Knowledge representation and reasoning

Knowledge representation and reasoning (often abbreviated KR&R, or just KR) is the branch of artificial intelligence concerned with encoding facts about the world in a form a machine can manipulate, and with the inference procedures that draw new conclusions from what has been encoded ^[1]. The two halves are inseparable in practice: a representation is only useful if some reasoning procedure can exploit it, and a reasoning procedure only means something relative to a representation whose symbols have a defined interpretation.

The field supplied most of the intellectual machinery of classical symbolic AI: first-order logic and resolution theorem proving, semantic networks, frames, production rules, description logics, and the ontologies and knowledge graphs that grew out of them. Its guiding assumption, stated most sharply by Allen Newell and Herbert A. Simon in the lecture for their 1975 ACM Turing Award, published in 1976, was that "a physical symbol system has the necessary and sufficient means for general intelligent action" ^[2][3].

Statistical machine learning displaced hand-built knowledge bases as the default way to build AI systems, and by the 2010s much of the KR vocabulary had fallen out of everyday industrial use. It did not disappear. Web-scale knowledge graphs, medical and biological ontologies, rule engines in insurance and compliance, and the retrieval layers wrapped around large language models all descend from this work, and whether a neural network's weights amount to a knowledge base in any useful sense is now actively contested.

The knowledge-based program

The founding statement is John McCarthy's "Programs with Common Sense," presented at the 1958 Teddington symposium on the mechanization of thought processes and published in the 1959 proceedings, which proposed a hypothetical program called the Advice Taker that would represent what it knew as sentences in a formal language and improve its behavior by being told new sentences rather than reprogrammed ^[4]. Newell, J. C. Shaw and Simon's General Problem Solver, built in 1957 and reported in 1959, treated problem solving as search through a space of symbolic states ^[1]. Both proposals assumed that intelligence is symbol manipulation, the premise the Dartmouth workshop generation had carried into the field.

McCarthy and Patrick Hayes formalized the idea of reasoning about action in "Some Philosophical Problems from the Standpoint of Artificial Intelligence" (1969), which built on the situation calculus McCarthy had introduced in 1963 and named the frame problem: using mathematical logic, how do you write formulas describing the effects of an action without also writing an enormous number of formulas describing the obvious non-effects ^[5][6]. Shooting a gun changes whether a person is alive; it does not change the color of the walls, the day of the week, or the location of every other object in the room. Classical logic gives no economical way to say so, and the difficulty of stating a "common sense law of inertia" inside a monotonic logic drove much of the theoretical work of the following two decades ^[5].

Logic as a representation language

Propositional logic is decidable but cannot quantify over individuals, so it cannot express "every dog is a mammal" without one sentence per dog. First-order logic (FOL) adds variables, quantifiers, functions and relations, and became the reference point against which every other representation was measured ^[6]. J. A. Robinson's resolution principle, published in the Journal of the ACM in 1965, gave FOL a single mechanizable inference rule and launched practical automated theorem proving ^[7]. Validity in FOL is only semi-decidable, which means a prover can confirm entailments but may run forever on non-entailments.

Logic programming narrowed FOL to Horn clauses to buy efficiency. Prolog was created around 1972 by Alain Colmerauer with Philippe Roussel at Aix-Marseille, on the basis of Robert Kowalski's procedural reading of Horn clauses, and executes queries by SLD resolution ^[8]. Japan's Fifth Generation Computer Systems project developed a Prolog variant called Kernel Language for its first operating system, and much of Prolog's later development came from that impetus, while Lisp played the equivalent role in American AI research ^[8].

Description logics went the other way, trimming FOL until reasoning became decidable and then measuring exactly how much expressiveness that cost. The first system in the family was KL-ONE, described by Ronald Brachman and James Schmolze in Cognitive Science in 1985 ^[9]. Description logics split a knowledge base into a TBox of terminological axioms (concept hierarchies and definitions) and an ABox of assertions about individuals, and name languages by the operators they permit: ALC, the attributive concept language with complements, as the prototypical member, with SHOIN(D) and SROIQ(D) as the richer languages underlying OWL DL and OWL 2 ^[10]. Hector Levesque and Brachman had already made the underlying economics explicit in "Expressiveness and tractability in knowledge representation and reasoning" (Computational Intelligence, 1987): the more a language can say, the worse the worst-case behavior of its inference engine ^[11].

