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This paper is an appendix to the paper "Reasoning with Justifiable Exceptions in Contextual Hierarchies" by Bozzato, Serafini and Eiter, 2018 [2]. It provides further details on the language, the complexity results and the datalog translation introduced in the main paper.

The idea of the Semantic Web is to annotate Web content and services with computer interpretable descriptions with the aim to automatize many tasks currently performed by human users. In the context of Web services, one of the most interesting tasks is their composition. In this paper we formalize this problem in the framework of a constructive description logic. In particular we propose a declarative service specification language and a calculus for service composition. We show by means of an example how this calculus can be used to define composed Web services and we discuss the problem of automatic service synthesis.

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