Infinitary Modal Logic: Propositional and Predicate

Collection of papers and books.

Papers

1. Infinitary modal logic and generalized Kripke semantics.
   Pierluigi Minari.
   Annali del Dipartimento di Filosofia (Nuova Serie), 2011, vol. XVII, pp. 135-166.
2. Non-denumerable infinitary modal logic.
   Max J. Cresswell.
   Journal of Universal Computer Science, 2009, vol. 14, no. 16, pp. 63-71.
3. Hybrid logics with infinitary proof systems.
   Barteld Kooi, Gerard Renardel de Lavalette, Rineke Verbrugge.
   Journal of Logic and Computation, 2006, volume 16, issue 2, pp. 161-175.
4. Cut-elimination theorems for some infinitary modal logics.
   Yoshihito Tanaka.
   Mathematical Logic Quarterly, 2001, volume 47, issue 3, pages 327-339.
5. Model existence in non-compact modal logic.
   Yoshihito Tanaka.
   Studia Logica, 2001, vol. 67, no. 1, pp. 61-73.
6. Kripke completeness of infinitary predicate multimodal logics.
   Yoshihito Tanaka.
   Notre Dame Journal of Formal Logic, 1999, volume 40, number 3, pp. 326-340.
7. Modal logic and non-well-founded Set Theory: translation, bisimulation and interpolation.
   Goivanna D’Agostino.
   PhD Thesis, 1999, Institute for Logic, Language and Computation, Amsterdam.
8. Interpolation, preservation, and pebble games.
   Jon Barwise and Johan van Benthem.
   The Journal of Symbolic Logic, 1999, vol. 64, No. 2, pp. 881-903.
9. Modality, bisimulation and interpolation in infinitary logic.
   J.F.A.K. van Benthem.
   Annals of Pure and Applied Logic, 1999, volume 96, issues 1-3, pp. 29-41.
10. Graded Modalities VI: An infinitary graded modal logic.
    Maurizio Fattorosi-Barnaba and Silvano Grassotti.
    Mathematical Logic Quarterly, 1995, vol. 41, pp. 547-563.
11. A model existence theorem in infinitary propositional modal logic.
    Krister Segerberg.
    Journal of Philosophical Logic, 1994, volume 23, issue 4, pp. 337-367.
12. Infinitary propositional normal modal logic.
    Slavian Radev.
    Studia Logica, 1987, volume 46, issue 4, pp 291-309.

Books

• J. Barwise, L. Moss. Vicious Circles. CSLI Lecture Notes, volume 60. CSLI Publications, Stanford, 1996.
  (Includes Infinitary Modal Logic, see Chapter 11.)
• Robert Goldblatt. Mathematics of Modality. CSLI Lecture Notes, volume 43. CSLI Publications, Stanford, 1993.
  (See Chapter 9: A framework for infinitary modal logic.)
• M. A. Dickmann. Large Infinitary Languages. Model Theory.
  Studies in Logic and the Foundations of Mathematics, volume 83. North-Holland, Amsterdam, 1975.
• H. J. Keisler. Model Theory for Infinitary Logic.
  Studies in Logic and the Foundations of Mathematics, volume 62. North-Holland, Amsterdam, 1971.
• C. Karp. Languages with Expressions of Infinite Length.
  Studies in Logic and the Foundations of Mathematics, volume 36. North-Holland, Amsterdam, 1964.

Theses on infinitary logic

• Yoshihito Tanaka. Representations of algebras and Kripke completeness of infinitary and predicate logics.
  Japan Advanced Institute of Science and Technology, 1999. [Infinitary intermediate (superintuitionistic) logics]
• Maaret Karttunen. Model theory for infinitely deep languages. University of Helsinki, 1984. [Infinitary first-order logic]
• Tapanu Hyttinen. Games and infinitary languages. University of Helsinki, 1987. [Infinitary first-order logic]