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Structured representations: networks, frames, and scripts

Logic was never the only option. Semantic networks represent knowledge as labeled nodes and edges, an idea implemented for computers by Richard H. Richens at the Cambridge Language Research Unit in 1956 as an interlingua for machine translation, and developed in the early 1960s by M. Ross Quillian and colleagues at System Development Corporation as a model of human semantic memory ^[12]. Allan Collins and Quillian's 1969 paper "Retrieval time from semantic memory" reported that the time people take to verify a sentence tracks the distance traversed in such a network, which gave the formalism a psychological warrant that logic-based approaches lacked ^[13].

Marvin Minsky's "A Framework for Representing Knowledge" (1974) proposed frames: data structures that carve knowledge into substructures representing stereotyped situations ^[14]. A frame has slots, each holding a value, a default, a procedure, or a pointer to another frame, and inheritance along a frame hierarchy lets a system assume that a specific bird flies because birds generally do, while allowing the penguin frame to override the default. Frame languages such as KRL and FRL turned the idea into working software, and KEE later merged frames with rules in one commercial environment ^[1][14].

Roger Schank and Robert Abelson extended the idea to episodes in Scripts, Plans, Goals and Understanding (Erlbaum, 1977), building on Schank's 1969 conceptual dependency theory ^[15]. A script encodes the expected sequence of events in a routine situation, so that a program reading "John ordered lasagna. He left a large tip." can infer that he ate and paid without either fact appearing in the text. That inferential gap-filling is exactly what natural language processing systems still have to solve, and scripts were an early, explicitly stated answer.

Rules and expert systems

The Stanford Heuristic Programming Project, led by Edward Feigenbaum, introduced expert systems around 1965 with the working hypothesis that performance comes from domain knowledge rather than general reasoning power ^[16]. DENDRAL inferred molecular structures from mass spectrometry data; MYCIN recommended antimicrobial therapy. In a blinded 1979 evaluation published in JAMA, eight infectious disease specialists rated therapy recommendations for ten meningitis cases; MYCIN drew a 65 percent acceptability rating while the five faculty specialists scored between 42.5 and 62.5 percent, and the program never failed to cover a treatable pathogen ^[17].

The architecture that made these systems reproducible was the split between a knowledge base of if-then rules and an inference engine that applies them, either forward from known facts or backward from a goal ^[16]. Charles Forgy at Carnegie Mellon made forward chaining practical with the Rete algorithm, first written up in 1974 and elaborated in his 1979 thesis and a 1982 paper; Rete caches partial matches so a rule engine processes only changes to working memory instead of re-testing every rule against every fact ^[18]. It still powers CLIPS, Jess, Drools, and commercial decision-management products.

The commercial peak came with XCON (originally R1), written in OPS5 by John P. McDermott of Carnegie Mellon to configure Digital Equipment Corporation computers. It entered use at DEC's Salem, New Hampshire plant in 1980, grew to roughly 2,500 rules, had processed 80,000 orders at 95-98 percent accuracy by 1986, and was estimated to save DEC about 25 million dollars a year ^[19]. The collapse that followed was not a failure of the idea so much as of its economics: acquiring expert knowledge was slow and expensive, specialized hardware lost its price advantage, large rule bases became hard to keep consistent, and by the early 1990s the second AI winter had emptied the market ^[16][20].

Reasoning that can be retracted

Classical logic is monotonic: adding premises never removes conclusions. Human commonsense reasoning is not, since "Tweety is a bird" supports "Tweety flies" only until someone says "Tweety is a penguin." Three papers in volume 13 of the journal Artificial Intelligence in 1980 founded the formal study of this behavior: McCarthy's circumscription, which prefers models that minimize the extension of chosen predicates; Reiter's default logic, whose rules license a conclusion in the presence of a prerequisite and the absence of contrary evidence; and McDermott and Doyle's modal treatment of non-monotonic logic ^{[21][22][23][6]}.

Related devices include the closed-world assumption, which treats anything not derivable as false, its procedural cousin negation as failure, and Robert Moore's 1985 autoepistemic logic for an agent reasoning about its own beliefs ^[24]. Michael Gelfond and Vladimir Lifschitz's stable model semantics (1988) grew into answer set programming, a declarative method for NP-hard search problems now implemented in solvers such as clingo, DLV and smodels and applied to planning, configuration and combinatorial problems ^[24][25].

None of this made the frame problem go away cleanly. Steve Hanks and Drew McDermott's 1987 Yale shooting problem, set out in "Nonmonotonic Logic and Temporal Projection," showed that a naive nonmonotonic formalization of a simple shooting scenario licenses counterintuitive conclusions, and repairing that case without breaking others occupied a substantial literature ^[5].

