arXiv subjects

Joseph Corneli

Publications and source records attributed to Joseph Corneli.

At least 19 recordsLinked to original sources

arXiv2026

A First Proof Sprint

This monograph reports a multi-agent proof sprint on ten research-level problems, combining rapid draft generation with adversarial verification, targeted repair, and explicit provenance. The workflow uses wiring-diagram decompositions of claim dependencies to localize gaps and coordinate reviewer-driven revisions. Final outcomes are heterogeneous but explicit: the manuscript distinguishes mathematical status from QC-validation status. Mathematically, Problem~3 has a validation-complete existence path under the scoped criterion used here (uniqueness/irreducibility treated as optional), Problem 5 is solved in a scope-limited form for $F_O$-local connective spectra, Problem 10 is conditional under clearly stated assumptions (with explicit necessity counterexamples when assumptions are dropped), and Problems 4 and 6 are partial with named remaining obligations in the general case (including an unconditional $K_n$ result for Problem 6 with $c_0 = 1/3$). Problem 7 is treated as provisionally closed via the rotation-route theorem chain, pending independent ledger re-check. At the QC layer, Problems~7 and~9 have node-level validation artifacts but still contain unresolved verifier gaps. The main methodological result is that structure-aware verification and layer-switching strategies improve reliability and calibration in compressed proof sprints.

cs.AI↗

arXiv2025

Patterns for a New Generation: AI and Agents

Design patterns have been used in various fields of inquiry and endeavour to externalize procedural knowledge in a form that supports human reasoning and coordination. In this paper, we show that contemporary Large Language Model (LLM)-based systems can also read, generate, and reason with design patterns written in a structured template. We describe an experimental workflow in which patterns function as shared priors for action selection, reflection, and revision in hybrid human/agent settings. Drawing on the Active Inference Framework, we illustrate how patterns can guide agent behavior without fully prescribing it. This provides a proof of concept that pattern-capable agents can be created using now-standard software tools. We discuss implications for software development, education, business, and AI governance.

cs.HC↗

arXiv2024

AI Future Envisioning with PLACARD

At EuroPLoP 2024 Mary Tedeschi led the "AI Future Envisioning with PLACARD" focus group in Germany. Three conference attendees joined in the room while Sridevi, Paola, and Charles co-facilitated remotely via a web conference. The participants were introduced to a Futures Studies technique with the goal of capturing envisionments of Artificial Intelligence (AI) going forward. To set an atmosphere a technology focused card game was used to make the session more interactive. To close everyone co-created a Project Action Review to recap of the event to capture learnings that has been summarized in this paper. The Focus Group was structured based on lessons learned over six earlier iterations.

cs.CY↗

arXiv2023

Patterns of Patterns II

Our earlier paper "Patterns of Patterns" combined three techniques from training, futures studies, and design in a design pattern called PLACARD that helps groups of people work together effectively. We used that pattern in five hands-on workshop case studies which took place at various locations in the US and the UK. This experience report documents what we learned, including the way our thinking about PLACARD evolved, together with additional patterns our work generated. We evaluate the reproducibility of our methods and results, and consider the broader economic implications of this way of working. We discuss implications of our prototyping work for the design of future platforms, drawing connections with recent developments in cognitive science and artificial intelligence. This positions our patterns of patterns as a toolkit for the design and governance of systems that combine social dynamics with technical components.

cs.SI↗

arXiv2021

Patterns of Patterns

This paper shows how we combine and adapt methods from elite training, future studies, and collaborative design, and apply them to address significant problems in social networks. We focus on three such methods: we use Project Action Reviews to implement social perception, Causal Layered Analysis to implement social cognition, and Design Pattern Languages to implement social action. We present the results of two studies: firstly, we use Causal Layered Analysis to explore the ways in which the design pattern discourse has been evolving. Secondly, to illustrate the three methods in combination, we develop a case study, showing how we applied the methods to bootstrap a distributed cross-disciplinary research seminar. Building on these analyses, we elaborate several scenarios for the future use of design patterns in large-scale distributed collaboration. Our case study suggests ways in which progress could be made towards realizing these scenarios. We conclude that the combination of methods is robust to uncertainty, insofar as they support adaptations as circumstances change, and incorporate diverse perspectives. In particular, we show how methods drawn from other domains enrich and are enriched by design patterns; we believe the analysis will be of interest to all of the communities whose methods we draw upon.

