scholarly journals On Redundant Topological Constraints (Extended Abstract)

2017 ◽  
Author(s):  
Sanjiang Li ◽  
Zhiguo Long ◽  
Weiming Liu ◽  
Matt Duckham ◽  
Alan Both
Keyword(s):  
Knowledge Representation ◽  
Important Task ◽  
Solution Set ◽  
Constraint Solving ◽  
Topological Constraints ◽  
Redundant Constraints ◽  
Region Connection Calculus

Redundancy checking is an important task in AI subfields such as knowledge representation and constraint solving. This paper considers redundant topological constraints, defined in the region connection calculus RCC8. We say a constraint in a set C of RCC8 constraints is redundant if it is entailed by the rest of C. A prime subnetwork of C is a subset of C which contains no redundant constraints and has the same solution set as C. It is natural to ask how to compute such a prime subnetwork, and when it is unique. While this problem is in general intractable, we show that, if S is a subalgebra of RCC8 in which weak composition distributes over nonempty intersections, then C has a unique prime subnetwork, which can be obtained in cubic time by removing all redundant constraints simultaneously from C. As a by-product, we show that any path-consistent network over such a distributive subalgebra is minimal.

Introduction to generic rectangular floor plans

2018 ◽  
Vol 32 (3) ◽  
pp. 331-350
Author(s):  
Krishnendra Shekhawat ◽  
José P. Duarte
Keyword(s):  
Theoretical Approach ◽  
Mathematical Theory ◽  
Architectural Design ◽  
Important Task ◽  
Floor Plan ◽  
Design Processes ◽  
Topological Constraints ◽  
Graph Theoretical Approach ◽  
Floor Plans

AbstractAn important task in the initial stages of most architectural design processes is the design of planar floor plans, that are composed of non-overlapping rooms divided from each other by walls while satisfying given topological and dimensional constraints. The work described in this paper is part of a larger research aimed at developing the mathematical theory for examining the feasibility of given topological constraints and providing a generic floor plan solution for all possible design briefs.In this paper, we mathematically describe universal (or generic) rectangular floor plans with n rooms, that is, the floor plans that topologically contain all possible rectangular floor plans with n rooms. Then, we present a graph-theoretical approach for enumerating generic rectangular floor plans upto nine rooms. At the end, we demonstrate the transformation of generic floor plans into a floor plan corresponding to a given graph.

Interval Algebra and Region Connection Calculus for Ontological Spatiotemporal Assembly Product Motion Knowledge Representation

2021 ◽  
pp. 1-18
Author(s):  
Md Tarique Hasan Khan ◽  
Frédéric Demoly ◽  
Kyoung Yun Kim
Keyword(s):  
Knowledge Representation ◽  
Semantic Knowledge ◽  
Added Value ◽  
Topological Spaces ◽  
Product Knowledge ◽  
Interval Algebra ◽  
Assembly Design ◽  
Knowledge Models ◽  
Region Connection Calculus

Over the last decades, noticeable efforts have been made to construct design knowledge during the detailed geometric definition phase systematically. However, physical products exhibit functional behaviors, which explain that they evolve over space and time. Hence, there is a need to extend assembly product knowledge towards the spatiotemporal dimension to provide more realistic knowledge models in assembly design. Systematic semantic knowledge representation via ontology enables designers to understand the anticipated product’s behavior in advance. In this article, Interval Algebra (IA) and Region Connection Calculus (RCC) are investigated to formalize and construct ontological spatiotemporal assembly product motion knowledge. IA is commonly used to represent the temporality between two entities, while RCC is more appropriate to represent the ‘part-to-part’ relationships of two topological spaces. This paper discusses the roles of IA and RCC and presents a case study of a nutcracker assembly model’s behavior. The assembly product motion ontology with the aid of IA and RCC is evaluated using a task-based approach. The evaluation shows the added value of the developed ontology compared to others published in the literature.

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