Ontologies and the Semantic Web

An ontology in the computational sense is an explicit account of the categories, properties and relations that exist in a domain. The standard definition comes from Tom Gruber's "A translation approach to portable ontology specifications" (Knowledge Acquisition, 1993): an ontology is an explicit specification of a conceptualization, meaning a formal description of the concepts and relationships that can exist for an agent or a community of agents ^[26][27]. What separates an ontology from a plain taxonomy is the axioms that constrain how its terms may be interpreted ^[28].

Tim Berners-Lee, James Hendler and Ora Lassila proposed extending this idea to the whole web in a May 2001 Scientific American article, and the W3C standards that followed remain the backbone of published structured data ^[29]. RDF represents facts as triples of subject, predicate and object, where the subject is an IRI or blank node, the predicate an IRI, and the object an IRI, literal or blank node ^[30]. RDF Schema adds classes and property hierarchies; OWL adds description-logic semantics; SPARQL queries the result.

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OWL 1 shipped in three sublanguages: OWL Lite for simple hierarchies, OWL DL for maximum expressiveness that still guarantees decidability, and OWL Full for the syntactic freedom of RDF with no computational guarantees ^[31]. OWL 2 added keys, property chains, qualified cardinality restrictions and richer datatypes, plus three profiles trading expressiveness for performance: EL for very large terminologies, QL for query answering over relational databases, and RL for rule-based implementations over triples ^[32]. The standards are still moving. RDF 1.2 Concepts and RDF 1.2 Semantics reached Candidate Recommendation on 7 April 2026, adding triple terms so that a triple can appear as the object of another triple and replacing the older reification vocabulary with a single rdf:reifies predicate, while the SPARQL 1.2 documents remained Working Drafts through mid-2026 ^[33][34].

Whether the Semantic Web succeeded depends on where you look. The vision of agents negotiating appointments over shared ontologies did not arrive, and critics pointed early to the cost of formalizing knowledge and to publishers' incentives to lie in metadata ^[29]. The plumbing, however, is everywhere. Schema.org, founded by Google, Bing, Yahoo and Yandex to standardize on-page markup for search engines, made structured data an ordinary part of web publishing ^[35]. Web Data Commons' extraction from the October 2024 Common Crawl corpus found structured markup on 16,525,070 of about 37.4 million domains, roughly 44 percent, yielding about 74 billion RDF quads ^[36]. Domain ontologies also carried on quietly: SNOMED CT contains more than 360,000 clinical concepts and is used in over eighty countries ^[37], and WordNet, begun under George Miller at Princeton's Cognitive Science Laboratory in 1985, remains standard NLP infrastructure, and its 2024 edition organizes 161,705 words into 120,630 synsets ^[38].

Knowledge graphs

The term knowledge graph predates its modern use, but the current sense dates from Google's announcement on 16 May 2012, when Amit Singhal introduced a database of "things, not strings" containing more than 500 million objects and more than 3.5 billion facts and relationships, assembled from public sources including Freebase, Wikipedia and the CIA World Factbook ^[39][40]. In substance a knowledge graph is a semantic network with an ontology layer: entities as nodes, typed relations as edges, and a schema that supports inference beyond what is explicitly stored ^[40].

Freebase itself came from Metaweb, ran publicly from March 2007, and was acquired by Google on 16 July 2010. Google announced its retirement on 16 December 2014, offering the contents to the Wikidata community, and shut it down on 2 May 2016; as of January 2014 it held roughly 44 million topics and 2.4 billion facts ^[41][42]. Wikidata, launched on 29 October 2012 as the first new Wikimedia project since 2006 and developed largely by Wikimedia Deutschland, absorbed much of that role. It publishes under CC0 and, as of mid-2026, holds more than 122 million items built from over 2.5 billion edits ^[43][44]. DBpedia, started in 2007 by researchers at the Free University of Berlin and Leipzig University with OpenLink Software, extracts RDF from Wikipedia and functions as a hub in the linked open data cloud ^[45].

Cyc and the maximal bet on hand-coded knowledge

If expert systems were brittle because they knew only their narrow domain, one response was to encode the background knowledge that everyone shares. Douglas Lenat began Cyc in July 1984 at the Microelectronics and Computer Technology Corporation, framed partly as a US answer to Japan's Fifth Generation project. Its representation language, CycL, started as an extension of RLL and by 1989 supported higher-order logic. Lenat spun the work out into Cycorp in 1994, with active development moving to the company from January 1995, and he ran it as CEO until his death ^[46].

