Incompletness of Lukasiewicz and Gödel logics
International Journal of Innovations in Engineering and Technology · 2017
Every k -valued logic is defined by a model such that every logical formula has a truth-table.We suppose that every truth-table of the model must have a logical formula, too.Then the logic is complete.This is a very strong condition since every model has n k k n -ary truth-tables.Nevertheless complete logics exist.But Lukasiewicz and Gödel logics are not complete. I. LOGIC, ALGEBRA AND COMPLETENESSEvery logic is a theory and every theory has a model.The model of a logic is an algebra.We name objects of a logic and its model formulas and functions respectively.