Textbook of AI

Knowledge Representation (KR) is the subfield of symbolic AI concerned with encoding facts, concepts, relationships and procedures in formal structures that support automated inference. It rests on a foundational hypothesis articulated most clearly by John McCarthy and Pat Hayes in their 1969 paper Some Philosophical Problems from the Standpoint of Artificial Intelligence: that intelligent behaviour can be produced by a system that explicitly represents what it knows about the world in a declarative form and reasons over those representations using domain-independent inference rules.

A representation must answer four questions, framed by Hector Levesque and Ron Brachman: what facts can be expressed, how efficiently they can be stored, how easily inferences can be drawn from them, and how naturally they correspond to human conceptions of the domain. The history of KR is the history of trade-offs among these criteria. Major formalisms include:

• Logic-based representations: first-order logic, description logics (the basis of OWL and the Semantic Web), modal and temporal logics, and non-monotonic logics for default reasoning. Inference proceeds via theorem proving (typically resolution), tableau methods, or specialised reasoners such as Pellet and HermiT.
• Frame-based representations: structured slot-and-filler organisations introduced by Marvin Minsky in A Framework for Representing Knowledge (1975). Frames bundle related properties together with default values and inheritance, a direct ancestor of object-oriented programming.
• Semantic networks: graphs of concept nodes connected by labelled relation edges, originating with Ross Quillian's 1968 thesis on semantic memory.
• Conceptual dependency: Roger Schank's (1972) meaning-preserving decomposition of natural-language sentences into a small set of primitive acts (PTRANS, ATRANS, MTRANS, ...), aimed at language-independent representation.
• Production rules: if–then condition–action rules in expert systems such as MYCIN (medical diagnosis), DENDRAL (chemistry) and R1/XCON (computer configuration); operationalised in production-system languages such as OPS5 and the SOAR architecture.
• Knowledge graphs: the modern embodiment, with subject–predicate–object triples stored at web scale. Examples include DBpedia, Wikidata, YAGO, Google's Knowledge Graph and schema.org, used to enrich search results, virtual assistants and enterprise data integration.

Modern AI has largely shifted from explicit symbolic KR to distributed representations learned by neural networks, vectors in $\mathbb{R}^d$ whose geometric structure encodes meaning. Where a symbolic system represents Paris is the capital of France as a triple, a language model represents it as a pattern of activation across billions of parameters. The two approaches have complementary strengths: symbolic representations are precise, auditable and support exact reasoning but are brittle and labour-intensive to construct; learned representations are robust, automatic and handle ambiguity gracefully but hallucinate and resist inspection. Neuro-symbolic AI seeks to combine them, using neural networks for perception and general-purpose reasoning while consulting structured knowledge for high-precision factual retrieval. Retrieval-Augmented Generation (RAG) is the dominant practical form of this synthesis in 2026: a large language model generates fluent text while drawing on a vector-indexed corpus or a knowledge graph for grounded facts.