Related papers: Learning Lambek grammars from proof frames
Recurrent neural network grammars (RNNG) are a recently proposed probabilistic generative modeling family for natural language. They show state-of-the-art language modeling and parsing performance. We investigate what information they…
Machine learning is a vital part of many real-world systems, but several concerns remain about the lack of interpretability, explainability and robustness of black-box AI systems. Concept Bottleneck Models (CBM) address some of these…
Mathematical theorem proving is an important testbed for large language models' deep and abstract reasoning capability. This paper focuses on improving LLMs' ability to write proofs in formal languages that permit automated proof…
This paper proposes a novel algorithm which learns a formal regular grammar from real-world continuous data, such as videos. Learning latent terminals, non-terminals, and production rules directly from continuous data allows the…
Continuous prompts have become widely adopted for augmenting performance across a wide range of natural language tasks. However, the underlying mechanism of this enhancement remains obscure. Previous studies rely on individual words for…
We show how categorial deduction can be implemented in higher-order (linear) logic programming, thereby realising parsing as deduction for the associative and non-associative Lambek calculi. This provides a method of solution to the parsing…
Can recurrent neural nets, inspired by human sequential data processing, learn to understand language? We construct simplified datasets reflecting core properties of natural language as modeled in formal syntax and semantics: recursive…
Black-box deep neural networks excel in text classification, yet their application in high-stakes domains is hindered by their lack of interpretability. To address this, we propose Text Bottleneck Models (TBM), an intrinsically…
This paper establishes the normalisation of natural deduction or lambda calculus formulation of Intuitionistic Non Commutative Logic --- which involves both commutative and non commutative connectives. This calculus first introduced by de…
We study algorithmic complexity and expressive power of fusion grammars, a novel formalism introduced in [Kreowski, Kuske, and Lye 2017], which extends hyperedge replacement grammars. In the first part of the work, we prove that the…
We address generating theorems from a given set of axioms, without proof goal, aiming at value from a mathematical point of view or as lemmas for automated proving. As benchmark, we convert a fragment of the Metamath database set.mm. Our…
In recent years, the compositional distributional approach in computational linguistics has opened the way for an integration of the \emph{lexical} aspects of meaning into Lambek's type-logical grammar program. This approach is based on the…
Inference in expressive probabilistic models is generally intractable, which makes them difficult to learn and limits their applicability. Sum-product networks are a class of deep models where, surprisingly, inference remains tractable even…
Lambek's production machines may be used to generate and recognize sentences in a subset of the language described by a production grammar. We determine in this paper the subset of the language of a grammar generated and recognized by such…
We propose a generic categorical framework for learning unknown formal languages of various types (e.g. finite or infinite words, weighted and nominal languages). Our approach is parametric in a monad T that represents the given type of…
Recent work on vector-based compositional natural language semantics has proposed the use of density matrices to model lexical ambiguity and (graded) entailment (e.g. Piedeleu et al 2015, Bankova et al 2019, Sadrzadeh et al 2018). Ambiguous…
We develop a probabilistic latent-variable model to discover semantic frames---types of events and their participants---from corpora. We present a Dirichlet-multinomial model in which frames are latent categories that explain the linking of…
Grammaticality and likelihood are distinct notions in human language. Pretrained language models (LMs), which are probabilistic models of language fitted to maximize corpus likelihood, generate grammatically well-formed text and…
Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates…
A major target of linguistics and cognitive science has been to understand what class of learning systems can acquire the key structures of natural language. Until recently, the computational requirements of language have been used to argue…