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Learning from Inconsistencies in an Integrated Cognitive Architecture The First Conference on Artificial General Intelligence (AGI-08) March 1st, 2008 Kai-Uwe Kühnberger (with Peter Geibel, Helmar Gust, Ulf Krumnack, Ekaterina Ovchinnikova, Angela Schwering, Tonio Wandmacher) Kai-Uwe Kühnberger et al. Universität Osnabrück The First Conference on Artificial General Intelligence (AGI-08) Memphis, March 1st, 2008 Overview Introduction Learning in Cognitive Systems The I-Cog Architecture General Overview of the System Learning from Inconsistencies General Remarks Learning from Inconsistencies in Analogy Making and the Overall System Conclusions Kai-Uwe Kühnberger et al. Universität Osnabrück The First Conference on Artificial General Intelligence (AGI-08) Memphis, March 1st, 2008 Introduction Learning in Cognitive Systems Kai-Uwe Kühnberger et al. Universität Osnabrück The First Conference on Artificial General Intelligence (AGI-08) Memphis, March 1st, 2008 Learning Usually cognitive architectures are based on a number of different modules. Example: Hybrid System Obviously, coherence problems and consistency clashes can occur, in particular, in hybrid systems. In hybrid architectures, two main questions can be asked: On which level should learning be implemented? What are plausible strategies in order to resolve inconsistencies? Idea of this talk: Use occurring inconsistencies as a mechanism (trigger) of learning. Kai-Uwe Kühnberger et al. Universität Osnabrück The First Conference on Artificial General Intelligence (AGI-08) Memphis, March 1st, 2008 The I-Cog Architecture General Overview Kai-Uwe Kühnberger et al. Universität Osnabrück The First Conference on Artificial General Intelligence (AGI-08) Memphis, March 1st, 2008 A Proposal: I-Cog I-Cog is a modular system consisting of three main modules: Analogy Engine (AE): Ontology Rewriting Device (ORD): Claim: AE is able to cover a variety of different reasoning abilities. Claim: Ontological background knowledge needs to be implemented in a way, such that dynamic updates are possible. Neuro-Symbolic Learning Device (NSLD): Claim: The neuro-symbolic learning device enables robust learning of symbolic theories form noisy data. Finally: these three modules interact in a non-trivial way and are governed by a heuristic-driven Control Device (CD). Kühnberger, K.-U. et al. (2007): I-Cog: A Computational Framework for Integrated Cognition of Higher Cognitive Abilities, in Proceedings of MICAI 2007, LNAI 4827, pp. 203-214, Springer. Kai-Uwe Kühnberger et al. Universität Osnabrück The First Conference on Artificial General Intelligence (AGI-08) Memphis, March 1st, 2008 The Overall I-Cog Architecture Kai-Uwe Kühnberger et al. Universität Osnabrück The First Conference on Artificial General Intelligence (AGI-08) Memphis, March 1st, 2008 Learning in I-Cog Learning is based on occurring inconsistencies In the case of ORD, rewriting algorithms make sure that inconsistencies are resolved (where this is possible). NSLD is a learning device, where weights are adjusted based on backpropagation of errors. Ovchinnikova, E. & Kühnberger, K.-U. (2007). Debugging Automatically Extended Ontologies, GLDV-Journal for Computational Linguistics and Language Technology, 23(2):19-33 . Gust, H., Kühnberger, K.-U. & Geibel, P. (2007). Learning Models of Predicate Logical Theories with Neural Networks Based on Topos Theory, in P. Hitzler & B. Hammer (eds.): Perspectives of NeuralSymbolic Integration, Series “Computational Intelligence”, Springer, pp. 209-240. In the case of AE, it is possible to reduce many adaptation processes to occurring inconsistencies. Claim 1: Learning is distributed over the whole system. Claim 2: Learning takes place because errors / inconsistencies occur triggering an adaptation process. Kai-Uwe Kühnberger et al. Universität Osnabrück The First Conference on Artificial General