One of the peculiar properties of logics based on triangular norms consists in the fact that to each formula we can associate a real-valued function. Indeed, the intended semantics for such logics is given by algebras over the real unit interval [0, 1]whose basic operations correspond to a left-continuous t-norm, its residuum, and the maximum and minimum operation. In this dissertation we investigate some issues concerning the definability of functions by terms in the framework of t-norm based logics. First, we study how to expand in general any t-norm based logic by means of an independent involutive negation. We establish the basic requirements for the obtained expansions to be complete w.r.t. to the related class of linearly ordered algebras, finitely strongly standard complete and standard complete. Second, we focus on the variety of LPi1/2-algebras, which form the strongest and more expressive variety of residuated algebras. We study the lattice of subvarieties of LPi1/2. We show how the universal theory of real closed fields can be faithfully translated in polynomial time in the equational theory of LPi1/2-algebras. This means that such theories share the same complexity class: indeed, they are both in PSPACE. Moreover we study the definability of triangular norms by terms and equations of LPi1/2, and prove that the main logics of the family of t-norm based logics are finitely strongly complete w.r.t. the related (class of) algebra(s) whose monoidal operation corresponds to a left-continuous t-norm definable in LPi1/2. From such completeness results we can prove decidability and PSPACE-containment for many t-norm based logics. Finally, we study the representation of both conditional and unconditional measures of uncertainty (i.e. probability, possibility, etc.) in the framework of t-norm based logics. We provide general tools, techniques, and results for an adequate logical representation of several classes of measures.