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The study of representations is of fundamental importance to any form of communication, and our ability to exploit them effectively is paramount. This article presents a novel theory -- Representational Systems Theory -- that is designed to…
Contextual memory integration remains a high challenge in the development of language models, particularly in tasks that require maintaining coherence over extended sequences. Traditional approaches, such as self-attention mechanisms and…
We discuss the notion of a span of cospans and define, for them, horizonal and vertical composition. These compositions satisfy the interchange law if working in a topos $\mathbf{C}$ and if the span legs are monic. A bicategory is then…
Extractive summarization suffers from irrelevance, redundancy and incoherence. Existing work shows that abstractive rewriting for extractive summaries can improve the conciseness and readability. These rewriting systems consider extracted…
Term rewriting is a Turing complete model of computation. When taught to students of computer science, key properties of computation as well as techniques to analyze programs on an abstract level are conveyed. This paper gives a swift…
Structural proof theory is praised for being a symbolic approach to reasoning and proofs, in which one can define schemas for reasoning steps and manipulate proofs as a mathematical structure. For this to be possible, proof systems must be…
This paper introduces a general approach for synthesizing procedural models of the state-transitions of a given discrete system. The approach is general in that it accepts different target languages for modeling the state-transitions of a…
SYNTAGMA is a rule-based parsing system, structured on two levels: a general parsing engine and a language specific grammar. The parsing engine is a language independent program, while grammar and language specific rules and resources are…
Logically constrained term rewriting is a rewriting framework that supports built-in data structures such as integers and bit vectors. Recently, constrained terms play a key role in various analyses and applications of logically constrained…
Compositionality is a cognitive mechanism that allows humans to systematically combine known concepts in novel ways. This study demonstrates how artificial neural agents acquire and utilize compositional generalization to describe…
Logically constrained term rewriting is a relatively new formalism where rules are equipped with constraints over some arbitrary theory. Although there are many recent advances with respect to rewriting induction, completion, complexity…
We develop a compositional framework for formal synthesis of hybrid systems using the language of category theory. More specifically, we provide mutually compatible tools for hierarchical, sequential, and independent parallel composition.…
Logically constrained term rewriting is a relatively new rewriting formalism that naturally supports built-in data structures, such as integers and bit vectors. In the analysis of logically constrained term rewrite systems (LCTRSs),…
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
This work establishes a robust mathematical foundation for compositional System Dynamics modeling, leveraging category theory to formalize and enhance the representation, analysis, and composition of system models. Here, System Dynamics…
We construct an internal language for cartesian closed bicategories. Precisely, we introduce a type theory modelling the structure of a cartesian closed bicategory and show that its syntactic model satisfies an appropriate universal…
A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations…
There has been considerable attention devoted to models that learn to jointly infer an expression's syntactic structure and its semantics. Yet, \citet{NangiaB18} has recently shown that the current best systems fail to learn the correct…
Learning music theory not only has practical benefits for musicians to write, perform, understand, and express music better, but also for both non-musicians to improve critical thinking, math analytical skills, and music appreciation.…
We present a unification problem based on first-order syntactic unification which ask whether every problem in a schematically-defined sequence of unification problems is unifiable, so called loop unification. Alternatively, our problem may…