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We present a full-spectrum dependently typed core language which includes both nontermination and computational irrelevance (a.k.a. erasure), a combination which has not been studied before. The two features interact: to protect type safety…
The semantic web is an open and distributed environment in which it is hard to guarantee consistency of knowledge and information. Under the standard two-valued semantics everything is entailed if knowledge and information is inconsistent.…
We introduce generative interpretation, a new approach to estimating contractual meaning using large language models. As AI triumphalism is the order of the day, we proceed by way of grounded case studies, each illustrating the capabilities…
Abstract Meaning Representation (AMR) parsing aims to extract an abstract semantic graph from a given sentence. The sequence-to-sequence approaches, which linearize the semantic graph into a sequence of nodes and edges and generate the…
It has recently been discovered that both quantum and classical propositional logics can be modelled by classes of non-orthomodular and thus non-distributive lattices that properly contain standard orthomodular and Boolean classes,…
Queries to large language models (LLMs) can be divided into two parts: the instruction/question and the accompanying context. The context for retrieval-augmented generation (RAG) systems in most benchmarks comes from Wikipedia or…
We investigate models for learning the class of context-free and context-sensitive languages (CFLs and CSLs). We begin with a brief discussion of some early hardness results which show that unrestricted language learning is impossible, and…
Non-confluent and non-terminating constructor-based term rewrite systems are useful for the purpose of specification and programming. In particular, existing functional logic languages use such kind of rewrite systems to define possibly…
The problem of identifying a probabilistic context free grammar has two aspects: the first is determining the grammar's topology (the rules of the grammar) and the second is estimating probabilistic weights for each rule. Given the hardness…
Automated text evaluation has long been a central issue in Natural Language Processing (NLP). Recently, the field has shifted toward using Large Language Models (LLMs) as evaluators-a trend known as the LLM-as-a-Judge paradigm. While…
Pretrained Language Models (PLMs) learn rich cross-lingual knowledge and can be finetuned to perform well on diverse tasks such as translation and multilingual word sense disambiguation (WSD). However, they often struggle at disambiguating…
We describe an extension of Earley's parser for stochastic context-free grammars that computes the following quantities given a stochastic context-free grammar and an input string: a) probabilities of successive prefixes being generated by…
Discrete modelling frameworks of Biological networks can be divided in two distinct categories: Boolean and Multi-valued. Although Multi-valued networks are more expressive for qualifying the regulatory behaviours modelled by more than two…
Large language models (LLMs) generate diverse, situated, persuasive texts from a plurality of potential perspectives, influenced heavily by their prompts and training data. As part of LLM adoption, we seek to characterize - and ideally,…
We look at non-classical negations and their corresponding adjustment connectives from a modal viewpoint, over complete distributive lattices, and apply a very general mechanism in order to offer adequate analytic proof systems to logics…
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…
Negation and uncertainty modeling are long-standing tasks in natural language processing. Linguistic theory postulates that expressions of negation and uncertainty are semantically independent from each other and the content they modify.…
While large models achieve impressive results, their learning dynamics are far from understood. Many domains of interest, such as natural language syntax, coding languages, arithmetic problems, are captured by context-free grammars (CFGs).…
Most of the successful and predominant methods for bilingual lexicon induction (BLI) are mapping-based, where a linear mapping function is learned with the assumption that the word embedding spaces of different languages exhibit similar…
Probabilistic context-free grammars have a long-term record of use as generative models in machine learning and symbolic regression. When used for symbolic regression, they generate algebraic expressions. We define the latter as equivalence…