In his famous book Mathematical Fuzzy Logic, Petr Hajek defined a new fuzzy logic, which he called BL. It is weaker than the three fundamental fuzzy logics Product, Lkasiewicz and Godel, which are in turn weaker than classical logic,
but axiomatic systems for each of them can be obtained by adding axioms to BL. Thus, Hajek placed all these logics in a unifying axiomatic framework.


In this dissertation, two problems concerning BL and other fuzzy
logics have been considered and solved. One was to construct tableaux
for BL and for BL with additional connectives. Tableaux are automatic
systems to verify whether a given formula must have given truth
values, or to build a model in which it does not have these specific
truth values. The other problem that was solved is to construct
strongly standard complete axiomatic systems for BL, Lukasiewicz and
Product logics, which was done by extending Hajek's axiomatic systems for them by an infinitary rule.