An Axiom System for a Spatial Logic with Convexity
An Axiom System for a Spatial Logic with Convexity
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DOI：
10.3233/978-1-60750-606-5-701
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发表时间：
2010-08
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影响因子：
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通讯作者：
A. Trybus
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文献类型：
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作者：
A. Trybus
本文介绍了正在进行的部分工作，将具有凸性和包含谓词的空间逻辑公理化（以下称为凸性逻辑），并对实平面进行了一些预期的解释。更正式地，令 Lconv,≤ 是一阶逻辑语言和两个非逻辑原语： conv （解释为凸集的属性）和 ≤ （解释为集合包含关系）。我们让变量的范围位于实平面中的规则开放有理多边形（表示为 ROQ(R2)）。我们将元组 M = 称为标准模型，其中原语的定义如上所示。我们提出了 M 理论的公理化，并证明了该公理化的合理性和完整性。
This paper presents a part of work in progress on axiomatizing a spatial logic with convexity and inclusion predicates (hereinafter called convexity logic), with some intended interpretation over the real plane. More formally, let Lconv,≤ be a language of first order logic and two non-logical primitives: conv (interpreted as a property of a set of being convex) and ≤ (interpreted as the set inclusion relation). We let variables range over regular open rational polygons in the real plane (denoted ROQ(R2)). We call the tuple M = ---where primitives are defined as indicated above ---a standard model. We propose an axiomatization of the theory of M and prove soundness and completeness for this axiomatization.