On strong standard completeness in some MTL expansions

In this paper, inspired by the previous work of Franco Montagna on infinitary axiomatizations for standard -algebras, we focus on a uniform approach to the following problem: given a left-continuous t-norm , find an axiomatic system (possibly with infinitary rules) which is strongly complete with respect to the standard algebra This system will be an expansion of Monoidal t-norm-based logic. First, we introduce an infinitary axiomatic system , expanding the language with and countably many truth constants, and with only one infinitary inference rule, that is inspired in Takeuti-Titani density rule. Then we show that is indeed strongly complete with respect to the standard algebra . Moreover, the approach is generalized to axiomatize expansions of these logics with additional operators whose intended semantics over [0, 1] satisfy some regularity conditions.