Analogy, Concept Blending, and Computational...

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)

Tarek R. Besold Analogy, Concept Blending & Computational Creativity

Analogy in the Wild (1)

Tarek R. Besold Analogy, Concept Blending & Computational Creativity

Analogy in the Wild (2)

Juliet is like the sun.

Tarek R. Besold Analogy, Concept Blending & Computational Creativity

Analogy in the Wild (2)

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

fields?

Tarek R. Besold Analogy, Concept Blending & Computational Creativity

Analogy in the Wild (2)

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

Solar System?

Tarek R. Besold Analogy, Concept Blending & Computational Creativity

Analogy in the Wild (2)

Juliet is like the sun.

Tarek R. Besold Analogy, Concept Blending & Computational Creativity

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.)

Tarek R. Besold Analogy, Concept Blending & Computational Creativity

A Schematic Account of Computational Analogy-Making

Tarek R. Besold Analogy, Concept Blending & Computational Creativity

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).

Tarek R. Besold Analogy, Concept Blending & Computational Creativity

Heuristic-Driven Theory Projection (2)

Tarek R. Besold Analogy, Concept Blending & Computational Creativity

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.

Tarek R. Besold Analogy, Concept Blending & Computational Creativity

Rutherford & HDTP (2)

Tarek R. Besold Analogy, Concept Blending & Computational Creativity

Rutherford & HDTP (3)

Tarek R. Besold Analogy, Concept Blending & Computational Creativity

Concept blending: A + B = ? (1)

Tarek R. Besold Analogy, Concept Blending & Computational Creativity

Concept blending: A + B = ? (2)

Tarek R. Besold Analogy, Concept Blending & Computational Creativity

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 .

Tarek R. Besold Analogy, Concept Blending & Computational Creativity

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.

Tarek R. Besold Analogy, Concept Blending & Computational Creativity

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

Tarek R. Besold Analogy, Concept Blending & Computational Creativity

COINVENT - Concept Invention Theory (2)

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.

Tarek R. Besold Analogy, Concept Blending & Computational Creativity

COINVENT - Concept Invention Theory (3)

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.

Tarek R. Besold Analogy, Concept Blending & Computational Creativity

The very last slide...

Thank you for your attention!

Questions: tbesold@uos.de

The unavoidable closing XKCD (#948):

Tarek R. Besold Analogy, Concept Blending & Computational Creativity