Analogy, Concept Blending, and Computational Creativity

Transcription

Analogy, Concept Blending,
and Computational Creativity
Tarek R. Besold
AI Research Group
Institute of Cognitive Science
University of Osnabrück
22. February 2014
Tarek R. Besold
Analogy, Concept Blending & Computational Creativity
Honor to whom honor is due...
The following presentation is based on joint work (mainly) by:
University of Osnabrück:
Kai-Uwe Kühnberger
Helmar Gust
Ute Schmid (University of Bamberg, Germany)
Angela Schwering (University of Münster, Germany)
Maricarmen Martinez Baldares (University of the Andes,
Bogotá, Colombia)
Ulf Krumnack
Martin Möhrmann (né Schmidt)
Ahmed Abdel-Fattah
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University of Edinburgh:
Alan Smaill
Markus Guhe
Alison Pease (University of Dundee, Scotland, UK)
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Analogy in the Wild (1)
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Juliet is like the sun.
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= Juliet consists of hot plasma interwoven with magnetic
fields?
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= Juliet accounts for about 99.68% of the total mass of the
Solar System?
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What’s it all about...
Analogy
“άναλογία” - analogia, “proportion”.
Informally: Claims of similarity, often used in argumentation
or when explaining complex situations.
A bit more formal: Analogy-making is the human ability of
perceiving dissimilar domains as similar with respect to
certain aspects based on shared commonalities in relational
structure or appearance.
(Incidental remark: In less complex forms also to be found in
some other primates.)
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A Schematic Account of Computational Analogy-Making
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Heuristic-Driven Theory Projection (1)
Heuristic-Driven Theory Projection (HDTP)
Computing analogical relations and inferences (domains
given as many-sorted first-order logic representation).
Base and target of analogy defined in terms of
axiomatisations, i.e., given by a finite set of formulae.
Aligning pairs of formulae by means of anti-unification
(extending classical Plotkin-style first-order anti-unification to
a restricted form of higher-order anti-unification).
Modeling generalization-guided analogical transfer between
source and target domain.
Proof-of-concept applications in modeling mathematical
reasoning (Argand, 1813) and concept blending in
mathematics (Lakoff & Núñez, 2000).
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Heuristic-Driven Theory Projection (2)
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Rutherford & HDTP (1)
Rutherford analogy (underlying the Bohr-Rutherford model of
the atom):
Analogy between solar system and
hydrogen atom:
...nucleus is more massive than electrons,
sun is more massive than planets.
...nucleus attracts electrons (Coulomb’s
law), sun attracts planets (Newton’s law
of gravity).
...attraction plus mass relation causes
electrons to revolve around nucleus,
similarly planets revolve around sun.
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Concept blending: A + B = ? (1)
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Concept blending: A + B = ? (2)
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Foundations of Theory Blending
Concept Blending
Given two domain theories I1 and I2 , representing two
conceptualizations...
...look for a generalization G ...
...construct the blend space B in such a way as to preserve
the correlations between I1 and I2 established by G .
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Mathematical Domain Formation (1)
Modeling (Argand, 1813)’s (re)discovery1 of complex plane as
geometric interpretation of complex numbers.
Not using detailed formalizations of domains, but formalizing
only the minimum necessary and highlighting dynamics of
selection and use of domains in network.
Network of domains in Argand’s reasoning:
1
Independent first discovery: Wallis, 1685.
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Mathematical Domain Formation (2)
Argand added vector domain (VECTORS), and subsequently
complex plane (CP), to already existing network of domains.
Together with complex arithmetic (CA) and number line
(NL), CP and VECTORS form diamond shape of blend.
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COINVENT - Concept Invention Theory (1)
European research project within the Future and Emerging
Technologies (FET) programme within the Seventh Framework
Programme for Research of the European Commission, under
FET-Open Grant number: 611553.
The COINVENT partners:
IIIA-CSIC, Barcelona, Spain
University of Edinburgh, Scotland, UK
University of Osnabrück, Germany
Univ. of Bremen, Germany/Univ. of Magdeburg, Germany
Goldsmiths, University of London, UK
Aristotle University of Thessaloniki, Greece
University of Dundee, Scotland, UK
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Goals
A novel, computationally feasible, formal model of concept
blending (based on Fauconnier and Turner’s theory).
A deeper understanding of conceptual blending and its role in
computational creativity.
A generic, creative computational system capable of
serendipitous invention and manipulation of novel abstract
concepts.
Validate model and computational realization in representative
working domains of creativity: mathematics and music.
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Expected Contributions: Working Domains
Mathematical reasoning: A computational system that...
...proposes potentially interesting novel definitions, theories,
and conjectures motivated by conceptual (not only formal)
reasons.
...evaluates the potential of ideas when proposed by
mathematicians.
Melodic harmonisation: A computational system that...
...proposes new harmonic concepts emerging from learned
harmonic spaces, examples and counter-examples.
...suggests new harmonic conceptualizations emerging from
blends of different harmonic spaces that give rise to potentially
interesting new harmonies.
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The very last slide...
Thank you for your attention!
Questions: [email protected]
The unavoidable closing XKCD (#948):
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Analogy, Concept Blending, and Computational Creativity

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