This article surveys previous work on combining planning techniques with expressive representations of knowledge in description logics to reason about tasks, plans, and goals. Description logics can reason about the logical definition of a class and automatically infer class-subclass subsumption relations as well as classify instances into classes based on their definitions. Descriptions of actions, plans, and goals can be exploited during plan generation, plan recognition, or plan evaluation. Another emerging use of these techniques is the semantic web, where current ontology languages based on description logics need to be extended to reason about goals and capabilities for web services and agents.
In this paper we will present a fuzzy extension of ALC, combining Zadeh's fuzzy logic with a classical DL. In particular, concepts becomes fuzzy and, thus, reasoning about imprecise concepts is supported. We will define its syntax, its semantics, describe its properties and present a constraint propagation calculus for reasoning in it.
A class of interval-based temporal languages for uniformly representing and reasoning about actions and plans is presented. Actions are represented by describing what is true while the action itself is occurring, and plans are constructed by temporally relating actions and world states. The temporal languages are members of the family of Description Logics, which are characterized by high expressivity combined with good computational properties. The subsumption problem for a class of temporal Description Logics is investigated and sound and complete decision procedures are given. The basic language TL-F is considered first: it is the composition of a temporal logic TL -- able to express interval temporal networks -- together with the non-temporal logic F -- a Feature Description Logic. It is proven that subsumption in this language is an NP-complete problem. Then it is shown how to reason with the more expressive languages TLU-FU and TL-ALCF. The former adds disjunction both at the temporal and non-temporal sides of the language, the latter extends the non-temporal side with set-valued features (i.e., roles) and a propositionally complete language.
We study a general framework for query rewriting in the presence of an arbitrary first-order logic ontology over a database signature. The framework supports deciding the existence of a safe-range first-order equivalent reformulation of a query in terms of the database signature, and if so, it provides an effective approach to construct the reformulation based on interpolation using standard theorem proving techniques (e.g., tableau). Since the reformulation is a safe-range formula, it is effectively executable as an SQL query. At the end, we present a non-trivial application of the framework with ontologies in the very expressive ALCHOIQ description logic, by providing effective means to compute safe-range first-order exact reformulations of queries.