Kripke semantics for intuitionistic Łukasiewicz logic (Q2021569)

Using the poset sum construction by \textit{S. Bova} and \textit{F. Montagna} [Theor. Comput. Sci. 410, No. 12--13, 1143--1158 (2009; Zbl 1159.03045)], the authors define a Kripke structure for what they call intuitionistic Lukasiewicz logic, corresponding to a common fragment of intuitionistic and Lukasiewicz logic also denoted by GBL\(_{ewf}\). In the proposed Kripke models, the evaluation of a formula in a world is a number in [0,1] and each variable is associated with a function from the set of worlds into [0,1] that is a {\em slopping} function, i.e., as soon as it takes a value greater than 0 on a world, then it takes value 1 on all the consequent worlds. By using the poset contruction, soundness and completeness are proved for such semantics.