# Composing cardinal directions relationship

### Syllogistic Reasoning for Cardinal Direction Relations | Ah-Lian Kor - btcmu.info

Cardinal Directions, Spatial Reasoning,Composition,Partialand Whole Regions In this paper we will concentrate on cardinal direction relations and improve. Composing Cardinal Direction Relations Basing on Interval Algebra Juan Chen, Haiyang Jia, Dayou Liu, and Changhai Zhang College of Computer Science. Composing Cardinal Direction Relations Spiros Skiadopoulos1 and Manolis Koubarakis2 1 Dept. of Electrical and Computer Engineering National Technical .

In this paper, we have developed an expressive hybrid model for direction relations. Based on this model, we derive two composition tables for expressive and weak direction relations.

Finally, we will demonstrate how the model could be used to make several types of existential inferences. The cone-shaped cardinal direction model could have 4, 8, or more partitions look at Figure 1. Cone-shaped direction model with 4 or 8 partitions ibid. Frank defines the four major cardinal directions north, south, east, and west as pair-wise opposites and half planes. When the two sets of half planes are combined, it yields four intermediate cardinal directions northeast, northwest, southeast, and southwest which are depicted in Figure 2.

Ligozat [ 21 ] applies the model to points in a two-dimensional space.

Thus, the referent object, Point B, will be given the four major directions. However, the relations between two objects will be denoted by one of the following basic relations: Cardinal directions defined by half-planes.

Frank [ 12 ] extends the half-planes to tiles for regions as shown in Figure 3. According to Frank, the O tile is considered a neutral zone, because in this tile, the relative cardinal direction between two regions cannot be determined due to their proximity. Cardinal directions defined by tiles for extended objects [ 12 ]. Frank compares and contrasts reasoning with the cone-shaped and the projection-based models for cardinal directions. The reasoning capability for both the systems is limited and weak though they do not differ substantially in their reasoning outcomes.

This hybrid model is well suited for applications of large-scale high-level vision, such as, for example, satellite-like surveillance of a geographic area. The cardinal direction calculus CDC [ 3 — 5 ] is a very expressive qualitative calculus for directional information of extended objects.

A direction relation matrix DRM in 1 is used to represent direction relations between connected plane regions. Liu and colleagues [ 2728 ] have shown that consistency checking of complete networks of basic CDC constraints is tractable, while reasoning with the CDC in general is NP hard.

However, if some constraints are unspecified, then consistency checking of incomplete networks of basic CDC constraints is intractable. The cardinal direction of a target object region b to a referent object region a as shown in Figure 4 is described by recording those tiles covered by the target object.

**North South East West - Cardinal Directions - Geography for Kids - Geography Games**

According to Goyal and Egenhofer [ 4 ], a matrix is employed to register the intersections between the target object and the tiles of the referent object see 1. The elements in the direction-relation matrix correspond to the tiles of the referent object, region a in Figure 4. Nine tiles with regions as the referent object and as the target object [ 45 ]. In 1the symbol represents empty tile while represents nonempty tile.

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These are used to describe cardinal directions at a coarse granularity level. Thus, these three tiles are considered nonempty while the rest are considered empty as shown in 1. Composition Direction Relations represented as: In our previous paper [Kor and Assume U is a universal set of the RCC-5 relations Bennett, ], we have developed a formula to compute between a region b and a tile t of region a.

However, in this region a is represented as: After substitution, Equation 1 will be as between two general entities. However, the procedure for follows: We use the generated topological relations 1. We shall verify the Use the Distributive Law and Equation 1. All b are in ne a and All c are in ne b Use D7, and the boolean algebraic expression for the above composition is as follows: All c is in the ne a tile. When we Table 3 to establish the relationship between ne b and compare the relation with assertion D8, then we have the ne a in order to make the appropriate transitive following conclusion: Some c is in the ne a tile.

Based on the information in Table 3, confirmed by the diagrammatic representation in Figure substitute the following into Equation 1: Based on the information in Table 3, becomes: Substitute this into Equation becomes: Use the composition table in Table 4 and Equation 2. Compare the relation with the aforementioned assertions 7. All c is All and Some to formalize quantified direction relations. This is confirmed by the diagrammatic composition of such quantified direction relations.

The representation in Figure 7 note: However, based on the worked out examples, the conclusions derived from the inferences made are rather weak. Thus, further research will be necessary to investigate ways to enhance the reasoning with RCC-5, cardinal directions and syllogisms. Maintaining Knowledge about interval Example 3.

### A Hybrid Reasoning Model for “Whole and Part” Cardinal Direction Relations

No b are in w a and All c are in n b intervals. Use D7 and D9, and the boolean algebraic expression for Balbiani, P. Model the above composition is as follows: Spatial Reasoning with Propositional Given the relation dr b, w ause Table 3 to establish the Logics. Strategies in appropriate transitive inferences. Based on the Syllogistic Reasoning.

Design of an extended Equation 3: Combinative Use the Distributive Law and Equation 3. Reasoning Mechanism forDOI: Composition for Cardinal Vol. Advanced ApplicationsLecture Notes in Computer eds. Science Volume, pp Cardinal Directions Li, S. Combining topological and directional between Spatial Objects: Information Sciences — Informatics and Computer Proceedings of the 20th international joint conference on Science: An International Journal Vol. Reasoning about Cardinal Directions.

Algorithms and Sciences, 90, pp. Spatial reasoning with Representation and Positional Information. Extending cardinal directions with local Intelligence, 95, pp. Spatial relations, Region Connection Calculus. Temporal Prepositions and Information.

Geographical Systems, 1 1pp. Proceedings of the Third Information and Analysis.

### Composing cardinal direction relations - Semantic Scholar

A framework based on CLP Reasoning. JVLC, Vol 3pp. Inferences from Freksa, C. Using orientation information for qualitative combined knowledge about topology and directions. American Association for Artificial Intelligence.