  In this article we give the definitions of log Fano varieties and log Calabi-Yau varieties in the framework of theory of log schemes of Fontain-Illusie-Kato and give congruences of the cardinalities of rational points of them over the log points of finite fields. 
Congruences of the cardinalities of rational points of log Fano   varieties and log Calabi-Yau varieties over the log points of finite fields