Formal Knowledge Representation

Formal knowledge representation is a field of artificial intelligence (AI), which captures the semantics (meaning) of concepts, properties, relationships, and individuals of specific knowledge domains, i.e., fields of interest or areas of concern, as structured data.

The Resource Description Framework (RDF) enables us to write machine-interpretable statements in the form of subject–predicate–object triples, called RDF triples, such as Router-isAn-AreaBorderRouter, formally (s, o, p) ∈ (𝕀 ∪ 𝔹) × 𝕀 × (𝕀 ∪ 𝕃 ∪ 𝔹), where 𝕀, 𝕃, and 𝔹 are pairwise disjoint infinite sets of IRIs, i.e., strings of Unicode characters of the form scheme:[//[user:password@]host[:port]][/]path[?query][#fragment]; RDF literals, i.e., either 1) self-denoting plain literals of the form ""(@<lang>)?, where <string> is a string and is an optional language tag, or 2) typed literals of the form "<string>"^^<datatype>, where <datatype> is an IRI denoting a datatype according to a schema, and <string> is an element of the lexical space corresponding to the datatype; and blank nodes, i.e., unique resources that are neither IRIs nor RDF literals. A set of RDF triples can be represented as an RDF graph, where the set of nodes is the set of subjects and objects of RDF triples in the graph.

The RDF vocabulary, which is capable of expressing core relationships, such as the isA relationship, was extended to be able to describe more sophisticated relationships between concepts and properties, such as taxonomical structures, resulting in the RDF Schema Language (RDFS) (RDF Vocabulary Description Language). Complex knowledge domains require even more representational capabilities, such as property cardinality constraints, domain and range restrictions, and enumerated classes, which led to the Web Ontology Language (OWL), a language specially designed for creating web ontologies with a rich set of modeling constructors and addressing the ontology engineering limitations of RDFS.

Formal grounding for OWL ontologies can be provided by description logics, many of which are decidable fragments of first-order predicate logic and all of which feature a different balance between expressivity and reasoning complexity by supporting different sets of mathematical constructors.

The uniform representation of expert knowledge enables important data validation tasks, such as automated data integrity checking, and inference mechanisms to make implicit statements explicit via automated reasoning.