We propose a novel formal framework (called 3D-NCDC-ASP) to represent and reason about cardinal directions between extended objects in 3-dimensional (3D) space, using Answer Set Programming (ASP). 3D-NCDC-ASP extends Cardinal Directional Calculus (CDC) with a new type of default constraints, and NCDC-ASP to 3D. 3D-NCDC-ASP provides a flexible platform offering different types of reasoning: Nonmonotonic reasoning with defaults, checking consistency of a set of constraints on 3D cardinal directions between objects, explaining inconsistencies, and inferring missing CDC relations. We prove the soundness of 3D-NCDC-ASP, and illustrate its usefulness with applications.

中文翻译：

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使用答案集编程推理 3 维扩展对象之间的基本方向

我们提出了一种新颖的形式框架（称为 3D-ñCDC-ASP) 使用答案集编程 (ASP) 来表示和推理 3 维 (3D) 空间中扩展对象之间的基本方向。3D-ñCDC-ASP 使用一种新类型的默认约束扩展了基本定向演算 (CDC)，并且ñCDC-ASP 到 3D。3D-ñCDC-ASP 提供了一个灵活的平台，提供不同类型的推理：具有默认值的非单调推理、检查对象之间 3D 基本方向的一组约束的一致性、解释不一致以及推断缺失的 CDC 关系。我们证明了 3D 的健全性-ñCDC-ASP，并说明它在应用程序中的用处。