Related papers: A Deep Inference System for Differential Linear Lo…
Differential Linear Logic (DiLL) is a sequent calculus that expresses differentiation via symmetries between linear and non-linear formulas. In this paper, we express categorical models of DiLL as a pair of Grothendieck fibrations equipped…
Neural networks (NNs) achieve outstanding performance in many domains; however, their decision processes are often opaque and their inference can be computationally expensive in resource-constrained environments. We recently proposed…
Full Intuitionistic Linear Logic (FILL) is multiplicative intuitionistic linear logic extended with par. Its proof theory has been notoriously difficult to get right, and existing sequent calculi all involve inference rules with complex…
The integration of reasoning, learning, and decision-making is key to build more general artificial intelligence systems. As a step in this direction, we propose a novel neural-logic architecture, called differentiable logic machine (DLM),…
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…
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…
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…
One approach to explaining the hierarchical levels of understanding within a machine learning model is the symbolic method of inductive logic programming (ILP), which is data efficient and capable of learning first-order logic rules that…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
Following the idea of Subexponential Linear Logic and Stratified Bounded Linear Logic, we propose a new parameterized version of Linear Logic which subsumes other systems like ELL, LLL or SLL, by including variants of the exponential rules.…
Multiplicative linear logic is a very well studied formal system, and most such studies are concerned with the one-sided sequent calculus. In this paper we look in detail at existing translations between a deep inference system and the…
Differentiable Logics are deployed in neuro-symbolic learning tasks as a way of embedding logical constraints in the training objective of neural networks. A differentiable logic consists of a syntax to write logical properties and a…
Masked Diffusion Language Models (MDLMs) enable parallel token decoding, providing a promising alternative to the sequential nature of autoregressive generation. However, their iterative denoising process remains computationally expensive…
This paper studies properties of the logic BV, which is an extension of multiplicative linear logic (MLL) with a self-dual non-commutative operator. BV is presented in the calculus of structures, a proof theoretic formalism that supports…
The capability of making interpretable and self-explanatory decisions is essential for developing responsible machine learning systems. In this work, we study the learning to explain problem in the scope of inductive logic programming…
Differential Linear Logic enriches Linear Logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. We present a proof-net syntax for Differential Linear Logic…
In Linear Logic ($\mathsf{LL}$), the exponential modality $!$ brings forth a distinction between non-linear proofs and linear proofs, where linear means using an argument exactly once. Differential Linear Logic ($\mathsf{DiLL}$) is an…
In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are…
Deep Learning experiments have critical requirements regarding the careful handling of their datasets as well as the efficient and correct usage of APIs that interact with hardware accelerators. On the one hand, software mistakes during…
Deep inference is a proof theoretic methodology that generalizes the standard notion of inference of the sequent calculus, whereby inference rules become applicable at any depth inside logical expressions. Deep inference provides more…