Work continued for close to four decades. By 2017 Cyc held roughly 1.5 million terms and about 24.5 million assertions, representing on the order of 2,000 person-years of work ^[46][47]. Free subsets were released and then withdrawn: OpenCyc appeared in 2002 and reached 239,000 concepts and 2.09 million facts in version 4.0 (June 2012) before being discontinued around March 2017, while ResearchCyc was offered to researchers from July 2006 ^[46]. Lenat, born 13 September 1950, died of bile duct cancer on 31 August 2023 ^[47]. His last paper, written with Gary Marcus and posted on 31 July 2023, argued that trustworthy general AI would have to hybridize statistical and knowledge-based methods rather than choose between them ^[48].

Knowledge representation in the era of large language models

Whether a language model "knows" anything in the KR sense is contested, and the evidence cuts both ways. Fabio Petroni and colleagues showed in "Language Models as Knowledge Bases?" (EMNLP 2019) that BERT recovers relational facts competitively with knowledge bases built by supervised extraction pipelines, purely from pretraining ^[49]. Kevin Meng and coauthors then localized the storage: causal tracing in "Locating and Editing Factual Associations in GPT" (NeurIPS 2022) traced factual predictions to middle-layer feed-forward modules at the subject token, and their ROME method edits a fact by a rank-one change to those weights, which is the basis of the knowledge editing literature ^[50].

The failures are equally informative. The reversal curse, documented by Lukas Berglund and colleagues in 2023, is that a model trained on "A is B" does not thereby learn "B is A": GPT-4 answered "Who is Tom Cruise's mother?" correctly 79 percent of the time and the mirrored question about Mary Lee Pfeiffer's son only 33 percent ^[51]. A symbolic knowledge base with a single stored triple answers both directions by construction. Adam Tauman Kalai and coauthors argued in September 2025 that hallucination persists partly because benchmarks reward confident guessing over admitting ignorance, so the incentive structure of evaluation, not just the architecture, keeps models asserting unsupported facts ^[52]. Model weights also lack the properties that make a knowledge base auditable: there is no explicit assertion to point at, no provenance, no consistency check, and no principled way to retract.

The practical response has been to put explicit knowledge back alongside the model. Retrieval-augmented generation, introduced by Patrick Lewis and colleagues at NeurIPS 2020, pairs a generator with a dense index so that answers are conditioned on retrieved text ^[53]. GraphRAG, from Microsoft Research, goes further by having an LLM build a knowledge graph from a corpus, cluster it into communities, and summarize those communities hierarchically; the April 2024 paper reports large gains in comprehensiveness and diversity over naive RAG on corpus-level questions, and Microsoft released the code on GitHub on 2 July 2024 ^[54][55]. Shirui Pan and colleagues mapped the design space in an IEEE TKDE roadmap that distinguishes knowledge-graph-enhanced LLMs, LLM-augmented knowledge graphs, and fully synergized systems ^[56]. Wikidata itself moved in this direction on 1 October 2025, when Wikimedia Deutschland launched the Wikidata Embedding Project with Jina.AI and DataStax, publishing a vector database over Wikidata that supports semantic search in more than 100 languages so AI applications can ground answers in a citable source ^[57].

Neurosymbolic AI is the broader research program behind these hybrids, and Henry Kautz's taxonomy of six integration patterns, from symbolic systems that call neural components to neural networks with symbolic reasoning embedded inside them, is its usual organizing frame ^[58]. The clearest demonstrations so far come from mathematics. AlphaGeometry, announced by Google DeepMind on 17 January 2024, pairs a neural language model that proposes auxiliary constructions with a symbolic deduction engine that derives the proof, trained on 100 million synthetic examples; it solved 25 of the 30 problems in the IMO-AG-30 geometry benchmark, against 10 for the previous state of the art and 25.9 for the average human gold medallist ^[59]. In July 2024, AlphaProof working in Lean together with AlphaGeometry 2 solved 4 of 6 International Mathematical Olympiad problems for 28 points out of 42, one point below that year's gold threshold of 29 ^[60]. Work continues in less glamorous places too: a July 2026 preprint describes Euclid-MCP, an open-source Model Context Protocol server that exposes a SWI-Prolog engine to LLM clients so that inference over compliance rule bases is delegated to a deterministic solver with inspectable proof traces ^[61].

Neither half has worked alone. Hand-built knowledge bases were precise and auditable but never scaled to open domains; learned models scale but supply neither property. Lenat and Marcus stated the conclusion plainly in 2023: any trustworthy general AI will have to hybridize the two approaches ^[48]. The systems now being built, whether retrieval pipelines, reasoning models that externalize chain of thought, or formal provers driven by neural search, are attempts to buy back some of what the connectionism turn gave up.

See also

• Symbolic AI
• Expert system
• Knowledge graph
• Cyc
• Commonsense reasoning
• Retrieval-augmented generation

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