We investigate logics and classes of problems below Fagin's existential second-order logic (ESO) and above Feder and Vardi's logic for constraint satisfaction problems (CSP), the so called monotone monadic SNP without inequality (MMSNP). It is known that MMSNP has a dichotomy between P and NP-complete but that the removal of any of these three restrictions imposed on SNP yields a logic that is Ptime equivalent to ESO: so by Ladner's theorem we have three stronger sibling logics that are nondichotomic above MMSNP. In this paper, we explore the area between these four logics, mostly by considering guarded extensions of MMSNP, with the ultimate goal being to obtain logics above MMSNP that exhibit such a dichotomy.

翻译：我们研究了在Fagin存在二阶逻辑（ESO）之下、Feder与Vardi约束满足问题（CSP）逻辑之上的逻辑与问题类，即所谓的无不等式单调一元SNP（MMSNP）。已知MMSNP在P与NP完全之间具有二分性，但移除SNP所施加的这三个限制中的任意一个，都会得到一个在Ptime意义下等价于ESO的逻辑：因此，根据Ladner定理，我们有三个更强的兄弟逻辑，它们在MMSNP之上不具二分性。在本文中，我们主要考虑MMSNP的守卫扩展，以探索这四个逻辑之间的区域，最终目标是获得MMSNP之上、且具有此类二分性的逻辑。