Description Logic

A Formal System for talking about collections of objects and their relations. It is at least as expressive as Propositional Logic with set-theoretic semantics, and it offers

individuals
relations

It has the following components.

a formal language $\mathcal{L}$ with logical constants $\sqcap, \bar{\circ}, \sqcup, \sqsubseteq, \equiv$
a set-theoretic semantics $\langle \mathcal{D}, [[\circ]] \rangle$ $⟨ D, [[\circ]]⟩$
- we get this for free when we can translate into First-Order Predicate Logic
Translation into First-Order Predicate Logic that is compatible with the set-theoretic semantics
a Calculus for $\mathcal{L}$ $L$ that includes a decision procedure for $\mathcal{L}$ $L$ satisfiability
- to verify we are still in the decidable region of logics

ABox

Closed World Assumption vs. Open World Assumption

TBoxes

TBox Concept Definition