Abstract
The 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.
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Acknowledgements
We appreciate the insightful comments and remarks of two anonymous reviewers for this journal. V. Aranda and M. Manzano are supported by Project PID2022-142378NB-I00 funded by MICIU/AEI/10.13039/501100011033 and by ERDF, EU. M. Martins was partially supported by FCT within the project UIDB/04106/2020 (https://doi.org/10.54499/UIDB/04106/2020).
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Aranda, V., Martins, M. & Manzano, M. Propositional Type Theory of Indeterminacy. Stud Logica (2024). https://doi.org/10.1007/s11225-024-10099-0
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DOI: https://doi.org/10.1007/s11225-024-10099-0