2026-06-07T19:16:09Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/1370772026-06-02T09:25:53Zcom_20.500.14352_14col_20.500.14352_21
Docta Complutense
author
Aranda Utrero, Víctor
author
Huertas, Antonia
author
Manzano, María
author
Martins, Manuel
editor
Antunes, Henrique
editor
Freire, Alfredo Roque
editor
Rodrigues, Abilio
2026-06-02T09:16:48Z
2026-06-02T09:16:48Z
2026
Aranda, V., Huertas, A., Manzano, M., Martins, M. (2026). On the Philosophy and Mathematics of Hybrid Partial Type Theory. In: Antunes, H., Freire, A.R., Rodrigues, A. (eds) Walter Carnielli on Reasoning, Paraconsistency, and Probability. Outstanding Contributions to Logic, vol 32. Springer, Cham. https://doi.org/10.1007/978-3-032-11027-5_3
978-3-032-11026-8978-3-032-11029-9978-3-032-11027-5
10.1007/978-3-032-11027-5_3
https://hdl.handle.net/20.500.14352/137077
https://doi.org/10.1007/978-3-032-11027-5_3
https://link.springer.com/chapter/10.1007/978-3-032-11027-5_3
The aim of this paper is to present the philosophical influences and motivations of Hybrid Partial Type Theory (HPTT), a partial type theory combined with a strong version of hybrid logic in which the concepts of existence and denotation emerge naturally. The text is divided into three main parts. Firstly, we present and discuss some formal systems dealing with existence and denotation in both first-order logic and type theory. Then, we move to the framework of modal logic, introducing the distinction between constant and varying domains, as well as the hybrid machinery. Finally, we give a succinct account of the semantics of HPTT and provide new definitions of existence and denotation within the system, together with a reflection on de dicto and de re statements and some validities sharing an explicit philosophical characterization.
eng
On the philosophy and mathematics of hybrid partial type theory
book part
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