cs.SI↗

arXiv2020

Patterns, anticipation and participatory futures

Patterns embody repeating phenomena, and, as such, they are partly but not fully detachable from their context. 'Design patterns' and 'pattern languages' are established methods for working with patterns. They have been applied in architecture, software engineering, and other design fields, but have so far seen little application in the field of future studies. We reimagine futures discourse and anticipatory practices using pattern methods. We focus specifically on processes for coordinating distributed projects, integrating multiple voices, and on play that builds capability to face what's yet to come. One of the advantages of the method as a whole is that it deals with local knowledge and does not subsume everything within one overall 'global' strategy, while nevertheless offering a way to communicate between contexts and disciplines.

cs.DC↗

arXiv2018

Argumentation theory for mathematical argument

To adequately model mathematical arguments the analyst must be able to represent the mathematical objects under discussion and the relationships between them, as well as inferences drawn about these objects and relationships as the discourse unfolds. We introduce a framework with these properties, which has been used to analyse mathematical dialogues and expository texts. The framework can recover salient elements of discourse at, and within, the sentence level, as well as the way mathematical content connects to form larger argumentative structures. We show how the framework might be used to support computational reasoning, and argue that it provides a more natural way to examine the process of proving theorems than do Lamport's structured proofs.

cs.CL↗

arXiv2016

X575: writing rengas with web services

Our software system simulates the classical collaborative Japanese poetry form, renga, made of linked haikus. We used NLP methods wrapped up as web services. Our experiments were only a partial success, since results fail to satisfy classical constraints. To gather ideas for future work, we examine related research in semiotics, linguistics, and computing.

cs.AI↗

arXiv2016

An institutional approach to computational social creativity

Modelling the creativity that takes place in social settings presents a range of theoretical challenges. Mel Rhodes's classic "4Ps" of creativity, the "Person, Process, Product, and Press," offer an initial typology. Here, Rhodes's ideas are connected with Elinor Ostrom's work on the analysis of economic governance to generate several "creativity design principles." These principles frame a survey of the shared concepts that structure the contexts that support creative work. The concepts are connected to the idea of computational "tests" to foreground the relationship with standard computing practice, and to draw out specific recommendations for the further development of computational creativity culture.

cs.CY↗

arXiv2016

Teaching natural language to computers

"Natural Language," whether spoken and attended to by humans, or processed and generated by computers, requires networked structures that reflect creative processes in semantic, syntactic, phonetic, linguistic, social, emotional, and cultural modules. Being able to produce novel and useful behavior following repeated practice gets to the root of both artificial intelligence and human language. This paper investigates the modalities involved in language-like applications that computers -- and programmers -- engage with, and aims to fine tune the questions we ask to better account for context, self-awareness, and embodiment.

cs.CL↗

arXiv2016

An Argument-based Creative Assistant for Harmonic Blending

Conceptual blending is a powerful tool for computational creativity where, for example, the properties of two harmonic spaces may be combined in a consistent manner to produce a novel harmonic space. However, deciding about the importance of property features in the input spaces and evaluating the results of conceptual blending is a nontrivial task. In the specific case of musical harmony, defining the salient features of chord transitions and evaluating invented harmonic spaces requires deep musicological background knowledge. In this paper, we propose a creative tool that helps musicologists to evaluate and to enhance harmonic innovation. This tool allows a music expert to specify arguments over given transition properties. These arguments are then considered by the system when defining combinations of features in an idiom-blending process. A music expert can assess whether the new harmonic idiom makes musicological sense and re-adjust the arguments (selection of features) to explore alternative blends that can potentially produce better harmonic spaces. We conclude with a discussion of future work that would further automate the harmonisation process.

