论文标题
无量词，可决定的语言的设定理论决策程序，该语言扩展了有限的量词
A Set-Theoretic Decision Procedure for Quantifier-Free, Decidable Languages Extended with Restricted Quantifiers
论文作者
论文摘要
令$ \ MATHCAL {L} _ {\ MATHCAL {X}} $为一阶，可决定理论$ \ MATHCAL {x} $的语言。考虑语言，$ \ nathcal {l} _ {\ Mathcal {rq}}}（\ Mathcal {x}）$，它扩展了$ \ Mathcal {l} _ {\ Mathcal {\ Mathcal {x}} $，并具有form $ \ forall x ports $ in a：drue（diver in a：v y：v formand） \在A：ϕ $（限制存在量化器，req）中，其中$ a $是有限的集合，$ ϕ $是由$ \ Mathcal {x} $ - 公式，RUQ和REQ制成的公式。也就是说，$ \ MATHCAL {L} _ {\ MATHCAL {RQ}}}（\ Mathcal {X}）$允许嵌套受限的量词。在本文中，我们基于已经定义的有限集集的Boolean代数定义的决策过程，介绍了$ \ Mathcal {l} _ {\ Mathcal {\ Mathcal {RQ}}（\ Mathcal {X}）$ $。还引入了决策过程作为$ \ {log \} $（`setLog'）工具的一部分的实现。该方法的有用性是通过从几个实际案例研究中得出的许多示例来显示的。
Let $\mathcal{L}_{\mathcal{X}}$ be the language of first-order, decidable theory $\mathcal{X}$. Consider the language, $\mathcal{L}_{\mathcal{RQ}}(\mathcal{X})$, that extends $\mathcal{L}_{\mathcal{X}}$ with formulas of the form $\forall x \in A: ϕ$ (restricted universal quantifier, RUQ) and $\exists x \in A: ϕ$ (restricted existential quantifier, REQ), where $A$ is a finite set and $ϕ$ is a formula made of $\mathcal{X}$-formulas, RUQ and REQ. That is, $\mathcal{L}_{\mathcal{RQ}}(\mathcal{X})$ admits nested restricted quantifiers. In this paper we present a decision procedure for $\mathcal{L}_{\mathcal{RQ}}(\mathcal{X})$ based on the decision procedure already defined for the Boolean algebra of finite sets extended with restricted intensional sets ($\mathcal{L}_\mathcal{RIS}$). The implementation of the decision procedure as part of the $\{log\}$ (`setlog') tool is also introduced. The usefulness of the approach is shown through a number of examples drawn from several real-world case studies.
