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Large language models (LLMs) have shown potential in identifying qualitative causal relations, but their ability to perform quantitative causal reasoning -- estimating effect sizes that parametrize functional relationships -- remains…
This reports introduces a novel sound and complete semantics for first order intuitionistic logic, in the framework of category theory and by the computational interpretation of the logic based on the so-called Curry-Howard isomorphism.…
A number of domain specific languages, such as circuits or data-science workflows, are best expressed as diagrams of boxes connected by wires. Unfortunately, functional languages have traditionally been ill-equipped to embed this sort of…
Classical (or Boolean) type theory is the type theory that allows the type inference $\sigma \to \bot) \to \bot => \sigma$ (the type counterpart of double-negation elimination), where $\sigma$ is any type and $\bot$ is absurdity type. This…
We show that differential calculus (in its usual form, or in the general form of topological differential calculus) can be fully imdedded into a functor category (functors from a small category of anchord tangent algebras to anchored sets).…
Weakly Supervised Semantic Segmentation (WSSS), which leverages image-level labels, has garnered significant attention due to its cost-effectiveness. The previous methods mainly strengthen the inter-class differences to avoid class semantic…
Semantic role labeling (SRL) is a crucial task of natural language processing (NLP). Although generative decoder-based large language models (LLMs) have achieved remarkable success across various NLP tasks, they still lag behind…
A categorial grammar assigns one of several syntactic categories to each symbol of the alphabet, and the category of a string is then deduced from the categories assigned to its symbols using two simple reduction rules. This paper…
We give new proofs of soundness (all representable functions on base types lies in certain complexity classes) for Elementary Affine Logic, LFPL (a language for polytime computation close to realistic functional programming introduced by…
There have been a huge number of benchmarks proposed to evaluate how large language models (LLMs) behave for logic inference tasks. However, it remains an open question how to properly evaluate this ability. In this paper, we provide a…
We advocate the use of de Bruijn's universal abstraction $\lambda^\infty$ for the quantification of schematic variables in the predicative setting and we present a typed $\lambda$-calculus featuring the quantifier $\lambda^\infty$…
We introduce a category-theoreticabstraction of a syntax with auxiliary functions, called an admissiblemonad morphism. Relying on an abstract form of structural recursion,we then design generic tools to construct admissible monad…
Stock and flow diagrams are already an important tool in epidemiology, but category theory lets us go further and treat these diagrams as mathematical entities in their own right. In this chapter we use communicable disease models created…
In this article we show that hybrid type-logical grammars are a fragment of first-order linear logic. This embedding result has several important consequences: it not only provides a simple new proof theory for the calculus, thereby…
We develop a denotational semantics of muLL, a version of propositional Linear Logic with least and greatest fixed points extending David Baelde's propositional muMALL with exponentials. Our general categorical setting is based on the…
Spoken language recognition (SLR) refers to the automatic process used to determine the language present in a speech sample. SLR is an important task in its own right, for example, as a tool to analyze or categorize large amounts of…
We investigate the possibility of a semantic account of the execution time (i.e. the number of \beta_v-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value {\lambda}-calculus. For…
We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with…
This paper presents the Functional Machine Calculus (FMC) as a simple model of higher-order computation with "reader/writer" effects: higher-order mutable store, input/output, and probabilistic and non-deterministic computation. The FMC…
We describe a type system with mixed linear and non-linear recursive types called LNL-FPC (the linear/non-linear fixpoint calculus). The type system supports linear typing, which enhances the safety properties of programs, but also supports…