We study extensions of expressive decidable fragments of first-order logic with circumscription, in particular the two-variable fragment FO$^2$, its extension C$^2$ with counting quantifiers, and the guarded fragment GF. We prove that if only unary predicates are minimized (or fixed) during circumscription, then decidability of logical consequence is preserved. For FO$^2$ the complexity increases from $\textrm{coNexp}$ to $\textrm{coNExp}^\textrm{NP}$-complete, for GF it (remarkably!) increases from $\textrm{2Exp}$ to $\textrm{Tower}$-complete, and for C$^2$ the complexity remains open. We also consider querying circumscribed knowledge bases whose ontology is a GF sentence, showing that the problem is decidable for unions of conjunctive queries, $\textrm{Tower}$-complete in combined complexity, and elementary in data complexity. Already for atomic queries and ontologies that are sets of guarded existential rules, however, for every $k \geq 0$ there is an ontology and query that are $k$-$\textrm{Exp}$-hard in data complexity.

翻译：我们研究了在限定条件下扩展具有表达力的可判定一阶逻辑片段，特别是二元片段FO$^2$、带计数量词扩展C$^2$以及守护片段GF。我们证明，若在限定过程中仅最小化（或固定）一元谓词，则逻辑后承的可判定性得以保持。对于FO$^2$，其复杂度从$\textrm{coNexp}$提升至$\textrm{coNExp}^\textrm{NP}$-完全；对于GF，其复杂度（引人注目地！）从$\textrm{2Exp}$提升至$\textrm{Tower}$-完全；而C$^2$的复杂度仍为开放问题。我们还研究了以GF句子为本体的限定知识库查询问题，证明对于合取查询的并集该问题是可判定的，其组合复杂度为$\textrm{Tower}$-完全，而数据复杂度为初等复杂度。然而，即使对于原子查询及以守护存在规则集合为本体的情形，对任意$k \geq 0$，均存在数据复杂度为$k$-$\textrm{Exp}$-困难的本体与查询。