# What is region connection calculus?

by Stephen M. Walker II, Co-Founder / CEO

## What is region connection calculus?

Region Connection Calculus (RCC) is a system intended for qualitative spatial representation and reasoning. It abstractly describes regions in Euclidean or topological space by their possible relations to each other.

RCC8, a popular version of RCC, consists of 8 basic relations that are possible between two regions:

1. Disconnected (DC): The two regions are completely disconnected, with no common pieces.
2. Externally Connected (EC): The boundaries of the regions touch, but their interiors are disjoint.
3. Partially Overlapping (PO): The two regions partially overlap, with disjoint subparts, and some part of one is included in some part of the other.
4. Equal (EQ): Two regions have the same spatial extent.
5. Tangential Proper Part (TPP): One region is a proper part of the other, and their boundaries touch.
6. Tangential Proper Part Inverse (TPPi): The inverse of TPP, where one region is a proper part of the other, and their boundaries touch.
7. Non-Tangential Proper Part (NTPP): One region is a proper part of the other, and their boundaries do not touch.
8. Non-Tangential Proper Part Inverse (NTPPi): The inverse of NTPP, where one region is a proper part of the other, and their boundaries do not touch.

RCC has been implemented in various systems, such as GQR, a reasoner for RCC-5, RCC-8, and RCC-23, and qualreas, a Python framework for qualitative reasoning over networks of relation algebras, such as RCC-8 and Allen's interval algebra.

RCC is used to describe spatial relationships between regions and the spatial arrangement of objects in the regions. It supports commonsense reasoning over geographic data.

## What are the advantages of using region connection calculus?

Region Connection Calculus (RCC) is a qualitative spatial calculus used to reason about the relations between regions. It offers several advantages:

1. Qualitative Reasoning — RCC enables machines to reason about spatial relationships in a qualitative manner. This provides robustness against inaccuracies in precise measurements and data, making it a reliable tool for spatial reasoning.

2. Spatial Relationships Description — RCC is used to describe spatial relationships between regions and the spatial arrangement of objects in the regions. This makes it a powerful tool for understanding and interpreting spatial data.

3. Topological Information — RCC provides a way to reason with topological information. It abstractly describes regions by their possible relations to each other, which can be particularly useful in fields like computer vision, robotics, and knowledge representation.

4. Flexibility — RCC can be extended and adapted to different needs. For example, fuzzy RCC allows for defining fuzzy relationships between regions, which can yield better results in certain applications. Similarly, probabilistic RCC introduces a probabilistic model for spatial relations, adding another layer of flexibility.

5. Integration with Other Calculi — Increasing the expressiveness of qualitative spatial calculi can be achieved by combining RCC with other calculi, such as qualitative direction calculi. This allows for expressing spatial information using relations from both calculi, meeting the requirements of various applications.

6. Support for Commonsense Reasoning — RCC supports commonsense reasoning over geographic data, which is essential for many applications in fields like geospatial analysis and geographic information systems.

7. Implementation in Programming Languages — RCC has been implemented in various programming languages, including Python, which makes it accessible for developers and researchers.

8. 3D Spatial Reasoning — Extensions of RCC, like RCC-3D, allow for qualitative spatial reasoning in three dimensions, further expanding its applicability.

## What are the basic principles of region connection calculus?

Region Connection Calculus (RCC) is a formalism used for qualitative spatial representation and reasoning. It is based on the concept of regions in space and the relationships between them. Here are the basic principles of RCC:

1. Qualitative Representation — RCC is used to describe spatial relations qualitatively rather than quantitatively, meaning it does not rely on precise measurements but on more abstract relationships between regions.

2. Topological Relationships — RCC leverages topological concepts to define the possible relations between regions. This includes whether regions are connected, overlap, or are disjoint.

3. RCC8 Relations — The most commonly referenced version of RCC is RCC8, which includes eight fundamental relations between two regions:

• Disconnected (DC): The regions have no common points.
• Externally Connected (EC): The regions share a boundary but do not overlap.
• Equal (EQ): The regions are identical in extent.
• Partially Overlapping (PO): Some parts of the regions overlap, while others do not.
• Tangential Proper Part (TPP): One region is a proper part of the other and shares a boundary.
• Tangential Proper Part Inverse (TPPi): The inverse of TPP.
• Non-Tangential Proper Part (NTPP): One region is a proper part of the other without sharing a boundary.
• Non-Tangential Proper Part Inverse (NTPPi): The inverse of NTPP.
4. Logical Formalism — RCC uses logical formalisms to reason about spatial configurations. This allows for the expression of complex spatial scenarios and the derivation of new information from known relationships.

5. Single Primitive Notion — RCC takes regions as the fundamental notion and is based on a single primitive binary relation, C (for connection), which is used to define all other relations.

6. Generalized RCC — There are generalized versions of RCC, such as RCC5, which uses only five basic relations, and RCC23, which includes additional relations for more complex reasoning.

7. Implementations — RCC has been implemented in various systems, such as GQR, a reasoner for RCC-5, RCC-8, and RCC-23, and qualreas, a Python framework for qualitative reasoning over networks of relation algebras.

RCC is widely used in artificial intelligence for tasks that require understanding the spatial arrangement of objects without needing precise numerical data, such as geographic information systems, robotics, and natural language processing.

## More terms

### What is machine learning?

Machine learning is a subset of artificial intelligence (AI) that deals with the design and development of algorithms that can learn from and make predictions on data. These algorithms are able to automatically improve given more data.

### Chain of Thought Prompting

Chain of thought or reasoning is a sequential process of understanding or decision-making that connects the ideas or arguments in a structured manner. It begins with an initial thought, leading to a series of logically connected ideas, and ends with a final conclusion. This reasoning process includes analysis, evaluation, and synthesis of information, and it is fundamental to problem-solving, decision-making, and critical thinking. The strength of the chain of thought depends on the quality and relevance of each link within the chain. Frequently, visual tools like flowcharts or diagrams are used to illustrate this chain of thought for better understanding.