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The Importance of Being Neural-Symbolic – A Wilde Position

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1 The Importance of Being Neural-Symbolic – A Wilde Position
The Second Conference on Artificial General Intelligence (AGI-09) March 7th, 2009 Kai-Uwe Kühnberger (with Pascal Hitzler) Kai-Uwe Kühnberger & Pascal Hitzler University of Osnabrück & University of Karlsruhe The Second Conference on Artificial General Intelligence (AGI-09) Arlington, March 7th, 2009

2 The Problem There is an obvious tension between symbolic and subsymbolic representations: The task is to close this gap. Symbolic Approaches Subsymbolic Approaches Methods Mainly logical and / or algebraic Mainly analytic Strengths Productivity, recursion, compositionality Robustness, learning, parsimony, adaptivity Weaknesses Consistency constraints, lower cognitive abilities Opaqueness, higher cognitive abilities Applications Reasoning, problem solving, planning etc. Learning, motor control, vision etc. Relation to Neurobiology Not biologically inspired Biologically inspired Other Features Crisp Fuzzy Kai-Uwe Kühnberger & Pascal Hitzler University of Osnabrück & University of Karlsruhe The Second Conference on Artificial General Intelligence (AGI-09) Arlington, March 7th, 2009

3 Where We Are Neural representations of propositional logic programs by the “core method”: An underlying feedforward network is constructed for every logic program P separately (by a translation algorithm). One can approximate for every propositional logic program P the semantics of the single-step operator TP by embedding this feedforward network into a recurrent network. Hölldobler & Kalinke (1994) Bader, Hitzler, Hölldobler & Witzel (2007) Kai-Uwe Kühnberger & Pascal Hitzler University of Osnabrück & University of Karlsruhe The Second Conference on Artificial General Intelligence (AGI-09) Arlington, March 7th, 2009

4 Were We Are The core method can be extended to first-order predicate logic. An alternative approach is Topos-based: Topos theory can be used to represent predicate logic in a variable-free manner allowing only one operation: concatenation of arrows in commuting diagrams. A real-valued vector representation of the arrows occurring in commuting diagrams can be used to learn representations of formulas in a feedforward network. Gust, Kühnberger & Geibel (2007) Kai-Uwe Kühnberger & Pascal Hitzler University of Osnabrück & University of Karlsruhe The Second Conference on Artificial General Intelligence (AGI-09) Arlington, March 7th, 2009

5 Where to Go to Improve the already established approaches.
Develop cognitive application scenarios. Integrate new ideas borrowed from other disciplines: Cognitive psychology Recent paradigms for artificial neural networks inspired by neurosciences Embed such a device into an integrated architecture. Kai-Uwe Kühnberger & Pascal Hitzler University of Osnabrück & University of Karlsruhe The Second Conference on Artificial General Intelligence (AGI-09) Arlington, March 7th, 2009

6 Thank you very much!! Kai-Uwe Kühnberger & Pascal Hitzler
University of Osnabrück & University of Karlsruhe The Second Conference on Artificial General Intelligence (AGI-09) Arlington, March 7th, 2009


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