Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-25T10:48:47.073Z Has data issue: false hasContentIssue false
  • English
  • Français

Interpolation for extended modal languages

Published online by Cambridge University Press:  12 March 2014

Balder ten Cate
Balder ten Cate*
Affiliation:
Institute for Logic, Language and Computation, University of Amsterdam, Nieuwe Doelenstraat 15, 1012CP Amsterdam, Netherlands, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Several extensions of the basic modal language are characterized in terms of interpolation. Our main results are of the following form: Language L′ is the least expressive extension of L with interpolation. For instance, let ℳ(D) be the extension of the basic modal language with a difference operator [7], First-order logic is the least expressive extension of ℳ(D) with interpolation. These characterizations are subsequently used to derive new results about hybrid logic, relation algebra and the guarded fragment.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 1 , March 2005 , pp. 223 - 234
Copyright
Copyright © Association for Symbolic Logic 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Andréka, Hajnal, van Benthem, Johan, and Námeti, István, Modal logics and bounded fragments of predicate logic, Journal of Philosophical Logic, vol. 27 (1998), no. 3, pp. 217–274.CrossRefGoogle Scholar
[2]Areces, Carlos, Blackburn, Patrick, and Marx, Maarten, Hybrid logics: Characterization, interpolation and complexity, this Journal, vol. 66 (2001), no. 3, pp. 977–1010.Google Scholar
[3]Barwise, Jon and Feferman, Solomon, Model-theoretic logics, Springer-Verlag, 1985.Google Scholar
[4]Blackburn, Patrick, de Rijke, Maarten, and Venema, Yde, Modal logic, Cambridge University Press, Cambridge, UK, 2001.CrossRefGoogle Scholar
[5]Conradie, Willem, Definability and changing perspectives: The Beth property for three extensions of modal logic, Master's thesis, ILLC, University of Amsterdam, 2002.Google Scholar
[6]Craig, William, Linear reasoning, a new form of the Herbrand-Gentzen theorem, this Journal, vol. 22 (1957), pp. 250–268.Google Scholar
[7]de Rijke, Maarten, The modal logic of inequality, this Journal, vol. 57 (1992), no. 2, pp. 566–584.Google Scholar
[8]Gabbay, Dov, Craig's interpolation theorem for modal logics, Conference in mathematical logic — London '70 (Hodges, Wilfrid, editor). Lecture Notes in Mathematics, Springer-Verlag, 1972, pp. 111–127.CrossRefGoogle Scholar
[9]Gargov, George and Goranko, Valentin, Modal logic with names, Journal of Philosophical Logic, vol. 22 (1993), no. 6, pp. 607–636.CrossRefGoogle Scholar
[10]Grädel, Erich, On the restraining power of guards, this Journal, vol. 64 (1999), no. 4, pp. 1719–1742.Google Scholar
[11]Hoogland, Eva and Marx, Maarten, Interpolation and definability in guarded fragments, Studia Logica, vol. 70 (2002), no. 3, pp. 373–409.CrossRefGoogle Scholar
[12]Marx, Maarten, Relation algebra with binders, Journal of Logic and Computation, vol. 11 (2001). no. 5, pp. 691–700.CrossRefGoogle Scholar
[13]Spaan, Edith, Complexity of modal logics, Ph.D. thesis, ILLC, University of Amsterdam, 1993.Google Scholar
[14]ten Cate, Balder, Marx, Maarten, and Viana, Petrucio, Sahlqvist theory for hybrid logic, Liber Amicorum Dick de Jongh (Troelstra, Anne, editor), University of Amsterdam, 2004, Available from http://staff.science.uva.nl/~bcate.Google Scholar
[15]Venema, Yde, Relational games, Algebraic logic (Andréka, Hajnal, Monk, Donald, and Németi, István, editors), North-Holland, 1991, pp. 695–718.Google Scholar