Analogy, Concept Blending, and Computational Creativityprosecco.computationalcreativity.net/sites/default/files/... · 2014-06-24 · Ahmed Abdel-Fattah Tarek R. Besold University

Analogy, Concept Blending,and Computational Creativity

Tarek R. Besold

AI Research GroupInstitute of Cognitive Science

University of Osnabruck

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 Osnabruck:Kai-Uwe KuhnbergerHelmar GustUte Schmid (University of Bamberg, Germany)Angela Schwering (University of Munster, Germany)Maricarmen Martinez Baldares (University of the Andes,Bogota, Colombia)Ulf KrumnackMartin Mohrmann (ne Schmidt)Ahmed Abdel-FattahTarek R. Besold

University of Edinburgh:

Alan SmaillMarkus GuheAlison Pease (University of Dundee, Scotland, UK)


Analogy in the Wild (1)



Juliet is like the sun.



Juliet is like the sun.= Juliet consists of hot plasma interwoven with magnetic

fields?



Juliet is like the sun.= Juliet accounts for about 99.68% of the total mass of the

Solar System?



Juliet is like the sun.


What’s it all about...

Analogy

“άναλογία” - analogia, “proportion”.

Informally: Claims of similarity, often used in argumentationor when explaining complex situations.

A bit more formal: Analogy-making is the human ability ofperceiving dissimilar domains as similar with respect tocertain aspects based on shared commonalities in relationalstructure or appearance.(Incidental remark: In less complex forms also to be found insome other primates.)


A Schematic Account of Computational Analogy-Making


Heuristic-Driven Theory Projection (1)

Heuristic-Driven Theory Projection (HDTP)

Computing analogical relations and inferences (domainsgiven as many-sorted first-order logic representation).

Base and target of analogy defined in terms ofaxiomatisations, 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 toa restricted form of higher-order anti-unification).

Modeling generalization-guided analogical transfer betweensource and target domain.

Proof-of-concept applications in modeling mathematicalreasoning (Argand, 1813) and concept blending inmathematics (Lakoff & Nunez, 2000).


Heuristic-Driven Theory Projection (2)


Rutherford & HDTP (1)

Rutherford analogy (underlying the Bohr-Rutherford model ofthe atom):

Analogy between solar system andhydrogen atom:

...nucleus is more massive than electrons,sun is more massive than planets.

...nucleus attracts electrons (Coulomb’slaw), sun attracts planets (Newton’s lawof gravity).

...attraction plus mass relation causeselectrons to revolve around nucleus,similarly planets revolve around sun.






Concept blending: A + B = ? (1)


Concept blending: A + B = ? (2)


Foundations of Theory Blending

Concept Blending

Given two domain theories I1 and I2, representing twoconceptualizations...

...look for a generalization G ...

...construct the blend space B in such a way as to preservethe correlations between I1 and I2 established by G .


Mathematical Domain Formation (1)

Modeling (Argand, 1813)’s (re)discovery1 of complex plane asgeometric interpretation of complex numbers.

Not using detailed formalizations of domains, but formalizingonly the minimum necessary and highlighting dynamics ofselection and use of domains in network.

Network of domains in Argand’s reasoning:

1Independent first discovery: Wallis, 1685.Tarek R. Besold Analogy, Concept Blending & Computational Creativity

Mathematical Domain Formation (2)

Argand added vector domain (VECTORS), and subsequentlycomplex 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.


COINVENT - Concept Invention Theory (1)

European research project within the Future and EmergingTechnologies (FET) programme within the Seventh FrameworkProgramme for Research of the European Commission, underFET-Open Grant number: 611553.

The COINVENT partners:

IIIA-CSIC, Barcelona, Spain

University of Edinburgh, Scotland, UK

University of Osnabruck, Germany

Univ. of Bremen, Germany/Univ. of Magdeburg, Germany

Goldsmiths, University of London, UK

Aristotle University of Thessaloniki, Greece

University of Dundee, Scotland, UK



Goals

A novel, computationally feasible, formal model of conceptblending (based on Fauconnier and Turner’s theory).

A deeper understanding of conceptual blending and its role incomputational creativity.

A generic, creative computational system capable ofserendipitous invention and manipulation of novel abstractconcepts.

Validate model and computational realization in representativeworking domains of creativity: mathematics and music.



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 bymathematicians.

Melodic harmonisation: A computational system that...

...proposes new harmonic concepts emerging from learnedharmonic spaces, examples and counter-examples....suggests new harmonic conceptualizations emerging fromblends of different harmonic spaces that give rise to potentiallyinteresting new harmonies.


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 Creativityprosecco.computationalcreativity.net/sites/default/files/... · 2014-06-24 · Ahmed Abdel-Fattah Tarek R. Besold University