Related papers: Using Inverse lambda and Generalization to Transla…
A fundamental theme in automata theory is regular languages of words and trees, and their many equivalent definitions. Salvati has proposed a generalization to regular languages of simply typed $\lambda$-terms, defined using denotational…
To support the understanding of declarative probabilistic programming languages, we introduce a lambda-calculus with a fair binary probabilistic choice that chooses between its arguments with equal probability. The reduction strategy of the…
The paper describes a system that uses large language model (LLM) technology to support the automatic learning of new entries in an intelligent agent's semantic lexicon. The process is bootstrapped by an existing non-toy lexicon and a…
Higher-order representations of objects such as programs, proofs, formulas and types have become important to many symbolic computation tasks. Systems that support such representations usually depend on the implementation of an intensional…
In this paper, we present a general realizability semantics for the simply typed $\lambda\mu$-calculus. Then, based on this semantics, we derive both weak and strong normalization results for two versions of the $\lambda\mu$-calculus…
This paper introduces a sentence to vector encoding framework suitable for advanced natural language processing. Our latent representation is shown to encode sentences with common semantic information with similar vector representations.…
In the quest to give a formal compositional semantics to natural languages, semanticists have started turning their attention to phenomena that have been also considered as parts of pragmatics (e.g., discourse anaphora and presupposition…
Temporal Logic (TL) can be used to rigorously specify complex high-level specification for systems in many engineering applications. The translation between natural language (NL) and TL has been under-explored due to the lack of dataset and…
Recent years have seen an increasing number of applications that have a natural language interface, either in the form of chatbots or via personal assistants such as Alexa (Amazon), Google Assistant, Siri (Apple), and Cortana (Microsoft).…
A comparison of Landin's form of lambda calculus with Church's shows that, independently of the lambda calculus, there exists a mechanism for converting functions with arguments indexed by variables to the usual kind of function where the…
Probing and enhancing large language models' reasoning capacity remains a crucial open question. Here we re-purpose the reverse dictionary task as a case study to probe LLMs' capacity for conceptual inference. We use in-context learning to…
We describe a data-driven approach for automatically explaining new, non-standard English expressions in a given sentence, building on a large dataset that includes 15 years of crowdsourced examples from UrbanDictionary.com. Unlike prior…
While it has become common to perform automated translations on natural language, performing translations between different representations of mathematical formulae has thus far not been possible. We implemented the first translator for…
The linear-algebraic lambda-calculus and the algebraic lambda-calculus are untyped lambda-calculi extended with arbitrary linear combinations of terms. The former presents the axioms of linear algebra in the form of a rewrite system, while…
A non-deterministic call-by-need lambda-calculus \calc with case, constructors, letrec and a (non-deterministic) erratic choice, based on rewriting rules is investigated. A standard reduction is defined as a variant of left-most outermost…
The Functional Machine Calculus (FMC) was recently introduced as a generalization of the lambda-calculus to include higher-order global state, probabilistic and non-deterministic choice, and input and output, while retaining confluence. The…
Distributional models that learn rich semantic word representations are a success story of recent NLP research. However, developing models that learn useful representations of phrases and sentences has proved far harder. We propose using…
Different from previous surveys in semantic parsing (Kamath and Das, 2018) and knowledge base question answering(KBQA)(Chakraborty et al., 2019; Zhu et al., 2019; Hoffner et al., 2017) we try to takes a different perspective on the study of…
It has been found that Transformer-based language models have the ability to perform basic quantitative reasoning. In this paper, we propose a method for studying how these models internally represent numerical data, and use our proposal to…
Recent advances in natural language processing (NLP), particularly large language models (LLMs), have motivated the automatic translation of natural language statements into formal logic without human intervention. This enables automated…