On the Łukasiewicz logic and some of its extensions

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.

Keywords:

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