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In a broader sense, parameterized mechanisms of knowledge representation — including [[Neural network (machine learning)|neural network]] architectures such as [[convolutional neural network]]<nowiki/>s and [[Transformer (deep learning architecture)|transformer]]<nowiki/>s — can also be regarded as a family of knowledge representation formalisms. The question of which formalism is most appropriate for knowledge-based systems has long been a subject of extensive debate. For instance, van Harmelen et al. discussed the suitability of logic as a knowledge representation formalism and reviewed arguments presented by anti-logicists.<ref>{{Cite book |last1=Porter |first1=Bruce |title=Handbook of knowledge representation |last2=Lifschitz |first2=Vladimir |last3=Van Harmelen |first3=Frank |date=2008 |publisher=Elsevier |isbn=978-0-444-52211-5 |edition=1st |series=Foundations of artificial intelligence |___location=Amsterdam Boston}}</ref> Smolensky criticized the limitations of symbolic formalisms and explored the possibilities of integrating it with connectionist approaches.<ref>{{Cite journal |last=Smolensky |first=Paul |date=March 1988 |title=On the proper treatment of connectionism |url=https://www.cambridge.org/core/product/identifier/S0140525X00052432/type/journal_article |journal=Behavioral and Brain Sciences |language=en |volume=11 |issue=1 |pages=1–23 |doi=10.1017/S0140525X00052432 |issn=0140-525X}}</ref>
More recently, Heng Zhang and his colleagues have demonstrated that all universal (or equally expressive and natural) formalisms of knowledge representation are recursively isomorphic, which indicates that mainstream knowledge representation formalisms are essentially equivalent in terms of their capacity for realizing [[artificial general intelligence]] (AGI); diverse technical approaches can draw insights from one another via recursive isomorphisms, yet the fundamental challenges are inherently shared.<ref>{{Cite journal |last1=Zhang |first1=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}}</ref>
== History ==
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