Related papers: Grammars over the Lambek Calculus with Permutation…
Recently researchers working in the LFG framework have proposed algorithms for taking advantage of the implicit context-free components of a unification grammar [Maxwell 96]. This paper clarifies the mathematical foundations of these…
We develop a categorical compositional distributional semantics for Lambek Calculus with a Relevant Modality !L*, which has a limited edition of the contraction and permutation rules. The categorical part of the semantics is a monoidal…
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…
Many advances in Natural Language Processing have been based upon more expressive models for how inputs interact with the context in which they occur. Recurrent networks, which have enjoyed a modicum of success, still lack the…
Ontology, and more broadly, Knowledge Graph Matching is a challenging task in which expressiveness has not been fully addressed. Despite the increasing use of embeddings and language models for this task, approaches for generating…
Boolean grammars generalize context-free rewriting by extending the possibilities when dealing with different rules for the same nonterminal symbol. By allowing not only disjunction (as in the case of usual context-free grammars), but also…
It is well-known that: (i) every context-free language over a singleton terminal alphabet is regular, and (ii) the class of languages that satisfy the Pumping Lemma is a proper super-class of the context-free languages. We show that any…
Diffusion language models (DLMs) promise parallel, order-agnostic generation, but on standard benchmarks they have historically lagged behind autoregressive models in sample quality and diversity. Recent continuous flow and diffusion…
Semantic word embeddings represent the meaning of a word via a vector, and are created by diverse methods. Many use nonlinear operations on co-occurrence statistics, and have hand-tuned hyperparameters and reweighting methods. This paper…
In typical non-idempotent intersection type systems, proof normalization is not confluent. In this paper we introduce a confluent non-idempotent intersection type system for the lambda-calculus. Typing derivations are presented using proof…
In the continuously advancing AI landscape, crafting context-rich and meaningful responses via Large Language Models (LLMs) is essential. Researchers are becoming more aware of the challenges that LLMs with fewer parameters encounter when…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…
The Distributional Compositional Categorical (DisCoCat) model is a mathematical framework that provides compositional semantics for meanings of natural language sentences. It consists of a computational procedure for constructing meanings…
Automated speech recognition coverage of the world's languages continues to expand. However, standard phoneme based systems require handcrafted lexicons that are difficult and expensive to obtain. To address this problem, we propose a…
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…
Answer Set Programming (ASP) is a declarative programming paradigm based on logic programming and non-monotonic reasoning. It is a tremendously powerful tool for describing and solving combinatorial problems. Like any other language, ASP…
Large language models (LLMs) exhibit outstanding performance in machine translation via in-context learning. In contrast to sentence-level translation, document-level translation (DOCMT) by LLMs based on in-context learning faces two major…
Context-free S grammars are introduced, for arbitrary (storage) type S, as a uniform framework for recursion-based grammars, automata, and transducers, viewed as programs. To each occurrence of a nonterminal of a context-free S grammar an…
Linear conjunctive grammars are a family of formal grammars with an explicit conjunction operation allowed in the rules, which is notable for its computational equivalence fo one-way real-time cellular automata, also known as trellis…
Long short-term memory(LSTM) units on sequence-based models are being used in translation, question-answering systems, classification tasks due to their capability of learning long-term dependencies. In Natural language generation, LSTM…