Related papers: Contextual Modal Type Theory with Polymorphic Cont…
We describe Elevator, a unifying polymorphic foundation for metaprogramming with memory management based on adjoint modalities. In this setting, we distinguish between multiple memory regions using modes where each mode has a specific set…
Simple type theory is suited as framework for combining classical and non-classical logics. This claim is based on the observation that various prominent logics, including (quantified) multimodal logics and intuitionistic logics, can be…
Modalities in homotopy type theory are used to create and access subuniverses of a given type universe. These have significant applications throughout mathematics and computer science, and in particular can be used to create universes in…
A primary goal in recent research on contextuality has been to extend this concept to cases of inconsistent connectedness, where observables have different distributions in different contexts. This article proposes a solution within the…
The formal system lambda-delta is a typed lambda calculus that pursues the unification of terms, types, environments and contexts as the main goal. lambda-delta takes some features from the Automath-related lambda calculi and some from the…
Conditionals are useful for modelling, but are not always sufficiently expressive for capturing information accurately. In this paper we make the case for a form of conditional that is situation-based. These conditionals are more expressive…
This thesis embarks on a comprehensive exploration of formal computational models that underlie typed programming languages. We focus on programming calculi, both functional (sequential) and concurrent, as they provide a compelling rigorous…
Large language model (LLM) development is currently driven by large-scale empirical iteration over data mixtures, reward models, routing strategies, and evaluation pipelines. Here, we argue that many central questions in LLM development and…
In this chapter we study modal logics of topological spaces in the combined language with the derivational modality and the difference modality. We give axiomatizations and prove completeness for the following classes: all spaces,…
Type systems usually characterize the shape of values but not their free variables. However, many desirable safety properties could be guaranteed if one knew the free variables captured by values. We describe CCsubBox, a calculus where such…
To answer a question, language models often need to integrate prior knowledge learned during pretraining and new information presented in context. We hypothesize that models perform this integration in a predictable way across different…
Large language models (LLMs) show strong reasoning abilities across diverse tasks, yet their performance on extended contexts remains inconsistent. While prior research has emphasized mid-context degradation in question answering, this…
Parametricity states that polymorphic functions behave the same regardless of how they are instantiated. When developing polymorphic programs, Wadler's free theorems can serve as free specifications, which can turn otherwise partial…
We develop a dependent type theory that is based purely on inductive and coinductive types, and the corresponding recursion and corecursion principles. This results in a type theory with a small set of rules, while still being fairly…
Broadly speaking, there are two kinds of semantics-aware assistant systems for mathematics: proof assistants express the semantic in logic and emphasize deduction, and computer algebra systems express the semantics in programming languages…
Multimodal foundation models aim to create a unified representation space that abstracts away from surface features like language syntax or modality differences. To investigate this, we study the internal representations of three recent…
Causality is one of the fundamental structures of spacetimes, determining the possible behaviour and propagation of physical information. Causal structure can be analysed through the various modal logics it induces. The modal logics for the…
This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized…
Given a programming language, can we give a monadic denotational semantics that is stable under language extension? Models containing only a single monad are not stable. Models based on type-and-effect systems, in which there is a monad for…
Programs are more distributed and concurrent today than ever before, and structural communications are at the core. Constructing and debugging such programs are hard due to the lack of formal specification/verification of concurrency. This…