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Title: A semantics for equational hybrid propositional type theory
Author: Manzano Arjona, María
Martins, Manuel A.
Huertas Sánchez, María Antonia
Others: Universidade de Aveiro
Universidad de Salamanca
Universitat Oberta de Catalunya (UOC)
Keywords: propositional type theory
first-order logic
second-order logic
equational hybrid logic
Issue Date: Jul-2014
Publisher: Bulletin of the Section of Logic
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.
Project identifier: info:eu-repo/grantAgreement/FFI-2009-09345MICINN
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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.
Language: English
ISSN: 0138-0680MIAR
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