cs.SD↗

arXiv2015

Implementing feedback in creative systems: A workshop approach

One particular challenge in AI is the computational modelling and simulation of creativity. Feedback and learning from experience are key aspects of the creative process. Here we investigate how we could implement feedback in creative systems using a social model. From the field of creative writing we borrow the concept of a Writers Workshop as a model for learning through feedback. The Writers Workshop encourages examination, discussion and debates of a piece of creative work using a prescribed format of activities. We propose a computational model of the Writers Workshop as a roadmap for incorporation of feedback in artificial creativity systems. We argue that the Writers Workshop setting describes the anatomy of the creative process. We support our claim with a case study that describes how to implement the Writers Workshop model in a computational creativity system. We present this work using patterns other people can follow to implement similar designs in their own systems. We conclude by discussing the broader relevance of this model to other aspects of AI.

cs.AI↗

arXiv2015

The Search for Computational Intelligence

We define and explore in simulation several rules for the local evolution of generative rules for 1D and 2D cellular automata. Our implementation uses strategies from conceptual blending. We discuss potential applications to modelling social dynamics.

cs.NE↗

arXiv2014

Modelling serendipity in a computational context

The term serendipity describes a creative process that develops, in context, with the active participation of a creative agent, but not entirely within that agent's control. While a system cannot be made to perform serendipitously on demand, we argue that its $\mathit{serendipity\ potential}$ can be increased by means of a suitable system architecture and other design choices. We distil a unified description of serendipitous occurrences from historical theorisations of serendipity and creativity. This takes the form of a framework with six phases: $\mathit{perception}$, $\mathit{attention}$, $\mathit{interest}$, $\mathit{explanation}$, $\mathit{bridge}$, and $\mathit{valuation}$. We then use this framework to organise a survey of literature in cognitive science, philosophy, and computing, which yields practical definitions of the six phases, along with heuristics for implementation. We use the resulting model to evaluate the serendipity potential of four existing systems developed by others, and two systems previously developed by two of the authors. Most existing research that considers serendipity in a computing context deals with serendipity as a service; here we relate theories of serendipity to the development of autonomous systems and computational creativity practice. We argue that serendipity is not teleologically blind, and outline representative directions for future applications of our model. We conclude that it is feasible to equip computational systems with the potential for serendipity, and that this could be beneficial in varied computational creativity/AI applications, particularly those designed to operate responsively in real-world contexts.

cs.AI↗

arXiv2014

NNexus Reloaded

Interlinking knowledge is one of the cornerstones of online collaboration. While wiki systems typically rely on links supplied by authors, in the early 2000s the mathematics encyclopedia at PlanetMath.org introduced a feature that provides automatic linking for previously defined concepts. The NNexus software suite was developed to support the necessary subtasks of concept indexing, concept discovery and link-annotation. In this paper, we describe our recent reimplementation and revisioning of the NNexus system.

cs.DL↗

arXiv2012

Reimplementing the Mathematical Subject Classification (MSC) as a Linked Open Dataset

The Mathematics Subject Classification (MSC) is a widely used scheme for classifying documents in mathematics by subject. Its traditional, idiosyncratic conceptualization and representation makes the scheme hard to maintain and requires custom implementations of search, query and annotation support. This limits uptake e.g. in semantic web technologies in general and the creation and exploration of connections between mathematics and related domains (e.g. science) in particular. This paper presents the new official implementation of the MSC2010 as a Linked Open Dataset, building on SKOS (Simple Knowledge Organization System). We provide a brief overview of the dataset's structure, its available implementations, and first applications.

cs.DL↗

arXiv2008

Double bubbles in $S^3$ and $H^3$

We prove the double bubble conjecture in the three-sphere $S^3$ and hyperbolic three-space $H^3$ in the cases where we can apply Hutchings theory: 1) in $S^3$, each enclosed volume and the complement occupy at least 10% of the volume of $S^3$; 2) in $H^3$, the smaller volume is at least 85% that of the larger. A balancing argument and asymptotic analysis reduce the problem in $S^3$ and $H^3$ to some computer checking. The computer analysis has been designed and fully implemented for both spaces.

math.DG↗

arXiv2003

The Double Bubble Problem on the Flat Two-Torus

We characterize the perimeter-minimizing double bubbles on all flat two-tori and, as corollaries, on the flat infinite cylinder and the flat infinite strip with free boundary. Specifically, we show that there are five distinct types of minimizers on flat two-tori, depending on the areas to be enclosed.

math.MG↗