变论域模型上带赋值算子的认知逻辑研究

On Epistemic Logic with Assignments over Varying Domain Models

本文扩展了王彦晶和谢立民(J.Seligman)所提出的带赋值算子的认知逻辑.该逻辑沿循库伊(B.Kooi)所提出的动态项模态逻辑(dynamic term-modal logic)的进路,而二者都可以追溯到费廷(M.Fitting)曾提出的项模态逻辑.在一阶动态项模态逻辑的基础之上,王彦晶和谢立民采取了一种最小化的方法,仅把基础的赋值算子引入无量词的项模态逻辑,就得到一个足以自然地区分开多种从物/从言知识情形的逻辑片段.但上述工作都集中在常论域模型上,这就启发我们进一步放松对论域的限制,讨论可能带来的不同情况.正如库伊在动态项模态逻辑提出之初所言,动态项模态逻辑的一个发展方向就是允许论域变化,并从认知的视角研究存在的问题.本文将在这个方向上做出尝试,并试图给出对变论域上的认知模型的定义.更进一步,本文还将放松对项的解释的限制,允许项空指的情况.在区分个体与个体的名字、不固定论域、不假定名字都有指的形式化设定下,文中给出了一个认知模型上有效公式的公理系统.

In this paper we extend the epistemic logic with assignment proposed by Yanjing Wang and Jeremy Seligman,which follows dynamic term-modal logic approach put forward by Barteld Kooi.Both of the work date back to term-modal logic proposed by Melvin Fitting.Y.Wang&J.Seligman introduces only the basic assignment modalities from dynamic logic combined with a quantifier-free term modal logic to obtain apretty powerful language for expressing various de dicto/de re distinctions in a natural way.However,both the work focus on logics over constant-domain models,which inspires us to ease this restriction and see what will happen.As mentioned by B.Kooi in the beginning of dynamic term-modal logic,it could be further developed by allowing varying domains such that matters of existence can also be investigated from an epistemic perspective,this paper wants to take a first step at this point.We will define the epistemic models over varying domains.Furthermore,we adopt the principle that terms always do designate,and modify the formal machinery to allow for nondesignating terms in our semantics.Then a sound and complete axiomatization for valid formulas over varying-domain epistemic models will be given.