 A formula \(\varphi\) is a consequence of a set of formulas \(\Gamma\) in MTL, denoted \(\Gamma \models_\mathrm{MTL} \varphi\), if for each left-continuous t-norm \(\ast\) and each \(\ast\)-evaluation \(e\) such that \(e(\psi) = 1\) for each \(\psi \in \Gamma\) we have \(e(\varphi) = 1\); in words, if the premises are totally true, so is the conclusion. A formula \(\varphi\) that always evaluates to \(1\) (i.e. \(\emptyset\models_\mathrm{MTL}\varphi\)) is called valid or a tautology of MTL. Note that the formula \(\varphi \mathbin{\&amp;} \psi \to \varphi \land \psi\) is a tautology in MTL but the converse implication \(\varphi \land \psi \to \varphi \mathbin{\&amp;} \psi\) is not, i.e., the conjunction \(\&amp;\) is stronger than \(\land\).