RT Book, Section
T1 On the philosophy and mathematics of hybrid partial type theory
A1 Aranda Utrero, Víctor
A1 Huertas, Antonia
A1 Manzano, María
A1 Martins, Manuel
A2 Antunes, Henrique
A2 Freire, Alfredo Roque
A2 Rodrigues, Abilio
AB 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.
PB Springer
SN 978-3-032-11026-8
SN 978-3-032-11029-9
SN 978-3-032-11027-5
YR 2026
FD 2026
LK https://hdl.handle.net/20.500.14352/137077
UL https://hdl.handle.net/20.500.14352/137077
LA eng
NO 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
NO First Online: 10 November 2025.
NO Comunidad de Madrid
NO Universidad Complutense de Madrid
DS Docta Complutense
RD 7 jun 2026