Intelligence (AGI-08) Memphis, March 1st, 2008 Learning from Inconsistencies The Example of Analogical Reasoning Kai-Uwe Kühnberger et al. Universität Osnabrück The First Conference on Artificial General Intelligence (AGI-08) Memphis, March 1st, 2008 General Remarks Inconsistencies are classically connected to logic If for a set of axioms (relative to a language L) can be entailed and can be entailed, then is inconsistent. We use the term “inconsistency” rather loosely and do not restrict this concept to logic. Here are some examples: Every analogy establishes a relation that resolves a clash of concepts, information, interpretations etc. Ontology generation / learning Ovchinnikova, E., Wandmacher, T. & Kühnberger, K.-U. (2007). Solving Terminological Inconsistency Problems in Ontology Design, IBIS 4:65-80. Non-monotonicity effects in reasoning. Kai-Uwe Kühnberger et al. Universität Osnabrück Gust, H. & Kühnberger, K.-U. (2006). Explaining Effective Learning by Analogical Reasoning, 28th Annual Conference of the Cognitive Science Society, pp. 1417-1422. Ovchinnikova, E. & Kühnberger, K.-U. (2006). Adaptive ALE-TBox for Extending Terminological Knowledge, in Proceedings of AI’06, LNAI 4304, Springer, pp. 1111-1115. The First Conference on Artificial General Intelligence (AGI-08) Memphis, March 1st, 2008 The Analogy Engine The Analogy Engine is based on Heuristic-Driven Theory Projection (HDTP). HDTP is a mathematically sound theory of computing analogies. It is based on anti-unification of a source theory ThS and a target theory ThT. It was applied to various domains like naïve physics, metaphors, geometric figures etc. Some features: Complex formulas can be anti-unified. A theorem prover allows the re-representation of formulas. Whole theories can be generalized. The involved processes are governed by heuristics. Gust, H., Kühnberger, K.-U. & Schmid, U. (2006). Metaphors and Heuristic-Driven Theory Projection (HDTP), Theoretical Computer Science, 354:98-117. Kai-Uwe Kühnberger et al. Universität Osnabrück The First Conference on Artificial General Intelligence (AGI-08) Memphis, March 1st, 2008 Recursion Example I Source ThS: Addition 1: x: add(x,0) = x 2: xy: add(x,s(y)) = s(add(x,y)) Target ThT: Multiplication 1: x: mult(x,s(0)) = x 2: xy: mult(x,s(y)) = add(x,mult(x,y)) Generalized Theory ThG: 1: x: OP1(x,E) = x 2: xy: Op1(x,s(y)) = Op2(Op1(x,y)) For the generalized theory, the following substitutions need to be established: 1: E 0, Op1 add, Op2 s 2: E s(0), Op1 mult, Op2 z.add(x,z) Kai-Uwe Kühnberger et al. Universität Osnabrück The First Conference on Artificial General Intelligence (AGI-08) Memphis, March 1st, 2008 Recursion Example II Source ThS: Addition 1: x: add(0,x) = x 2: xy: add(s(y),x) = add(y,s(x)) Target ThT: Multiplication 1: x: mult(0,x) = 0 2: xy: mult(s(y),x) = add(x,mult(x,y)) Generalized Theory ThG: 1: x: Op(E,x) = x Trying to anti-unify 1 and 1 is not possible. But by using axioms 1 and 2 we can derive mult(s(0),x) = add(x,mult(0,x)) = add(x,0) = … = add(0,x) Hence we can derive: 3: x: mult(s(0),x) = x For the generalized theory, the following substitutions can be established: 1: E 0, Op add Kai-Uwe Kühnberger et al. Universität Osnabrück and 2: E s(0), Op mult The First Conference on Artificial General Intelligence (AGI-08) Memphis, March 1st, 2008 Conclusion Main claims: In cognitive architectures “inconsistencies” (as used in the broad sense here) should be considered as a trigger for learning and adaptation. These adaptation processes can be relevant for: Adapting background knowledge, Reasoning processes of various types, Neuro-based learning approaches. Learning in the systems is therefore distributed and continuously realized. Kai-Uwe Kühnberger et al. Universität Osnabrück The First Conference on Artificial General Intelligence (AGI-08) Memphis, March 1st, 2008 Thank you very much!! Questions? Kai-Uwe Kühnberger et al. Universität Osnabrück The First Conference on Artificial General Intelligence (AGI-08) Memphis, March 1st, 2008 References Analogical Reasoning (Selection) Gust, H., Kühnberger, K.