Henkin and Hybrid Logic

Bidragets oversatte titel: Henkin og Hybridlogikken

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

Publikation: Bidrag til bog/antologi/rapportBidrag til bog/antologiForskningpeer review

Resumé

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
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
Blackburn, Patrick Rowan ; Huertas, Antonia ; Manzano, Maria ; Jørgensen, Klaus Frovin. / Henkin and Hybrid Logic. The Life and Work of Leon Henkin: Essays on His Contributions. red. / Maria Manzano ; Ildiko Sain ; Enrique Alonso. Basel : Birkhäuser Verlag, 2014. s. 279-306 (Studies in Universal Logic).
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Blackburn, PR, Huertas, A, Manzano, M & Jørgensen, KF 2014, Henkin and Hybrid Logic. i M Manzano, I Sain & E Alonso (red), The Life and Work of Leon Henkin: Essays on His Contributions. Birkhäuser Verlag, Basel, Studies in Universal Logic, s. 279-306.

Henkin and Hybrid Logic. / Blackburn, Patrick Rowan; Huertas, Antonia; Manzano, Maria ; Jørgensen, Klaus Frovin.

The Life and Work of Leon Henkin: Essays on His Contributions. red. / Maria Manzano; Ildiko Sain; Enrique Alonso. Basel : Birkhäuser Verlag, 2014. s. 279-306 (Studies in Universal Logic).

Publikation: Bidrag til bog/antologi/rapportBidrag til bog/antologiForskningpeer review

TY - CHAP

T1 - Henkin and Hybrid Logic

AU - Blackburn, Patrick Rowan

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N2 - 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.

AB - 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.

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Blackburn PR, Huertas A, Manzano M, Jørgensen KF. Henkin and Hybrid Logic. I Manzano M, Sain I, Alonso E, red., The Life and Work of Leon Henkin: Essays on His Contributions. Basel: Birkhäuser Verlag. 2014. s. 279-306. (Studies in Universal Logic).