Related papers: GADTs, Functoriality, Parametricity: Pick Two
Motivated by interpretability and reliability, we investigate whether large language models (LLMs) deploy universal geometric structures to encode discrete, graph-structured knowledge. To this end, we present two complementary experimental…
Dedukti is a very expressive logical framework which unlike most frameworks, such as the Edinburgh Logical Framework (LF), allows for the representation of computation alongside deduction. However, unlike LF encodings, Dedukti encodings…
In translation, a concept represented by a single word in a source language can have multiple variations in a target language. The task of lexical selection requires using context to identify which variation is most appropriate for a source…
This research focuses on assessing the ability of large language models (LLMs) in representing geometries and their spatial relations. We utilize LLMs including GPT-2 and BERT to encode the well-known text (WKT) format of geometries and…
Galilean Conformal Algebras (GCA) have been recently proposed as a different non-relativistic limit of the AdS/CFT conjecture. In this note, we look at the representations of the GCA. We also construct explicitly the two and three point…
Classical AI planners provide solutions to planning problems in the form of long and opaque text outputs. To aid in the understanding transferability of planning solutions, it is necessary to have a rich and comprehensible representation…
Recursive algebraic data types (term algebras, ADTs) are one of the most well-studied theories in logic, and find application in contexts including functional programming, modelling languages, proof assistants, and verification. At this…
Catamorphisms are functions that are recursively defined on list and trees and, in general, on Algebraic Data Types (ADTs), and are often used to compute suitable abstractions of programs that manipulate ADTs. Examples of catamorphisms…
In previous work we have illustrated the benefits that compositional data types (CDTs) offer for implementing languages and in general for dealing with abstract syntax trees (ASTs). Based on Swierstra's data types \'a la carte, CDTs are…
Distributional and neural approaches to natural language semantics have been built almost exclusively on conventional linear algebra: vectors, matrices, tensors, and the operations that accompany them. These methods have achieved remarkable…
Formal languages let us define the textual representation of data with precision. Formal grammars, typically in the form of BNF-like productions, describe the language syntax, which is then annotated for syntax-directed translation and…
Graph Transformers (GTs) have emerged as powerful architectures for graph-structured data, yet remain constrained by rigid designs and lack quantifiable interpretability. Current state-of-the-art GTs commit to fixed GNN types across all…
Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…
We introduce a variant of linear logic with second order quantifiers and type fixpoints, both restricted to purely linear formulas. The Church encodings of binary words are typed by a standard non-linear type `Church,' while the Scott…
Graph matching is an important and persistent problem in computer vision and pattern recognition for finding node-to-node correspondence between graph-structured data. However, as widely used, graph matching that incorporates pairwise…
This paper presents \tdl, a typed feature-based representation language and inference system. Type definitions in \tdl\ consist of type and feature constraints over the boolean connectives. \tdl\ supports open- and closed-world reasoning…
Predicting program properties such as names or expression types has a wide range of applications. It can ease the task of programming and increase programmer productivity. A major challenge when learning from programs is $\textit{how to…
The semantics of notation systems can naturally be meta-modelled as a network of transformations, starting with the syntactic elements of the notation and ending with the parameters of an execution. In this context, a digital encoding…
Today's propositional satisfiability (SAT) solvers are extremely powerful and can be used as an efficient back-end for solving NP-complete problems. However, many fundamental problems in knowledge representation and reasoning are located at…
This paper is based on and advocates the trend in software engineering of extending the use of software patterns as means of structuring solutions to software development problems (be they motivated by best practice or by company interests…