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 L_(conv), ≤ 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(R~2)). We call the tuple M = (ROQ, conv, ≤) - 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.
展开▼
机译:转换术语± Sup> [n i Sub>] f(+/-) min sup>的条件最小化结构的逻辑动态过程的方法Sub> AND ± Sup> [m i Sub>] f(+/-) min Sub>在功能添加结构中± Sup> f < Sub> 1 Sub>(Σ RU Sub>) min Sub>,不带纹波f 1 Sub>(± Sup>←←)和循环ΔtΣ Sub>→5∙f(&)-和5个条件逻辑函数f(&)-,并通过三元数系统的算术公理同时转换术语参数的过程f RU Sub>(+ 1,0,-1)及其实现其的功能结构(俄罗斯逻辑版本)