Related papers: Neural Proof Nets
Given a logic presented in a sequent calculus, a natural question is that of equivalence of proofs: to determine whether two given proofs are equated by any denotational semantics, ie any categorical interpretation of the logic compatible…
This article studies (multilayer perceptron) neural networks with an emphasis on the transformations involved --- both forward and backward --- in order to develop a semantical/logical perspective that is in line with standard program…
Semi-algebraic proof systems such as sum-of-squares (SoS) have attracted a lot of attention recently due to their relation to approximation algorithms: constant degree semi-algebraic proofs lead to conjecturally optimal polynomial-time…
This paper presents a simple notion of proof net for multiplicative linear logic with units. Cut elimination is direct and strongly normalising, in contrast to previous approaches which resorted to moving jumps (attachments) of par units…
Characterizing the computational power of neural network architectures in terms of formal language theory remains a crucial line of research, as it describes lower and upper bounds on the reasoning capabilities of modern AI. However, when…
Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems. However, in safety-critical contexts, the use of…
Neuro-symbolic systems combine the abilities of neural perception and logical reasoning. However, end-to-end learning of neuro-symbolic systems is still an unsolved challenge. This paper proposes a natural framework that fuses neural…
Seq2seq models based on Recurrent Neural Networks (RNNs) have recently received a lot of attention in the domain of Semantic Parsing for Question Answering. While in principle they can be trained directly on pairs (natural language…
This paper presents LEXR, a framework for explaining the decision making of recurrent neural networks (RNNs) using a formal description language called Linear Temporal Logic (LTL). LTL is the de facto standard for the specification of…
Linear logic has provided new perspectives on proof-theory, denotational semantics and the study of programming languages. One of its main successes are proof-nets, canonical representations of proofs that lie at the intersection between…
To verify and validate networks, it is essential to gain insight into their decisions, limitations as well as possible shortcomings of training data. In this work, we propose a post-hoc, optimization based visual explanation method, which…
Deep learning is currently playing a crucial role toward higher levels of artificial intelligence. This paradigm allows neural networks to learn complex and abstract representations, that are progressively obtained by combining simpler…
Artificial networks have been studied through the prism of statistical mechanics as disordered systems since the 80s, starting from the simple models of Hopfield's associative memory and the single-neuron perceptron classifier. Assuming…
The large language models (LLMs) might produce a persuasive argument within mathematical and logical fields, although such argument often includes some minor missteps, including the entire omission of side conditions, invalid inference…
Current open-domain neural semantics parsers show impressive performance. However, closer inspection of the symbolic meaning representations they produce reveals significant weaknesses: sometimes they tend to merely copy character sequences…
We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie "non-computational" proofs from probability theory,…
Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…
A hallmark of human cognition is the ability to continually acquire and distill observations of the world into meaningful, predictive theories. In this paper we present a new mechanism for logical theory acquisition which takes a set of…
Computers have already changed the way that humans do mathematics: they enable us to compute efficiently. But will they soon be helping us to reason? And will they one day start reasoning themselves? We give an overview of recent…
We propose Modal Logical Neural Networks (MLNNs), a neurosymbolic framework that integrates deep learning with the formal semantics of modal logic, enabling reasoning about necessity and possibility. Drawing on Kripke semantics, we…