximation, we give a complete characterization of all linearly repetitive cut and project sets with…
Post-hoc explanations provide transparency and are essential for guiding model optimization, such as prompt engineering and data sanitation. However, applying model-agnostic techniques to Large Language Models (LLMs) is hindered by…
In this paper, we give a new linear time correctness condition for proof nets of Multiplicative Linear Logic without units. Our approach is based on a rewriting system over trees. We have only three rewrite rules. Compared with previous…
The paper advocates for LLMs to enhance the accessibility, usage and explainability of rule-based legal systems, contributing to a democratic and stakeholder-oriented view of legal technology. A methodology is developed to explore the…
State-of-the-art neural networks can be trained to become remarkable solutions to many problems. But while these architectures can express symbolic, perfect solutions, trained models often arrive at approximations instead. We show that the…
Differentiable logics (DL) have recently been proposed as a method of training neural networks to satisfy logical specifications. A DL consists of a syntax in which specifications are stated and an interpretation function that translates…
The use of meta-rules in logic, i.e., rules whose content includes other rules, has recently gained attention in the setting of non-monotonic reasoning: a first logical formalisation and efficient algorithms to compute the (meta)-extensions…
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…
Metric Temporal Logic $\mathsf{MTL}[\until_I,\since_I]$ is one of the most studied real time logics. It exhibits considerable diversity in expressiveness and decidability properties based on the permitted set of modalities and the nature of…
We use a new approach with a matrix transformation to obtain a new global solvability criterion for matrix Riccati equations. The proven theorem completes an well known result in directions of extension of classes of coefficient of…
Explainability is highly-desired in Machine Learning (ML) systems supporting high-stakes policy decisions in areas such as health, criminal justice, education, and employment. While the field of explainable ML has expanded in recent years,…