关于函数依赖关系的认知逻辑（英文）

Epistemic Logic with Functional Dependency Operator

对非经典知识,尤其是"知道是什么"的研究几乎是与对经典的认知逻辑的研究同时开始的,并且近来此类研究又吸引了诸多学者的注意。此种"知道是什么"算子能用来表达认知主体对个别变量的值的知识,但仅靠其自身却无法表达主体对变量之间的关系的知识。本文尝试提出一种算子来表达主体对变量间的函数关系的知识。不同于相关研究中类似的用于表达函数依赖关系的其它算子,这种算子的语义引入了一个先验函数域,用以表达认知主体对函数依赖关系的先验可能性的限制。我们将讨论该种语义下由不同的先验函数域引出的三种单主体逻辑,然后将其统一到一个逻辑当中并扩充为多主体逻辑。

Epistemic logic with non-standard knowledge operators, especially the “knowingvalue”operator, has recently gathered much attention. With the “knowing-value” operator,we can express knowledge of individual variables, but not of the relations between them in general. In this paper, we propose a new operator Kf to express knowledge of the functional dependencies between variables. The semantics of this Kf operator uses a function domain which imposes a constraint on what counts as a functional dependency relation. By adjusting this function domain, different interesting logics arise, and in this paper we axiomatize three such logics in a single agent setting. Then we show how these three logics can be unified by allowing the function domain to vary relative to different agents and possible worlds. A multiagent axiomatization is given in this case.