Modelling the way mathematics is actually done
@article{Corneli2017ModellingTW, title={Modelling the way mathematics is actually done}, author={Joseph Corneli and Ursula Martin and Dave Murray-Rust and Alison Pease and Raymond S Puzio and Gabriela Asli Rino Nesin}, journal={Proceedings of the 5th ACM SIGPLAN International Workshop on Functional Art, Music, Modeling, and Design}, year={2017} }
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…
8 Citations
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References
SHOWING 1-10 OF 77 REFERENCES
Towards Mathematical AI via a Model of the Content and Process of Mathematical Question and Answer Dialogues
- Computer ScienceCICM
- 2017
It is asserted that modelling the Q&A process computationally provides a route to domain understanding that is compatible with the day-to-day practices of mathematicians and students.
Parsing and Disambiguation of Symbolic Mathematics in the Naproche System
- Computer ScienceCalculemus/MKM
- 2011
The difficulties that a program for parsing and disambiguating symbolic mathematics must face are discussed and how these difficulties have been tackled in the Naproche system are presented.
Symbol Grounding via Chaining of Morphisms
- Computer ScienceArXiv
- 2017
The abstractions introduced here are shown to naturally model the structures and systems currently being deployed in the context of using the OpenCog cognitive architecture to control Hanson Robotics humanoid robots.
Memory, meaning, and syntax
- Linguistics
- 1980
The role of syntax in computational theories of natural language is explored and the integrated processing hypothesis, which contends that meaning and world knowledge play a crucial part in language understanding even at the earliest points in the process is discussed.
The interaction of representation and reasoning
- Computer ScienceProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2013
This paper will illustrate the automation of representational change by drawing on recent work in the research group, with a special interest in the way that representation and reasoning interact.
'Chasing' the Diagram - the Use of Visualizations in Algebraic Reasoning
- Computer ScienceRev. Symb. Log.
- 2017
It will be argued that one of the reasons why CDs form a good notation is that they are highly mathematically tractable: experts can obtain valid results by ‘calculating’ with CDs.
Scripts, plans, goals and understanding: an inquiry into human knowledge structures
- Education
- 1977
For both people and machines, each in their own way, there is a serious problem in common of making sense out of what they hear, see, or are told about the world. The conceptual apparatus necessary…
Presupposition Projection and Accommodation in Mathematical Texts
- PhilosophyKONVENS
- 2010
How presuppositions handling was implemented in the Naproche system for checking natural language mathematical proofs turned out to have equivalent projection predictions to an existing account of presupposition projection.
A Model for Processing Illocutionary Structures and Argumentation in Debates
- SociologyLREC
- 2014
This paper introduces the development corpus, and a computational model designed for the identification of discourse minimal units in the context of argumentation and the illocutionary force associated with each unit.