Traditional KRR focuses more on the declarative representation of knowledge. Related knowledge representation formalisms mainly include [[Vocabulary|vocabularies]], [[thesaurus]], [[semantic network]]s, [[Axiom system|axiom systems]], [[Frame (artificial intelligence)|frames]], [[Rule-based system|rules]], [[Logic programming|logic programs]], and [[Ontology (information science)|ontologies]]. Examples of [[automated reasoning]] engines include [[inference engine]]s, [[Automated theorem proving|theorem prover]]s, [[Boolean satisfiability problem|model generators]], and [[Statistical classification|classifiers]].
In a broader sense, parameterized mechanismsmodels ofin knowledge[[machine representationlearning]] — including [[Neural network (machine learning)|neural network]] architectures such as [[Convolutional neural network|convolutional neural networks]] and [[Transformer (deep learning architecture)|transformers]] — 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, Frank 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> Paul 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 andet his colleaguesal. have demonstrated that all universal (or equally expressive and natural) knowledge representation formalisms are recursively isomorphic.<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|arxiv=2412.11855 }}</ref> The authors suggest that thisThis isomorphismfinding impliesindicates an essential equivalence among mainstream knowledge representation formalisms with respect to their capacity for supporting [[artificial general intelligence]] (AGI). They further argue that while diverse technical approaches may draw insights from one another via recursive isomorphisms, the fundamental challenges remain inherently shared.
