Ghasem Khakshoor - Department of Mathematics,Technical and Vocational university(TVU),Tehran,Iran
Seyed Mohammad Amin Khatam - Department of Computer Science, Birjand University of Technology, Birjand, Iran

In this short paper, firstly we have a review over the history of the Łukasiewicz logic. Then we study new result around the Łukasiewicz logic and its famous extensions like as Pavelka logic and continuous logic. Finally, we try to generalize the subject to another t-norm based fuzzy logic, namely Gödel logic.

Łukasiewicz logic, Pavelka logic, continuous logic, fuzzy logic, completeness theorem, compactness theorem.