A Survey of Qualitative Spatial and Temporal Calculi

Dylla, Frank; Lee, Jae Hee; Mossakowski, Till; Schneider, Thomas; Delden, André van; Ven, Jasper van de; Wolter, Diedrich

doi:10.1145/3038927

Cited by 64 publications

(53 citation statements)

References 125 publications

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“…In this section, we provide a formalisation of qualitative calculi, closely following that of Dylla et al (2017). For the sake of simplicity, definitions are restricted to the binary case, although we acknowledge the existence of a few ternary calculi in literature, most notably the double-cross calculus (Freksa and Zimmermann 1992).…”

Section: Qualitative Calculimentioning

confidence: 99%

“…GEN-0 is designed to be applicable to any qualitative calculus, without making any assumptions about additional properties that may hold (such as the ones in Definitions 3.4 and 3.5). This allows GEN-0 to be applicable to calculi which correspond to weakly associative or associative Boolean algebras (Dylla et al 2017), such as the Rectangle Cardinal Direction (RCD) calculus (Navarrete et al 2013) and the connected variant of the Cardinal Direction Constraints (CDC) calculus (Skiadopoulos and Koubarakis 2005). While GEN-0 affords maximum applicability, this inevitably results in decreased performance.…”

Section: Optimisations Based On Algebraic Propertiesmentioning

confidence: 99%

“…The majority of qualitative calculi, as analysed in Dylla et al (2017), correspond to full relational algebras, satisfying, among others, both the involution of converse property of Definition 3.4 and the identity law of Definition 3.5. Calculi in this case include the well-known Allen's interval algebra and all variants of RCC.…”

Section: Identity Optimisationmentioning

confidence: 99%

See 2 more Smart Citations

A Generalised Approach for Encoding and Reasoning with Qualitative Theories in Answer Set Programming

Baryannis¹,

Tachmazidis²,

Batsakis³

et al. 2020

Theory and Practice of Logic Programming

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Qualitative reasoning involves expressing and deriving knowledge based on qualitative terms such as natural language expressions, rather than strict mathematical quantities. Well over 40 qualitative calculi have been proposed so far, mostly in the spatial and temporal domains, with several practical applications such as naval traffic monitoring, warehouse process optimisation and robot manipulation. Even if a number of specialised qualitative reasoning tools have been developed so far, an important barrier to the wider adoption of these tools is that only qualitative reasoning is supported natively, when real-world problems most often require a combination of qualitative and other forms of reasoning. In this work, we propose to overcome this barrier by using ASP as a unifying formalism to tackle problems that require qualitative reasoning in addition to non-qualitative reasoning. A family of ASP encodings is proposed which can handle any qualitative calculus with binary relations. These encodings are experimentally evaluated using a real-world dataset based on a case study of determining optimal coverage of telecommunication antennas, and compared with the performance of two well-known dedicated reasoners. Experimental results show that the proposed encodings outperform one of the two reasoners, but fall behind the other, an acceptable trade-off given the added benefits of handling any type of reasoning as well as the interpretability of logic programs.

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Section: Qualitative Calculimentioning

confidence: 99%

Section: Optimisations Based On Algebraic Propertiesmentioning

confidence: 99%

See 1 more Smart Citation

A Generalised Approach for Encoding and Reasoning with Qualitative Theories in Answer Set Programming

Baryannis¹,

Tachmazidis²,

Batsakis³

et al. 2020

Theory and Practice of Logic Programming

View full text Add to dashboard Cite

show abstract

“…Some of these formalisms focus on topology (DIR9 [14], RCC8 [9]), direction (cone and projection based [16], LR [27], Double-cross [17], Dipole [34], SV [25], OPRA [32], Rectangle Algebra [2,3], Cardinal Directional Calculus [20,41]), distance [46,31,15,21], size [16], and shape [12,19,44,38,11]. An overview of qualitative spatial and temporal calculus can be found in recent surveys [10,7,13].…”

Section: Related Literaturementioning

confidence: 99%

Reasoning about Qualitative Direction and Distance between Extended Objects using Answer Set Programming

Izmirlioglu

2019

Electron. Proc. Theor. Comput. Sci.

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In this thesis, we introduce a novel formal framework to represent and reason about qualitative direction and distance relations between extended objects using Answer Set Programming (ASP). We take Cardinal Directional Calculus (CDC) as a starting point and extend CDC with new sorts of constraints which involve defaults, preferences and negation. We call this extended version as nCDC. Then we further extend nCDC by augmenting qualitative distance relation and name this extension as nCDC+. For CDC, nCDC, nCDC+, we introduce an ASP-based general framework to solve consistency checking problems, address composition and inversion of qualitative spatial relations, infer unknown or missing relations between objects, and find a suitable configuration of objects which fulfills a given inquiry.

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“…Spatial calculi are of interest when relative and not absolute information is available in spatial data [6]. Beside the famous region connection calculus, other calculi exist and deal with topology, distance, orientation and shape for a variety of application scenarios [4].…”

Section: Introductionmentioning

confidence: 99%

Modeling CDC in a fuzzy description logic A comparison of different approaches

Unold

Cruz

2019

Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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Relative information about locations of places can be described using the cardinal direction calculus (CDC). Some extensions of the calculus allow to express vague information and others include nearness/closeness. The development of description logics for qualitative spatial calculi has also been done. In this paper, we propose several knowledge bases for fuzzy description logics to manage information on relative positions of points of interest (POI) with respect to cardinal directions and distance. The theory of vague description logics is used and applied on the cardinal direction calculus. The paper compares the different approaches and aims to objectify the comparison by generating artificial datasets that form the basis for the evaluation. The evaluation is performed in different scenarios with different parameters and the results are discussed. The advantages and disadvantages of each model are related to potential application scenarios.

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A Survey of Qualitative Spatial and Temporal Calculi

Cited by 64 publications

References 125 publications

A Generalised Approach for Encoding and Reasoning with Qualitative Theories in Answer Set Programming

A Generalised Approach for Encoding and Reasoning with Qualitative Theories in Answer Set Programming

Reasoning about Qualitative Direction and Distance between Extended Objects using Answer Set Programming

Modeling CDC in a fuzzy description logic A comparison of different approaches

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