Abstract. This paper presents a graph-based spatial model which can serve as a reference for guiding pedestrians inside buildings. We describe a systematic approach to construct the model from geometric data. In excess of the well-known topological relations, the model accounts for two important aspects of pedestrian navigation: firstly, visibility within spatial areas and, secondly, generating route descriptions. An algorithm is proposed which partitions spatial regions according to visibility criteria. It can handle simple polygons as encountered in floor plans. The model is structured hierarchically -each of its elements corresponds to a certain domain concept ('room', 'door', 'floor' etc.) and can be annotated with meta information. This is useful for applications in which such information have to be evaluated.

Abstract. In this article we propose a hybrid spatial model for indoor environments. The model consists of hierarchically structured graphs with typed edges and nodes. The model is hybrid in the sense that nodes and edges can be labelled with qualitative as well as quantitative information. The graphs support wayfinding and, in addition, provide helpful information for generating human-oriented descriptions of an indoor (and outdoor) path.

Time intervals like 'tonight', which are usually not very precise, can be modeled as fuzzy sets. But this causes the problem that the relations between points and intervals and between two intervals, which are usually very trivial, become very complex when the intervals are fuzzy sets. Moreover, there are many different possibilities to define such relations. In this paper a very flexible operator-based approach to point-interval and interval-interval relations is proposed, where the intervals are fuzzy time intervals over the real numbers. The relations yield non-trivial fuzzy values even if the intervals are crisp. As an example for an application, consider a database with, say, a cinema timetable, and you query the timetable "give me all performances ending before midnight". The usual 'before' relation will exclude the performances ending a second after midnight. With the fuzzy before relation you can get instead of a sharp drop to 0 at midnight decreasing fuzzy values after midnight, and these can be used to order the results of the query.The intervals and relations are implemented in the FuTIRe library (Fuzzy Time Intervals and Relations). FuTIRe is an open source C++ library.

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A general framework for translating logical formulae from one logic into another logic is presented. The framework is instantiated with two different approaches to translating modal logic formulae into predicate logic. The first one, the well known 'relational' translation makes the modal logic's possible worlds structure explicit by introducing a distinguished predicate symbol to represent the accessibility relation. In the second approach, the 'functional' translation method, paths in the possible worlds structure are represented by compositions of functions which map worlds to accessible worlds. On the syntactic level this means that every flexible symbol is parametrized with particular terms denoting whole paths from the initial world to the actual world. The 'target logic' for the translation is a first-order many-sorted logic with built in equality. Therefore the 'source logic' may also be first-order many-sorted with built in equality. Furthermore flexible function symbols are allowed. The modal operators may be parametrized with arbitrary terms and particular properties of the accessibility relation may be specified within the logic itself.