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...inements) and with no metric on the refinements. For the other relations, the degree of holding has not been covered at all in the semantics of the relationship (though there are fuzzy versions of RCC=-=[16]-=-). This paper explores this idea of a distance1 based interpretation for mereotopology. By introducing a distance measure between x and y, and for various Boolean combinations of x and y, we show that...

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...ach iteration) Table 1: Recognition results using types (leave-one-out testing) Events pos ex 4 2 Rear Loading 10 7 [1, 0, 2, 1, 4, 0, 2] Rear Unloading 5 1 [4, 1, 0, 0, 1, 1, 0] Aircraft Arrival 7 2 =-=[2, 3, 0, 8, 1, 6, 16]-=- Aircraft Departure 7 4 [3, 3, 7, 4, 1, 1, 1] Jet Bridge Positioning 7 1 [0, 0, 2, 11, 8, 1, 4] 4 True Positives (all iterations) 2 False Positives (in each iteration) Table 2: Recognition results wit...

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... or FIRE [19]. In this work, we make a first step in extending fuzzy DLs towards fuzzy spatial reasoning, by supporting both fuzzy spatial relations of the region connection calculus (RCC) [5], [14], =-=[18]-=- as well as application domain dependent fuzzy spatial relations such as“close”, “far”, “over” (see, e.g. [9], [17]). The need for such an extension is particularly evident in the image interpretation...

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...systematic development of these logics would provide a unified approach to a range of topics considered in the literature such as fuzzy belief [22, 17], spatial reasoning in the presence of vagueness =-=[27]-=-, fuzzy similarity measures [18], and fuzzy description logics, which may be understood, analogously to classical description logics, as multi-modal fuzzy logics (see, e.g., [30, 21, 6]). Fuzzy modal ...

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... since the late 1980s — is robotics, for automated planning purposes [31]. In particular, simultaneous localization and mapping (SLAM) [53, 41, 17] is a technique used in (mobile) robotics to build up a map within an unknown environment. Estimating uncertain spatial relationships is then one of the key issues. In spite of preliminary early attempts [27, 22] there have been few applications of fuzzy set based methods in robot navigation, with [58, 43, 49] being some of the exceptions. However, outside robotics, some works have focused on representing and reasoning about fuzzy spatial relations [18, 21, 34, 7, 50]. Uncertainty in Geographic Information Systems From artificial intelligence and robotics, we go to another domain where spatial uncertainty is definitely a big issue: cartographic mapping. Cartographic representations, land surveys, remote sensing, geographic information systems, and global positioning are providing data for the two main subdomains of mapping: the mapping of administrative and man-made spatial features, on the one hand, and the mapping of natural resources on the other. It has been a long time before men were able to use maps in the way we know them today. Cadastres are as ol...

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...oaches for the first problem, that have been modeled as ontologies in some works. The RCC8 model proposed in [30] is used for the ontology in [31], [32], and a fuzzy version (fuzzy RCC-8) proposed in =-=[33]-=- is employed in [32]. In [2] the proposal in [34] is employed. In [35] an ontology is built taking into account the spatial relationships proposed in [36] and [37]. Regarding the determination of spat...

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...er discs its exact complexity is still an open problem (see proposition 1). An extension of RCC-8 with Boolean operations over sets has been studied in [6]. Soft semantics for RCC-8 are also given in =-=[15,18]-=-. 6.2 Constrained Graph Drawing Drawing with Constraint. Constraints have long been used for graph drawing. Generally, the positions of constrained objects to draw can be computed in polynomial time. ...

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...for solving a variety of problems. Indeed, many fuzzy reasoning tasks can be reduced to SAT∞, including reasoning about vague concepts in the context of the semantic web [11], fuzzy spatial reasoning =-=[9]-=- and fuzzy answer set programming [7], which in itself is an important framework for non-monotonic reasoning over continuous domains (see e.g. [8, 13]). Importantly, the transition into fuzzy logics m...

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... of the components of a movement can be modified without altering much the general framework: for instance, the components of relative position and cardinal direction could be enriched in the line of =-=[33, 24]-=-. The paper is organized as follows: Section 2 introduces the preliminary definitions and notations to be used in the rest of the paper; Section 3 is devoted to present our approach in different scena...