Please use this identifier to cite or link to this item:
http://hdl.handle.net/10609/99589
Title: | Completeness in Equational Hybrid Propositional Type Theory |
Author: | Manzano Arjona, María Martins, Manuel A. Huertas, M. Antonia |
Citation: | Manzano Arjona, M., Huertas, M.A. & Martins, M.A. (2018). Completeness in Equational Hybrid Propositional Type Theory. Studia Logica, (), 1-40. doi: 10.1007/s11225-018-9833-5 |
Abstract: | Equational hybrid propositional type theory (EHPTT) is a combination of propositional type theory, equational logic and hybrid modal logic. The structures used to interpret the language contain a hierarchy of propositional types, an algebra (a nonempty set with functions) and a Kripke frame. The main result in this paper is the proof of completeness of a calculus specifically defined for this logic. The completeness proof is based on the three proofs Henkin published last century: (i) Completeness in type theory, (ii) The completeness of the first-order functional calculus and (iii) Completeness in propositional type theory. More precisely, from (i) and (ii) we take the idea of building the model described by the maximal consistent set; in our case the maximal consistent set has to be named, -saturated and extensionally algebraic-saturated due to the hybrid and equational nature of EHPTT. From (iii), we use the result that any element in the hierarchy has a name. The challenge was to deal with all the heterogeneous components in an integrated system. |
Keywords: | Propositional type theory Hybrid logic Equational logic Completeness |
DOI: | 10.1007/s11225-018-9833-5 |
Document type: | info:eu-repo/semantics/article |
Version: | info:eu-repo/semantics/acceptedVersion |
Issue Date: | 20-Oct-2018 |
Publication license: | https://creativecommons.org/licenses/by/4.0/ |
Appears in Collections: | Articles Articles cientÍfics |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Manzano_StudiaLogica_Completeness.pdf | 699,95 kB | Adobe PDF | View/Open |
Share:
Items in repository are protected by copyright, with all rights reserved, unless otherwise indicated.