Editing Connectionism (section)

==Symbolism vs. connectionism debate==

Smolensky's Subsymbolic Paradigm<ref>P. Smolensky: On the proper treatment of connectionism. In: Behavioral and Brain Sciences. Band 11, 1988, S. 1-74.</ref><ref>P. Smolensky: The constituent structure of connectionist mental states: a reply to Fodor and Pylyshyn. In: T. Horgan, J. Tienson (Hrsg.): Spindel Conference 1987: Connectionism and the Philosophy of Mind. The Southern Journal of Philosophy. Special Issue on Connectionism and the Foundations of Cognitive Science. Supplement. Band 26, 1988, S. 137-161.</ref> has to meet the Fodor-Pylyshyn challenge<ref>J.A. Fodor, Z.W. Pylyshyn: Connectionism and cognitive architecture: a critical analysis. Cognition. Band 28, 1988, S. 12-13, 33-50.</ref><ref>J.A. Fodor, B. McLaughlin: Connectionism and the problem of systematicity: why Smolensky's solution doesn't work. Cognition. Band 35, 1990, S. 183-184.</ref><ref>B. McLaughlin: The connectionism/classicism battle to win souls. Philosophical Studies, Band 71, 1993, S. 171-172.</ref><ref>B. McLaughlin: Can an ICS architecture meet the systematicity and productivity challenges? In: P. Calvo, J. Symons (Hrsg.): The Architecture of Cognition. Rethinking Fodor and Pylyshyn's Systematicity Challenge. MIT Press, Cambridge/MA, London, 2014, S. 31-76.</ref> formulated by classical symbol theory for a convincing theory of cognition in modern connectionism. In order to be an adequate alternative theory of cognition, Smolensky's Subsymbolic Paradigm would have to explain the existence of systematicity or systematic relations in language cognition without the assumption that cognitive processes are causally sensitive to the classical constituent structure of mental representations. The subsymbolic paradigm, or connectionism in general, would thus have to explain the existence of systematicity and compositionality without relying on the mere implementation of a classical cognitive architecture. This challenge implies a dilemma: If the Subsymbolic Paradigm could contribute nothing to the systematicity and compositionality of mental representations, it would be insufficient as a basis for an alternative theory of cognition. However, if the Subsymbolic Paradigm's contribution to systematicity requires mental processes grounded in the classical constituent structure of mental representations, the theory of cognition it develops would be, at best, an implementation architecture of the classical model of symbol theory and thus not a genuine alternative (connectionist) theory of cognition.<ref>J.A. Fodor, B. McLaughlin: Connectionism and the problem of systematicity: Why Smolensky's solution doesn't work. Cognition. Band 35, 1990, S. 183-184.</ref> The classical model of symbolism is characterized by (1) a combinatorial syntax and semantics of mental representations and (2) mental operations as structure-sensitive processes, based on the fundamental principle of syntactic and semantic constituent structure of mental representations as used in Fodor's "Language of Thought (LOT)".<ref>J.A. Fodor: The language of thought. Harvester Press, Sussex, 1976, ISBN 0-85527-309-7.</ref><ref>J.A. Fodor: LOT 2: The language of thought revisited. Clarendon Press, Oxford, 2008, ISBN 0-19-954877-3.</ref> This can be used to explain the following closely related properties of human cognition, namely its (1) productivity, (2) systematicity, (3) compositionality, and (4) inferential coherence.<ref>J.A. Fodor, Z.W. Pylyshyn (1988), S. 33-48.</ref>

This challenge has been met in modern connectionism, for example, not only by Smolensky's "Integrated Connectionist/Symbolic (ICS) Cognitive Architecture",<ref>P. Smolenky: Reply: Constituent structure and explanation in an integrated connectionist / symbolic cognitive architecture. In: C. MacDonald, G. MacDonald (Hrsg.): Connectionism: Debates on psychological explanation. Blackwell Publishers. Oxford/UK, Cambridge/MA. Vol. 2, 1995, S. 224, 236-239, 242-244, 250-252, 282.</ref><ref>P. Smolensky, G. Legendre: The Harmonic Mind: From Neural Computation to Optimality-Theoretic Grammar. Vol. 1: Cognitive Architecture. A Bradford Book, The MIT Press, Cambridge, London, 2006a, ISBN 0-262-19526-7, S. 65-67, 69-71, 74-75, 154-155, 159-202, 209-210, 235-267, 271-342, 513.</ref> but also by Werning and Maye's "Oscillatory Networks".<ref>M. Werning: Neuronal synchronization, covariation, and compositional representation. In: M. Werning, E. Machery, G. Schurz (Hrsg.): The compositionality of meaning and content. Vol. II: Applications to linguistics, psychology and neuroscience. Ontos Verlag, 2005, S. 283-312.</ref><ref>M. Werning: Non-symbolic compositional representation and its neuronal foundation: towards an emulative semantics. In: M. Werning, W. Hinzen, E. Machery (Hrsg.): The Oxford Handbook of Compositionality. Oxford University Press, 2012, S. 633-654.</ref><ref>A. Maye und M. Werning: Neuronal synchronization: from dynamics feature binding to compositional representations. Chaos and Complexity Letters, Band 2, S. 315-325.</ref> An overview of this is given for example by Bechtel & Abrahamsen,<ref>Bechtel, W., Abrahamsen, A.A. ''Connectionism and the Mind: Parallel Processing, Dynamics, and Evolution in Networks.'' 2nd Edition. Blackwell Publishers, Oxford. 2002</ref> Marcus<ref>G.F. Marcus: The algebraic mind. Integrating connectionism and cognitive science. Bradford Book, The MIT Press, Cambridge, 2001, ISBN 0-262-13379-2.</ref> and Maurer.<ref>H. Maurer: Cognitive science: Integrative synchronization mechanisms in cognitive neuroarchitectures of the modern connectionism. CRC Press, Boca Raton/FL, 2021, ISBN 978-1-351-04352-6. https://doi.org/10.1201/9781351043526</ref>

Recently, Heng Zhang and his colleagues have demonstrated that mainstream knowledge representation formalisms are, in fact, recursively isomorphic, provided they possess equivalent expressive power.<ref>{{Cite journal |last=Zhang |first=Heng |last2=Jiang |first2=Guifei |last3=Quan |first3=Donghui |date=2025-04-11 |title=A Theory of Formalisms for Representing Knowledge |url=https://ojs.aaai.org/index.php/AAAI/article/view/33674 |journal=Proceedings of the AAAI Conference on Artificial Intelligence |language=en |volume=39 |issue=14 |pages=15257–15264 |doi=10.1609/aaai.v39i14.33674 |issn=2374-3468|arxiv=2412.11855 }}</ref> This finding implies that there is no fundamental distinction between using symbolic or connectionist knowledge representation formalisms for the realization of [[artificial general intelligence]] (AGI). Moreover, the existence of recursive isomorphisms suggests that different technical approaches can draw insights from one another.