Algebraic terminological representation - Schmidt, Renate Anneliese (Department of Mathematics and Applied Mathematics, 2016)
This thesis investigates terminological representation languages, as used in KL-ONE-type knowledge representation systems, from an algebraic point of view. Terminological representation languages are based on two primitive syntactic types, called concepts and roles, which are usually interpreted model-theoretically as sets and relations, respectively. I propose an algebraic rather than a model-theoretic approach. I show that terminological representations can be naturally accommodated in equational algebras of sets interacting with relations, and I use equational logic as a vehicle for reasoning about concepts interacting with roles.