Related papers: Interpreting a concurrent $\lambda$-calculus in di…

The verification problem for neural networks is verifying whether a neural network will suffer from adversarial samples, or approximating the maximal allowed scale of adversarial perturbation that can be endured. While most prior work…

We propose a formal model of reasoning limitations in large neural net models for language, grounded in the depth of their neural architecture. By treating neural networks as linear operators over logic predicate space we show that each…

Petri nets are a well-known model of concurrency and provide an ideal setting for the study of fundamental aspects in concurrent systems. Despite their simplicity, they still lack a satisfactory causally reversible semantics. We develop…

Recently, Logic Explained Networks (LENs) have been proposed as explainable-by-design neural models providing logic explanations for their predictions. However, these models have only been applied to vision and tabular data, and they mostly…

Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a…

In this position paper, we would like to offer and defend a new template to study equivalences between programs -- in the particular framework of process algebras for concurrent computation.We believe that our layered model of development…

Large language models (LLMs) have shown an impressive ability to perform tasks believed to require thought processes. When the model does not document an explicit thought process, it becomes difficult to understand the processes occurring…

We introduce a first proofs-as-parallel-programs correspondence for classical logic. We define a parallel and more powerful extension of the simply typed lambda calculus corresponding to an analytic natural deduction based on the excluded…

We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…

Recent work has found that adversarially-robust deep networks used for image classification are more interpretable: their feature attributions tend to be sharper, and are more concentrated on the objects associated with the image's…

There is increasing interest within the research community in the design and use of recursive probability models. Although there still remains concern about computational complexity costs and the fact that computing exact solutions can be…

When we are faced with challenging image classification tasks, we often explain our reasoning by dissecting the image, and pointing out prototypical aspects of one class or another. The mounting evidence for each of the classes helps us…

Argumentation frameworks, consisting of arguments and an attack relation representing conflicts, are fundamental for formally studying reasoning under conflicting information. We use methods from mathematical logic, specifically…

With the increasing capabilities of Large Language Models (LLMs), parallel reasoning has emerged as a new inference paradigm that enhances reasoning robustness by concurrently exploring multiple lines of thought before converging on a final…

Many theories of semantic interpretation use lambda-term manipulation to compositionally compute the meaning of a sentence. These theories are usually implemented in a language such as Prolog that can simulate lambda-term operations with…

Because of the pervasive usage of Neural Networks in human sensitive applications, their interpretability is becoming an increasingly important topic in machine learning. In this work we introduce a simple way to interpret the output…

A linking theory explains how verbs' semantic arguments are mapped to their syntactic arguments---the inverse of the Semantic Role Labeling task from the shallow semantic parsing literature. In this paper, we develop the Computational…

The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this…

The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…

Recent work exhibited that distributed word representations are good at capturing linguistic regularities in language. This allows vector-oriented reasoning based on simple linear algebra between words. Since many different methods have…