分划逻辑与着色卵石博奕

Partition Logics and Coloured Pebble Games

将Ｍａｌｉｔｚ量词Ｑ￣（ｍ，ｎ）的基数限制去掉，再作多分划拓广，便得到各种ｍｏｎａｄｉｃ型的分划量词。本文引入了分划逻辑的着色卵石博奕方法，证明了相应的Ｅｈｒｅｎｆｅｎｃｈｔ－Ｆｒａｓｓｅ定理，作为此方法的一个应用，证明了在表达能力上，ｍｏｎａｄｉｃ型的分划逻辑严格地弱于ｍｏｎａｄｉｃ二阶逻辑。

Monadic partition quantifiers are obtained through multi-partition extensionsof Malitz quantifier Q￣(m,n) deleting its cardinality restriction. In this article the methods ofcoloured pebble games for partition logics are introduced and the corresponding Ehrenfencht-Fraisse theorems are proved.As an application of the stated methods it can be shown that forthe monadic type the expressive power of the partition logic is strictly weaker than that of thesecond order logic.