CAJ | 학술논문

在可能世界语义中,如果根据是否含有模态算子而将一个点上为真的公式分为两类,那么可以认为不含模态算子的公式描述的是当前点的信息,其它公式描述的是其它点的信息,以及当前点与其它点的关系。通过对不同点上命题真值指派的比较,我们可以在可能世界语义模型上定义出一种状态相似性。本文构造了三类刻画状态相似性的模型,并给出了分别刻画其中两类模型的完全的系统。本文最后讨论这些模型在时态逻辑和信念逻辑中的应用。
재가능세계어의중,여과근거시부함유모태산자이장일개점상위진적공식분위량류,나요가이인위불함모태산자적공식묘술적시당전점적신식,기타공식묘술적시기타점적신식,이급당전점여기타점적관계。통과대불동점상명제진치지파적비교,아문가이재가능세계어의모형상정의출일충상태상사성。본문구조료삼류각화상태상사성적모형,병급출료분별각화기중량류모형적완전적계통。본문최후토론저사모형재시태라집화신념라집중적응용。
In virtue of possible world semantics,logicians have developed many formalisms which are used to describe or analyze the rules of important phenomenon in many research areas,such as philosophy,linguistic,cognitive science,computer science and so on.The basic structures of those formalisms are a series of transitions among states. Structural similarity is an important issue.In these semantics,a state（or node,possible world）which represents certain situation is described by propositions that are true at the state.On the other hand,formulas with modal operators describe the accessibility relation among these states. We argue that,there should be some kind of relationship between states that are connected by the accessibility relation.We discuss structural similarity in this paper in the sense that states connected by accessibility relations should be similar in a prescribed degree.For example,in temporal logic,events that happen in time should be in a manageable manner.Two adjacent time points should be similar,because no so much happened between them,and therefore no so much have been changed from one to the other.It means that for a description of situation at two different points,the more the points are close,the more they are similar. In this paper,similarity between two states is directly defined by numbers of propositions that share the same value at the two states.We define degrees of similarity in three kinds of models,and present two complete systems which character the first and the third kinds of models.We discuss the applications of these models in temporal logic and doxastic logic.