Henkin and Hybrid Logic

Bidragets oversatte titel: Henkin og Hybridlogikken

Patrick Rowan Blackburn, Antonia Huertas, Maria Manzano, Klaus Frovin Jørgensen

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Abstrakt

Leon Henkin was not a modal logician, but there is a branch of modal logic that has been deeply influenced by his work. That branch is hybrid logic, a family of logics that extend orthodox modal logic with special proposition symbols (called nominals) that name worlds. This paper explains why Henkin’s techniques are so important in hybrid logic. We do so by proving a completeness result for a hybrid type theory called HTT, probably the strongest hybrid logic that has yet been explored. Our completeness result builds on earlier work with a system called BHTT, or basic hybrid type theory, and draws heavily on Henkin’s work. We prove our Lindenbaum lemma using a Henkin-inspired strategy, witnessing ◊-prefixed expressions with nominals. Our use of general interpretations and the construction of the type hierarchy is (almost) pure Henkin. Finally, the generality of our completeness result is due to the first-order perspective, which lies at the heart of Henin’s best known work and hybrid logic.
OriginalsprogEngelsk
TitelThe Life and Work of Leon Henkin : Essays on His Contributions
RedaktørerMaria Manzano, Ildiko Sain, Enrique Alonso
Udgivelses stedBasel
ForlagBirkhäuser Verlag
Publikationsdato14 dec. 2014
Sider279-306
ISBN (Trykt)978-3-319-09718-3
ISBN (Elektronisk)978-3-319-09719-0
DOI
StatusUdgivet - 14 dec. 2014
NavnStudies in Universal Logic

Citer dette

Blackburn, P. R., Huertas, A., Manzano, M., & Jørgensen, K. F. (2014). Henkin and Hybrid Logic. I M. Manzano, I. Sain, & E. Alonso (red.), The Life and Work of Leon Henkin: Essays on His Contributions (s. 279-306). Basel: Birkhäuser Verlag. Studies in Universal Logic https://doi.org/10.1007/978-3-319-09719-0_19