Completeness in Equational Hybrid Propositional Type Theory
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 mai...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Oberta de Catalunya (UOC) |
| Repositorio: | O2, repositorio institucional de la UOC |
| OAI Identifier: | oai:openaccess.uoc.edu:10609/99589 |
| Acceso en línea: | http://hdl.handle.net/10609/99589 |
| Access Level: | acceso abierto |
| Palabra clave: | Propositional type theory Hybrid logic Equational logic Completeness Algebra Àlgebra Álgebra |
| Sumario: | 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. |
|---|