Related papers: The Relative Monadic Metalanguage
While the reasoning capabilities of Large Language Models (LLMs) excel in analytical tasks such as mathematics and code generation, their utility for abstractive summarization remains widely assumed but largely unverified. To bridge this…
We give a domain-theoretic semantics to a statistical programming language, using the plain old category of dcpos, in contrast to some more sophisticated recent proposals. Remarkably, our monad of minimal valuations is commutative, which…
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…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
Large language models (LLMs) can handle a wide variety of general tasks with simple prompts, without the need for task-specific training. Multimodal Large Language Models (MLLMs), built upon LLMs, have demonstrated impressive potential in…
We introduce a framework for universal algebra in categories of relational structures given by finitary relational signatures and finitary or infinitary Horn theories, with the arity $\lambda$ of a Horn theory understood as a strict upper…
Intuitionistic modal logics (IMLs) extend intuitionistic propositional logic with modalities such as the box and diamond connectives. Advances in the study of IMLs have inspired several applications in programming languages via the…
Large language models (LLMs) exhibit strong semantic understanding, yet struggle when user instructions involve ambiguous or conceptually misaligned terms. We propose the Language Graph Model (LGM) to enhance conceptual clarity by…
The use of monoids in the study of word languages recognized by finite-state automata has been quite fruitful. In this work, we look at the same idea of "recognizability by finite monoids" for other monoids. In particular, we attempt to…
Linearity and dependency analyses are key to several applications in computer science, especially, in resource management and information flow control. What connects these analyses is that both of them need to model at least two different…
We present a simple technique for semantic, open logical relations arguments about languages with recursive types, which, as we show, follows from a principled foundation in categorical semantics. We demonstrate how it can be used to give a…
We develop a method to incrementally construct programming languages. Our approach is categorical: each layer of the language is described as a monad. Our method either (i) concretely builds a distributive law between two monads, i.e.…
Describing systems in terms of choices and their resulting costs and rewards offers the promise of freeing algorithm designers and programmers from specifying how those choices should be made; in implementations, the choices can be realized…
Pretrained large Language Models (LLMs) are able to answer questions that are unlikely to have been encountered during training. However a diversity of potential applications exist in the broad domain of reasoning systems and considerations…
The planning ability of Large Language Models (LLMs) has garnered increasing attention in recent years due to their remarkable capacity for multi-step reasoning and their ability to generalize across a wide range of domains. While some…
The theory of regular cost functions is a quantitative extension to the classical notion of regularity. A cost function associates to each input a non-negative integer value (or infinity), as opposed to languages which only associate to…
In recent years, large language models (LLMs) have made significant advancements in developing human-like and engaging dialogue systems. However, in tasks such as consensus-building and persuasion, LLMs often struggle to resolve conflicts…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
The AMR (Abstract Meaning Representation) formalism for representing meaning of natural language sentences was not designed to deal with scope and quantifiers. By extending AMR with indices for contexts and formulating constraints on these…
The rapid development of large language and vision models (LLVMs) has been driven by advances in visual instruction tuning. Recently, open-source LLVMs have curated high-quality visual instruction tuning datasets and utilized additional…