This paper draws chiefly on the ideas and methods in Peters and Westerst?hl (2006), Moss (2010, 2011), and Chow Ka Fat (2012), etc. The new facts and corollaries discovered and proved in this paper are 11 and 2 respectively. These facts and corollaries mainly summarize three inferential patterns of generalized quantifiers as follows: (1) argument structure inferences; (2) monotonicities inferences; (3) generalized syllogistic inferences. These patterns are illustrated by many instances in this paper. Since generalized quantifiers are ubiquitous in natural languages, the study is very important for knowledge representation and reasoning in computer science.