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Traditionally categorical data analysis (e.g. generalized linear models) works with simple, flat datasets akin to a single table in a database with no notion of missing data or conflicting versions. In contrast, modern data analysis must…
In traditional justification logic, evidence terms have the syntactic form of polynomials, but they are not equipped with the corresponding algebraic structure. We present a novel semantic approach to justification logic that models…
The database community lacks a unified relational query language for subset selection and optimisation queries, limiting both user expression and query optimiser reasoning about such problems. Decades of research (latterly under the rubric…
Reasoning about images/objects and their hierarchical interactions is a key concept for the next generation of computer vision approaches. Here we present a new framework to deal with it through a visual hierarchical context-based…
Constraint Handling Rules provide descriptions for constraint solvers. However, they fall short when those constraints specify some binding structure, like higher-rank types in a constraint-based type inference algorithm. In this paper, the…
Refinement types are types equipped with predicates that specify preconditions and postconditions of underlying functional languages. We propose a general semantic construction of dependent refinement type systems from underlying type…
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…
Since the early Sixties and Seventies it has been known that the regular and context-free languages are characterized by definability in the monadic second-order theory of certain structures. More recently, these descriptive…
We present ReasonBert, a pre-training method that augments language models with the ability to reason over long-range relations and multiple, possibly hybrid contexts. Unlike existing pre-training methods that only harvest learning signals…
Text-to-image generative models often exhibit bias related to sensitive attributes. However, current research tends to focus narrowly on single-object prompts with limited contextual diversity. In reality, each object or attribute within a…
Case-based reasoning is known to play an important role in several legal settings. In this paper we focus on a recent approach to case-based reasoning, supported by an instantiation of abstract argumentation whereby arguments represent…
Recent research has made significant progress in localizing and editing image regions based on text. However, most approaches treat these regions in isolation, relying solely on local cues without accounting for how each part contributes to…
Definite descriptions are phrases of the form 'the $x$ such that $\varphi$', used to refer to single entities in a context. They are often more meaningful to users than individual names alone, in particular when modelling or querying data…
In human cognition, the binding problem describes the open question of how the brain flexibly integrates diverse information into cohesive object representations. Analogously, in machine learning, there is a pursuit for models capable of…
Relation Extraction (RE) aims to label relations between groups of marked entities in raw text. Most current RE models learn context-aware representations of the target entities that are then used to establish relation between them. This…
We study how large language models (LLMs) reason about memorized knowledge through simple binary relations such as equality ($=$), inequality ($<$), and inclusion ($\subset$). Unlike in-context reasoning, the axioms (e.g., $a < b, b < c$)…
The relational semantics of linear logic is a powerful framework for defining resource-aware models of the $\lambda$-calculus. However, its quantitative aspects are not reflected in the preorders and equational theories induced by these…
Identifying metaphors in text is very challenging and requires comprehending the underlying comparison. The automation of this cognitive process has gained wide attention lately. However, the majority of existing approaches concentrate on…
When we work with information from multiple sources, the formalism each employs to handle uncertainty may not be uniform. In order to be able to combine these knowledge bases of different formats, we need to first establish a common basis…
An answer set is a plain set of literals which has no further structure that would explain why certain literals are part of it and why others are not. We show how argumentation theory can help to explain why a literal is or is not contained…