Modelling the way mathematics is actually done

Joseph Corneli; Ursula Martin; Dave Murray-Rust; Alison Pease; Raymond Puzio; Gabriela Rino Nesin

doi:10.1145/3122938.3122942

Modelling the way mathematics is actually done

Joseph Corneli, Ursula Martin, Dave Murray-Rust, Alison Pease, Raymond Puzio, Gabriela Rino Nesin

Computing

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

4 Citations (Scopus)

897 Downloads (Pure)

Abstract

Whereas formal mathematical theories are well studied, computers cannot yet adequately represent and reason about mathematical dialogues and other informal texts. To address this gap, we have developed a representation and reasoning strategy that draws on contemporary argumentation theory and classic AI techniques for representing and querying narratives and dialogues. In order to make the structures that these modelling tools produce accessible to computational reasoning, we encode representations in a higherorder nested semantic network. This system, for which we have developed a preliminary prototype in LISP, can represent both the content of what people say, and the dynamic reasoning steps that move from one step to the next.

Original language	English
Title of host publication	FARM 2017
Subtitle of host publication	Proceedings of the 5th ACM SIGPLAN International Workshop on Functional Art, Music, Modeling, and Design
Place of Publication	New York
Publisher	Association for Computing Machinery (ACM)
Pages	10-19
Number of pages	10
ISBN (Print)	9781450351805
DOIs	https://doi.org/10.1145/3122938.3122942
Publication status	Published - 9 Sept 2017
Event	5th ACM SIGPLAN International Workshop on Functional Art, Music, Modeling, and Design (FARM) - Oxford, United Kingdom Duration: 9 Sept 2017 → 9 Sept 2017 http://functional-art.org/2017/

Workshop

Workshop	5th ACM SIGPLAN International Workshop on Functional Art, Music, Modeling, and Design (FARM)
Country/Territory	United Kingdom
City	Oxford
Period	9/09/17 → 9/09/17
Internet address	http://functional-art.org/2017/

Keywords

Arxana
Conceptual dependency
Exposition
Formal proof
Inference anchoring theory
Knowledge representation and reasoning
Mathematics
Natural language

Access to Document

10.1145/3122938.3122942

Author Accepted ManuscriptAccepted author manuscript, 1.23 MB

Example-Driven Machine-Human Collaboration in Mathematics
Pease, A. (Investigator)
Engineering and Physical Sciences Research Council
1/06/17 → 31/05/19
Project: Research

Cite this

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title = "Modelling the way mathematics is actually done",

abstract = "Whereas formal mathematical theories are well studied, computers cannot yet adequately represent and reason about mathematical dialogues and other informal texts. To address this gap, we have developed a representation and reasoning strategy that draws on contemporary argumentation theory and classic AI techniques for representing and querying narratives and dialogues. In order to make the structures that these modelling tools produce accessible to computational reasoning, we encode representations in a higherorder nested semantic network. This system, for which we have developed a preliminary prototype in LISP, can represent both the content of what people say, and the dynamic reasoning steps that move from one step to the next.",

keywords = "Arxana, Conceptual dependency, Exposition, Formal proof, Inference anchoring theory, Knowledge representation and reasoning, Mathematics, Natural language",

author = "Joseph Corneli and Ursula Martin and Dave Murray-Rust and Alison Pease and Raymond Puzio and Nesin, {Gabriela Rino}",

note = "The authors acknowledge the financial support of the EPSRC via Ursula Martin{\textquoteright}s fellowship “The Social Machine of Mathematics” (EP/K040251/1). The paper also benefitted from conversations at the Isaac Newton Institute residential programme on “Big Proof” (EP/K032208/1). ; 5th ACM SIGPLAN International Workshop on Functional Art, Music, Modeling, and Design (FARM) ; Conference date: 09-09-2017 Through 09-09-2017",

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isbn = "9781450351805",

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Corneli, J, Martin, U, Murray-Rust, D, Pease, A, Puzio, R & Nesin, GR 2017, Modelling the way mathematics is actually done. in FARM 2017: Proceedings of the 5th ACM SIGPLAN International Workshop on Functional Art, Music, Modeling, and Design. Association for Computing Machinery (ACM), New York, pp. 10-19, 5th ACM SIGPLAN International Workshop on Functional Art, Music, Modeling, and Design (FARM), Oxford, United Kingdom, 9/09/17. https://doi.org/10.1145/3122938.3122942

Modelling the way mathematics is actually done. / Corneli, Joseph; Martin, Ursula; Murray-Rust, Dave et al.
FARM 2017: Proceedings of the 5th ACM SIGPLAN International Workshop on Functional Art, Music, Modeling, and Design. New York: Association for Computing Machinery (ACM), 2017. p. 10-19.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AU - Martin, Ursula

AU - Murray-Rust, Dave

AU - Pease, Alison

AU - Puzio, Raymond

AU - Nesin, Gabriela Rino

N1 - The authors acknowledge the financial support of the EPSRC via Ursula Martin’s fellowship “The Social Machine of Mathematics” (EP/K040251/1). The paper also benefitted from conversations at the Isaac Newton Institute residential programme on “Big Proof” (EP/K032208/1).

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N2 - Whereas formal mathematical theories are well studied, computers cannot yet adequately represent and reason about mathematical dialogues and other informal texts. To address this gap, we have developed a representation and reasoning strategy that draws on contemporary argumentation theory and classic AI techniques for representing and querying narratives and dialogues. In order to make the structures that these modelling tools produce accessible to computational reasoning, we encode representations in a higherorder nested semantic network. This system, for which we have developed a preliminary prototype in LISP, can represent both the content of what people say, and the dynamic reasoning steps that move from one step to the next.

AB - Whereas formal mathematical theories are well studied, computers cannot yet adequately represent and reason about mathematical dialogues and other informal texts. To address this gap, we have developed a representation and reasoning strategy that draws on contemporary argumentation theory and classic AI techniques for representing and querying narratives and dialogues. In order to make the structures that these modelling tools produce accessible to computational reasoning, we encode representations in a higherorder nested semantic network. This system, for which we have developed a preliminary prototype in LISP, can represent both the content of what people say, and the dynamic reasoning steps that move from one step to the next.

KW - Arxana

KW - Conceptual dependency

KW - Exposition

KW - Formal proof

KW - Inference anchoring theory

KW - Knowledge representation and reasoning

KW - Mathematics

KW - Natural language

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DO - 10.1145/3122938.3122942

M3 - Conference contribution

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SN - 9781450351805

SP - 10

EP - 19

BT - FARM 2017

PB - Association for Computing Machinery (ACM)

CY - New York

T2 - 5th ACM SIGPLAN International Workshop on Functional Art, Music, Modeling, and Design (FARM)

Y2 - 9 September 2017 through 9 September 2017

ER -

Modelling the way mathematics is actually done

Abstract

Workshop

Keywords

Access to Document

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Projects

Example-Driven Machine-Human Collaboration in Mathematics

Cite this