01
What a representation must provide
A representation should be expressive enough to encode relevant knowledge, structured enough to support useful inference and tractable enough for a computer to process. These requirements are often in tension.
02
Logic
Propositional logic operates over true or false propositions. First-order logic adds variables, predicates, functions and quantifiers, allowing general statements about objects and their relationships.
∀x Human(x) → Mortal(x)
The strength of first-order logic comes with computational cost. General inference is not guaranteed to terminate when a conclusion does not follow, so practical systems often use restricted fragments.
03
Knowledge graphs
Knowledge graphs represent entities and relationships as graph structures. A typical statement can be expressed as a subject, predicate and object, such as (Paris, capitalOf, France). Graph structures are especially useful for integration, exploration and relationship-aware search.
04
Ontologies
An ontology defines concepts and relationships within a domain and provides a shared vocabulary for describing entities. Ontologies become valuable when multiple systems need to interpret data consistently.
- Classes define categories of entities.
- Properties define relationships or attributes.
- Constraints define permissible structures.
- Inference can derive new information from explicit facts.
05
Expressiveness versus tractability
A representation powerful enough to express every interesting fact may make inference expensive or undecidable. A restricted representation may provide extremely fast reasoning but be unable to describe important relationships. Good knowledge engineering therefore involves selecting exactly the expressive power required by the task.