Lakatos-style collaborative mathematics through dialectical, structured and abstract argumentation

The simulation of mathematical reasoning has been a driving force throughout the history of Artificial Intelligence research. However, despite significant successes in computer mathematics, computers are not widely used by mathematicians apart from their quotidian applications. An oft-cited reason f...

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Vydáno v:Artificial intelligence Ročník 246; s. 181 - 219
Hlavní autoři: Pease, Alison, Lawrence, John, Budzynska, Katarzyna, Corneli, Joseph, Reed, Chris
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 01.05.2017
Elsevier Science Ltd
Témata:
Abstract argumentation
Argumentation
Automated reasoning
Automated theorem proving
Collaboration
Collaborative intelligence
Computer simulation
Dialogue games
Game theory
Lakatos
Logic
Mathematical analysis
Mathematical argument
Mathematical models
Mathematics
Philosophy of mathematical practice
Reasoning
Semantics
Social creativity
Social factors
Structured argumentation
Theorem proving
Automated reasoning
Abstract argumentation
Argumentation
Mathematical argument
Structured argumentation
Philosophy of mathematical practice
Automated theorem proving
Lakatos
Collaborative intelligence
Social creativity
Dialogue games
ISSN:0004-3702, 1872-7921
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Shrnutí:The simulation of mathematical reasoning has been a driving force throughout the history of Artificial Intelligence research. However, despite significant successes in computer mathematics, computers are not widely used by mathematicians apart from their quotidian applications. An oft-cited reason for this is that current computational systems cannot do mathematics in the way that humans do. We draw on two areas in which Automated Theorem Proving (ATP) is currently unlike human mathematics: firstly in a focus on soundness, rather than understandability of proof, and secondly in social aspects. Employing techniques and tools from argumentation to build a framework for mixed-initiative collaboration, we develop three complementary arcs. In the first arc – our theoretical model – we interpret the informal logic of mathematical discovery proposed by Lakatos, a philosopher of mathematics, through the lens of dialogue game theory and in particular as a dialogue game ranging over structures of argumentation. In our second arc – our abstraction level – we develop structured arguments, from which we induce abstract argumentation systems and compute the argumentation semantics to provide labelings of the acceptability status of each argument. The output from this stage corresponds to a final, or currently accepted proof artefact, which can be viewed alongside its historical development. Finally, in the third arc – our computational model – we show how each of these formal steps is available in implementation. In an appendix, we demonstrate our approach with a formal, implemented example of real-world mathematical collaboration. We conclude the paper with reflections on our mixed-initiative collaborative approach.
Bibliografie:ObjectType-Article-1
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ISSN:0004-3702
1872-7921
DOI:10.1016/j.artint.2017.02.006