Abstract
We study provability in Hilbert-style calculi obtained by adding standard modal logic axioms to Monoidal T-norm based Logic (MTL) by automated theorem proving methods. The aim of this paper is to present some basic properties of systems K, D, T, S4 and S5 over MTL.
These system are defined in the same way as are in classical propositional logic. It is shown that many classically valid formulae become unprovable.