Related papers: Actegories, Copowers, and Higher-Order Message Pas…
We consider the problem of symbolic reachability analysis of higher-order context-free processes. These models are generalizations of the context-free processes (also called BPA processes) where each process manipulates a data structure…
Classical Processes (CP) is a calculus where the proof theory of classical linear logic types communicating processes with mobile channels, a la pi-calculus. Its construction builds on a recent propositions as types correspondence between…
Probabilistic couplings are the foundation for many probabilistic relational program logics and arise when relating random sampling statements across two programs. In relational program logics, this manifests as dedicated coupling rules…
In-context learning (ICL) enables large language models to perform new tasks by conditioning on a sequence of examples. Most prior work reasonably and intuitively assumes that which examples are chosen has a far greater effect on…
Message-passing software systems exhibit non-trivial forms of concurrency and distribution; they are expected to follow intended protocols among communicating services, but also to never "get stuck". This intuitive requirement has been…
Quantum supermaps provide a framework in which higher order quantum processes can act on lower order quantum processes. In doing so, they enable the definition and analysis of new quantum protocols and causal structures. Recently, key…
Large language models (LLMs) have shown an impressive ability to perform tasks believed to require thought processes. When the model does not document an explicit thought process, it becomes difficult to understand the processes occurring…
Large Language Models (LLMs) are intended to reflect human linguistic competencies. But humans have access to a broad and embodied context, which is key in detecting and resolving linguistic ambiguities, even in isolated text spans. A…
Large LMs such as GPT-3 are powerful, but can commit mistakes that are obvious to humans. For example, GPT-3 would mistakenly interpret "What word is similar to good?" to mean a homophone, while the user intended a synonym. Our goal is to…
Originally inspired by categorical quantum mechanics (Abramsky and Coecke, LiCS'04), the categorical compositional distributional model of natural language meaning of Coecke, Sadrzadeh and Clark provides a conceptually motivated procedure…
We investigate program equivalence for linear higher-order(sequential) languages endowed with primitives for computational effects. More specifically, we study operationally-based notions of program equivalence for a linear…
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)}…
In this position paper, we would like to offer and defend a new template to study equivalences between programs -- in the particular framework of process algebras for concurrent computation.We believe that our layered model of development…
Session types define protocols that processes must follow when communicating. The special case of binary session types, i.e. type annotations of protocols between two parties, is known to be in a propositions-as-types correspondence with…
Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…
State of the art language models return a natural language text continuation from any piece of input text. This ability to generate coherent text extensions implies significant sophistication, including a knowledge of grammar and semantics.…
A semantical embedding of input/output logic in classical higher-order logic is presented. This embedding enables the mechanisation and automation of reasoning tasks in input/output logic with off-the-shelf higher-order theorem provers and…
Abstract Meaning Representation (AMR) parsing aims to translate sentences to semantic representation with a hierarchical structure, and is recently empowered by pretrained sequence-to-sequence models. However, there exists a gap between…
This paper seeks to apply categorical logic to the design of artificial intelligent agents that reason symbolically about objects more richly structured than sets. Using Johnstone's sequent calculus of terms- and formulae-in-context, we…
In generative commonsense reasoning tasks such as CommonGen, generative large language models (LLMs) compose sentences that include all given concepts. However, when focusing on instruction-following capabilities, if a prompt specifies a…