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http://hdl.handle.net/10609/123586
Title: | A semantics for equational hybrid propositional type theory |
Author: | Manzano Arjona, María Martins, Manuel A. Huertas, M. Antonia |
Others: | Universidade de Aveiro Universidad de Salamanca Universitat Oberta de Catalunya (UOC) |
Citation: | Manzano, M., Martins, M.A. & Huertas, A. (2014). A semantics for equational hybrid propositional type theory. Bulletin of the Section of Logic, 43(3-4), 121-138. |
Abstract: | The definition of identity in terms of other logical symbols is a recurrent issue in logic. In particular, in First-Order Logic (FOL) there is no way of defining the global relation of identity, while in standard Second-Order Logic (SOL) this definition is not only possible, but widely used. In this paper, the reverse question is posed and affirmatively answered: Can we define with only equality and abstraction the remaining logical symbols? Our present work is developed in the context of an equational hybrid logic (i.e. a modal logic with equations as propositional atoms enlarged with the hybrid expressions: nominals and the @ operator). Our logical base is propositional type theory. We take the propositional equality, abstraction, nominals, and @ operators as primitive symbols and we demonstrate that all of the remaining logical symbols can be defined, including propositional quantifiers and equational equality. |
Keywords: | propositional type theory first-order logic second-order logic equational hybrid logic |
Document type: | info:eu-repo/semantics/article |
Version: | info:eu-repo/semantics/publishedVersion |
Issue Date: | Jul-2014 |
Publication license: | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
Appears in Collections: | Articles Articles cientÍfics |
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Huertas_BSL_A_Semantics.pdf | 400,81 kB | Adobe PDF | View/Open |
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