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== Reference ==
Felix Bou, Marco Schorlemmer, Joe Corneli, Danny Gomez Ramirez, Ewen Maclean, Alan Smaill and Alison Pease: [[The role of blending in mathematical invention]]. In: [[Computational Creativity 2015 ICCC 2015]], 55-62.

== DOI ==

== Abstract ==
We model the mathematical process whereby new
mathematical theories are invented. Here we explain the
use of conceptual blending for this purpose, and show
examples to illustrate the process in action. Our longerterm
goal is to support machine and human mathematical
creativity.

== Extended Abstract ==

== Bibtex ==
@inproceedings{
author = {Bou, Felix and Schorlemmer, Marco and Corneli, Joe and Ramirez, Danny Gomez and Maclean, Ewen and Smaill, Alan and Pease, Alison},
title = {The role of blending in mathematical invention},
booktitle = {Proceedings of the Sixth International Conference on Computational Creativity},
series = {ICCC2015},
year = {2015},
month = {Jun},
location = {Park City, Utah, USA},
pages = {55-62},
url = {http://computationalcreativity.net/iccc2015/proceedings/3_2Bou.pdf},
url = {http://de.evo-art.org/index.php?title=The_role_of_blending_in_mathematical_invention},
publisher = {International Association for Computational Creativity},
keywords = {computational, creativity},
}

== Used References ==
Alexander, J. (2011). ‘Blending in mathematics’. Semiotica,
2011(187), 1–48.

Arbib, M. A., and Hesse, M. B. (1986). The construction
of reality. Cambridge, England: Cambridge University
Press.

Astesiano, E. et al. (2002). ‘CASL: the common algebraic
specification language’. Theoretical Computer Science,
286(2), 153–196.

Boden, M. A. (1977). Artificial intelligence and natural
man. Harvester Press.

Deleuze, G. (1994). Difference and repetition. Translated by
Paul Patton. London: Bloomsbury Academic.

Eisenbud, D. (1995). Commutative algebra with a view toward
algebraic geometry. Graduate Texts in Mathematics.
Springer.

Fauconnier, G., and Turner, M. (1998). ‘Conceptual integration
networks’. Cognitive Science, 22(2), 133–187.
Extended version 2001 on-line.

Fauconnier, G., and Turner, M. (2002). The way we think:
conceptual blending and the mind’s hidden complexities.
Basic Books.

Goguen, J. A. (1992). ‘Sheaf semantics for concurrent interacting
objects’. Mathematical Structures in Computer
Science, 159–191.

Goguen, J. A. (1999). ‘An introduction to algebraic semiotics,
with application to user interface design’.
In Computation for metaphors, analogy, and agents
(Vol. 1562, pp. 242–291). LNCS. Springer.

Goguen, J. A. (2005). ‘What is a concept?’ In Conceptual
structures: common semantics for sharing knowledge
(Vol. 3596, pp. 52–57). LNAI. Springer.

Grothendieck, A., and Dieudonné, J. (1971). Eléments de
géométrie algébrique I (seconde édition). Springer.

Gust, H., Kühnberger, K.-U., and Schmidt, U. (2006).
‘Metaphors and heuristic-driven theory projection
(HDTP)’. Theoretical Computer Science, 354, 98–
117.

Hedblom, M., Kutz, O., and Neuhaus, F. (2014). ‘On the
cognitive and logical role of image schemas in computational
conceptual blending’. In A. Lieto et al. (Eds.),
Proceedings of the second international workshop
on artificial intelligence and cognition (AIC 2014)
(Vol. 1315, pp. 110–121). CEUR Workshop Proceedings.

Koestler, A. (1964). The act of creation. Hutchinson.
Kutz, O., Neuhaus, F., Mossakowski, T., and Codescu, M.
(2014). ‘Blending in the Hub – towards a collaborative
concept invention platform’. In Proceedings of the
fifth international conference on computational creativity,
ICCC 2014.

Lakoff, G., and Núñez, R. (2000). Where mathematics
comes from: how the embodied mind brings mathematics
into being. New York: Basic Books.

Larvor, B. (2011). ‘Albert Lautman: Dialectics in Mathematics’.
Foundations of the Formal Sciences VII.

Lautman, A. (2011). Mathematics, ideas and the physical
real. Translated by Simon Duffy. A&C Black.

Mandler, J. M., and Canovás, C. P. (2014). ‘On defining image
schemas’. Language and Cognition, 6, 510–532.

Martinez, M. et al. (2014). ‘Algorithmic aspects of theory
blending’. In 12th international conference on Artificial
Intelligence and Symbolic Computation. Sevilla,
Spain.

Mossakowski, T., Maeder, C., and Lüttich, K. (2007). ‘The
Heterogeneous Tool Set’. In O. Grumberg, and M.
Huth (Eds.), Tacas 2007 (Vol. 4424, pp. 519–522).
Lecture Notes in Computer Science. Springer.

Núñez, R. (2005). ‘Creating mathematical infinities: the
beauty of transfinite cardinals’. Journal of Pragmatics,
37(10), 1717–1741.

Pereira, F. C. (2007). Creativity and artificial intelligence: a
conceptual blending approach. Applications of Cognitive
Linguistics. Mouton de Gruyter.

Schmidt, M. (2010). Restricted higher-order anti-unification
for heuristic-driven theory projection (PICS-Report
No. 31-2010). Univ. Osnabrück. Germany.

Steiner, G. (2001). Grammars of creation. London: Faber
and Faber.

Turner, M. (2005). ‘Mathematics and narrative’. In International
conference on mathematics and narrative.
Mykonos, Greece.

Turner, M. (2014). The origin of ideas: blending, creativity
and the human spark. Oxford: OUP.

Weil, A. (1960). ‘De la métaphysique aux mathématiques’.
Sciences. in (Weil, 1979, pp 408–412).

Weil, A. (1979). OEuvres scientifiques/collected papers. Corrected
second printing. New York: Springer.

== Links ==
=== Full Text ===
http://computationalcreativity.net/iccc2015/proceedings/3_2Bou.pdf

[[intern file]]

=== Sonstige Links ===

@@ Zeile 24: / Zeile 24: @@
    location = {Park City, Utah, USA},
    pages = {55-62},
-   url = {http://computationalcreativity.net/iccc2015/proceedings/3_2Bou.pdf },
+   url = {http://computationalcreativity.net/iccc2015/proceedings/3_2Bou.pdf http://de.evo-art.org/index.php?title=The_role_of_blending_in_mathematical_invention },
    publisher = {International Association for Computational Creativity},
    keywords = {computational, creativity},

The role of blending in mathematical invention - Versionsgeschichte

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Gubachelier: Die Seite wurde neu angelegt: „== Reference == Felix Bou, Marco Schorlemmer, Joe Corneli, Danny Gomez Ramirez, Ewen Maclean, Alan Smaill and Alison Pease: The role of blending in mathemati…“