This study focuses on the possible extensions of current temporal logics. In this study, 4 extensions are proposed: self-referring events, nonexisting events, multiple recurrence of events, and an improvement on anterior past events. Each of these extensions is on a different level of temporal logics. The main motivation behind the extensions is the temporal analysis of Turkish. Similar to temporal logic studies built on other natural languages, like French, Ukrainian, Italian, Korean, English, or Romanian, this is the first time that the Turkish language has been deeply questioned in the sense of computable temporal logic using the view of a standardized temporal markup language. This study keeps the methodology of TimeML and researches Turkish from the perspectives of Reichenbach and Allen's temporal logics. Reichenbach's temporal logic is perfectly capable of handling the anterior temporal feeling, but it is not enough to handle the sense of 'learnt' or 'study', which are 2 past tenses in Turkish. Moreover, Allen's temporal logic cannot handle 2 events following each other continuously, which is called recurring events in this study for the first time. Finally, based on the experiences from a 4-year PhD study on natural language texts, this study underlines the absence of self-referring or a reference to nonexisting events in temporal logics. After adding the above extensions to computable temporal logic, the capability of tagging the events in Turkish texts is measured with an increase from 18% to 100%, creating a Turkish corpus for the first time. Moreover, new software is implemented to visualize the tagged events and previous software is developed to handle events tagged for Turkish.