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