Appendix 1 Description Logic Terminology

The purpose of this appendix is to introduce (in a compact manner) the syntax and semantics of the most prominent DLs occurring in this handbook. More information and explanations as well as some less familiar DLs can be found in the respective chapters. For DL constructors whose semantics cannot be described in a compact manner, we will only introduce the syntax and refer the reader to the respective chapter for the semantics. Following Chapter 2 on Basic Description Logics, we will first introduce the basic DL AL, and then describe several of its extensions. Thereby, we will also fix the notation employed in this handbook. Finally, we will comment on the naming schemes for DLs that are employed in the literature and in this handbook. A1.1 Notational conventions Before starting with the definitions, let us introduce some notational conventions. The letters A,B will often be used for atomic concepts, and C, D for concept descriptions. For roles, we often use the letters R, S, and for functional roles (features, attributes) the letters f, g. Nonnegative integers (in number restrictions) are often denoted by n,m, and individuals by a, b. In all cases, we may also use subscripts. This convention is followed when defining syntax and semantics and in abstract examples. In concrete examples, the following conventions are used: concept names start with an uppercase letter followed by lowercase letters (e.g., Human, Male), role names (also functional ones) start with a lowercase letter (e.g., hasChild, marriedTo), and individual names are all uppercase (e.g., CHARLES, MARY).