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In the framework of propositional Łukasiewicz logic, a suitable notion of implicit definability, tailored to the intended real-valued semantics and referring to the elements of its domain, is introduced. Several variants of implicitly defining each of the rational elements in the standard semantics are explored, and based on that, a faithful interpretation of theories in Rational Pavelka logic in...
Computational complexity of the semigroup fragment (of the algebraic semantics) and the implicational fragment of some fuzzy logics is studied, from the perspective of the complexity of the full logic. The available results appear to confirm the key role of the implicational fragments. Some other language fragments, as well as the notion of language fragment itself, are discussed.
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