Related papers: Interpreting a concurrent $\lambda$-calculus in di…
Driven by the interest of reasoning about probabilistic programming languages, we set out to study a notion of unicity of normal forms for them. To provide a tractable proof method for it, we define a property of distribution confluence…
We develop a point of view on reduction of multiplicative proof nets based on quantum error-correcting codes. To each proof net we associate a code, in such a way that cut-elimination corresponds to error correction.
Human communication is based on a variety of inferences that we draw from sentences, often going beyond what is literally said. While there is wide agreement on the basic distinction between entailment, implicature, and presupposition, the…
We study the correspondence between Bayesian Networks and graphical representation of proofs in linear logic. The goal of this paper is threefold: to develop a proof-theoretical account of Bayesian inference (in the spirit of the…
In this paper we propose that a restricted version of logical inference can be implemented with self-attention networks. We are aiming at showing that LLMs (Large Language Models) constructed with transformer networks can make logical…
We consider a logic used to describe sets of configurations of distributed systems, whose network topologies can be changed at runtime, by reconfiguration programs. The logic uses inductive definitions to describe networks with an unbounded…
We describe a new class of learning models called memory networks. Memory networks reason with inference components combined with a long-term memory component; they learn how to use these jointly. The long-term memory can be read and…
Language models are often used as the backbone of modern dialogue systems. These models are pre-trained on large amounts of written fluent language. Repetition is typically penalised when evaluating language model generations. However, it…
Machine learning plays a role in many deployed decision systems, often in ways that are difficult or impossible to understand by human stakeholders. Explaining, in a human-understandable way, the relationship between the input and output of…
With a view towards models of quantum computation and/or the interpretation of linear logic, we define a functional language where all functions are linear operators by construction. A small step operational semantic (and hence an…
This paper explores proof-theoretic aspects of hybrid type-logical grammars , a logic combining Lambek grammars with lambda grammars. We prove some basic properties of the calculus, such as normalisation and the subformula property and also…
A key functionality of emerging connected autonomous systems such as smart cities, smart transportation systems, and the industrial Internet-of-Things, is the ability to process and learn from data collected at different physical locations.…
We provide here a proof theoretic account of constraint programming that attempts to capture the essential ingredients of this programming style. We exemplify it by presenting proof rules for linear constraints over interval domains, and…
We propose a novel framework that leverages large language models (LLMs) to guide the rank selection in tensor network models for higher-order data analysis. By utilising the intrinsic reasoning capabilities and domain knowledge of LLMs,…
We develop Boolean-valued domain theory and show how the lambda-calculus can be interpreted in using domain-valued random variables. We focus on the reflexive domain construction rather than the language and its semantics. The notion of…
Distance-based classifiers, such as k-nearest neighbors and support vector machines, continue to be a workhorse of machine learning, widely used in science and industry. In practice, to derive insights from these models, it is also…
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…
I comment on the PDDL 2.1 language and its use in the planning competition, focusing on the choices made for accommodating time and concurrency. I also discuss some methodological issues that have to do with the move toward more expressive…
We will investigate proof-theoretic and linguistic aspects of first-order linear logic. We will show that adding partial order constraints in such a way that each sequent defines a unique linear order on the antecedent formulas of a sequent…
We introduce layer systems for proving generalizations of the modularity of confluence for first-order rewrite systems. Layer systems specify how terms can be divided into layers. We establish structural conditions on those systems that…