-U. & Schmid, U. (2006). Metaphors and HeuristicDriven Theory Projection (HDTP), Theoretical Computer Science, 354:98117. Gust, H. & Kühnberger, K.-U. (2006). Explaining Effective Learning by Analogical Reasoning, in: R. Sun & N. Miyake (eds.): 28th Annual Conference of the Cognitive Science Society, Lawrence Erlbaum, pp. 14171422. Gust, H., Krumnack, U., Kühnberger, K.-U. & Schwering, A. (2007). An Approach to the Semantics of Analogical Relations, in S. Vosniadou et al. (eds.): Proceedings of EuroCogSci 2007, Lawrence Erlbaum, pp. 640-645. Krumnack, U., Schwering, A., Gust, H. & Kühnberger, K.-U. (2007). Restricted Higher-Order Anti-Unification for Analogy Making, to appear in Proceedings of AI’07, Springer. Gust, H., Krumnack, U., Kühnberger, K.-U. & Schwering, A. (2008). Analogical Reasoning: A Core of Cognition, to appear in Künstliche Intelligenz 1/2008. Kai-Uwe Kühnberger et al. Universität Osnabrück The First Conference on Artificial General Intelligence (AGI-08) Memphis, March 1st, 2008 References Neuro-Symbolic Integration (Selection) Gust, H., Kühnberger, K.-U. & Geibel, P. (2007). Learning and Memorizing Models of Logical Theories in a Hybrid Learning Device, to appear in Proceedings of ICONIP 2007, Springer. Gust, H., Kühnberger, K.-U. & Geibel, P. (2007). Learning Models of Predicate Logical Theories with Neural Networks Based on Topos Theory, in P. Hitzler & B. Hammer (eds.): Perspectives of Neural-Symbolic Integration, Series “Computational Intelligence”, Springer, pp. 209-240. Ontology Rewriting (Selection) Ovchinnikova, E. & Kühnberger, K.-U. (2007). Debugging Automatically Extended Ontologies, GLDV-Journal for Computational Linguistics and Language Technology, volume 23(2). Ovchinnikova, E., Wandmacher, T. & Kühnberger, K.-U. (2007). Solving Terminological Inconsistency Problems in Ontology Design, International Journal of Interoperability in Business Information Systems, 4:65-80. Ovchinnikova, E. & Kühnberger, K.-U. (2006). Adaptive ALE-TBox for Extending Terminological Knowledge, in A. Sattar & B. H. Kang (eds.): Proceedings of AI’06, LNAI 4304, Springer, pp. 1111-1115. Kai-Uwe Kühnberger et al. Universität Osnabrück The First Conference on Artificial General Intelligence (AGI-08) Memphis, March 1st, 2008 References I-Cog Kühnberger, K.-U., Geibel, P., Gust, H., Krumnack, U., Ovchinnikova, E., Schwering, A. & Wandmacher, T. (2008): Learning from Inconsistencies in an Integrated Cognitive Architecture, to appear in Proceedings of AGI 2008, IOS Press. Kühnberger, K.-U. (2007): Principles for the Foundation of Integrated Higher Cognition (Abstract). In: D. S. McNamara & J. G. Trafton (Eds.), Proceedings of the CogSci 2007, (p. 1796). Austin, TX: Cognitive Science Society. Kühnberger, K.-U., Wandmacher T., Schwering, A., Ovchinnikova, E., Krumnack, U., Gust, H. & Geibel, P. (2007): I-Cog: A Computational Framework for Integrated Cognition of Higher Cognitive Abilities, in Proceedings of MICAI 2007, LNAI 4827, pp. 203-214, Springer. Kühnberger, K.-U., Wandmacher, T., Schwering, A., Ovchinnikova, E., Krumnack, U., Gust, H. & Geibel, P. (2007): Modeling Human-Level Intelligence by Integrated Cognition in a Hybrid Architecture, in P. Hitzler, T. Roth-Berghofer, S. Rudolph: FAInt-07, Workshop at KI 2007, CEUR-WS, vol. 277, pp. 1-15. Kai-Uwe Kühnberger et al. Universität Osnabrück The First Conference on Artificial General Intelligence (AGI-08) Memphis, March 1st, 2008 Members of the AI group Peter Geibel Jens Michaelis Karl Gerhards Ekaterina Ovchinnikova Helmar Gust Angela Schwering Konstantin Todorov Ulf Krumnack Ulas Türkmen Kai-Uwe Kühnberger Tonio Wandmacher Kai-Uwe Kühnberger et al. Universität Osnabrück The First Conference on Artificial General Intelligence (AGI-08) Memphis, March 1st, 2008