Aranda Utrero, VíctorMartins, ManuelManzano Arjona, María Gracia2024-05-162024-05-162024-05-03Aranda, V., Martins, M. & Manzano, M. Propositional Type Theory of Indeterminacy. Studia Logica (2024). https://doi.org/10.1007/s11225-024-10099-01572-873010.1007/s11225-024-10099-0https://hdl.handle.net/20.500.14352/104079Special Issue: Strong and weak Kleene logics. Edited by Gavin St. John and Francesco PaoliThe aim of this paper is to define a partial Propositional Type Theory. Our system is partial in a double sense: the hierarchy of (propositional) types contains partial functions and some expressions of the language, including formulas, may be undefined. The specific interpretation we give to the undefined value is that of Kleene’s strong logic of indeterminacy. We present a semantics for the new system and prove that every element of any domain of the hierarchy has a name in the object language. Finally, we provide a proof system and a (constructive) proof of completeness.engAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/journal article0039-3215https://doi.org/10.1007/s11225-024-10099-0https://link.springer.com/article/10.1007/s11225-024-10099-0open access16Type theoryPartial logicThree-valued logicKleene logicLógica (Filosofía)11 Lógica