Knowledge representation (KR) aims to model information in a structured manner to formally represent it as knowledge in knowledge-based systems whereas knowledge representation and reasoning (KRR, KR&R, or KR²) also aims to understand, reason, and interpret knowledge. KRR is widely used in the field of artificial intelligence (AI) with the goal to represent information about the world in a form that a computer system can use to solve complex tasks, such as diagnosing a medical condition or having a natural-language dialog. KR incorporates findings from psychology about how humans solve problems and represent knowledge, in order to design formalisms that make complex systems easier to design and build. KRR also incorporates findings from logic to automate various kinds of reasoning.

Traditional KRR focuses more on the declarative representation of knowledge. Related knowledge representation formalisms mainly include vocabularies, thesaurus, semantic networks, axiom systems, frames, rules, logic programs, and ontologies. Examples of automated reasoning engines include inference engines, theorem provers, model generators, and classifiers.

In a broader sense, parameterized models in machine learning — including neural network architectures such as convolutional neural networks and 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. Paul Smolensky criticized the limitations of symbolic formalisms and explored the possibilities of integrating it with connectionist approaches.

More recently, Heng Zhang et al. have demonstrated that all universal (or equally expressive and natural) knowledge representation formalisms are recursively isomorphic. This finding indicates a theoretical 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.

The earliest work in computerized knowledge representation was focused on general problem-solvers such as the General Problem Solver (GPS) system developed by Allen Newell and Herbert A. Simon in 1959 and the Advice Taker proposed by John McCarthy also in 1959. GPS featured data structures for planning and decomposition. The system would begin with a goal. It would then decompose that goal into sub-goals and then set out to construct strategies that could accomplish each subgoal. The Advisor Taker, on the other hand, proposed the use of the predicate calculus to implement common sense reasoning.

Many of the early approaches to knowledge representation in Artificial Intelligence (AI) used graph representations and semantic networks, similar to knowledge graphs today. In such approaches, problem solving was a form of graph traversal or path-finding, as in the A* search algorithm. Typical applications included robot plan-formation and game-playing.

Other researchers focused on developing automated theorem-provers for first-order logic, motivated by the use of mathematical logic to formalise mathematics and to automate the proof of mathematical theorems. A major step in this direction was the development of the resolution method by John Alan Robinson.

In the meanwhile, John McCarthy and Pat Hayes developed the situation calculus as a logical representation of common sense knowledge about the laws of cause and effect. Cordell Green, in turn, showed how to do robot plan-formation by applying resolution to the situation calculus. He also showed how to use resolution for question-answering and automatic programming.