An Overview of Fibred Semantics and the Combination of Logics

Part of the Applied Logic Series book series (APLS, volume 3)


This paper presents an overview of the authors methodology of Fibred Semantics and The Combinations of Logics presented in a series of papers under the same title. We explain the ideas behind fibring and illustrate them in several case studies. We include fibring modal and intuitionistic logics, fibring with fuzzy logics as well as self fibring of predicate logics.


Modal Logic Actual World Intuitionistic Logic Kripke Model Fibred Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. G. Amati and F. Pirri. Uniform tableaux methods for intuitionistic modal logic I, to appear Studia Logica.Google Scholar
  2. A. R. Anderson and N. D. Belnap. Entailment, vol. 1. Princeton University Press, 1975.Google Scholar
  3. F. Baader and K. Schulz. On the combination of symbolic constraints, solution domains and constraint solvers. In Proc. CP-95, 1995, Lecture notes in Computer Science, 976, pp. 380 - 397, Springer Verlag 1995.MathSciNetGoogle Scholar
  4. F. Baader and K. Schulz. Combination of Constraints Solving Techniques: An Algebraic Point of View. Research report CIS-Rep-94–75, University of Munich, 1994. A short version has appeared in Proc. RTA-95, Lecture Notes in Computer Science 914, pp. 352–366, Springer-Verlag, 1995.Google Scholar
  5. F. Baader and K. Schulz. Combination of constraint solvers for free and quasi-free structures. Research Report, CIS-Rep-95-120 University of Munich, 1995.Google Scholar
  6. E. Bencivenga. Free logic.In D. M. Gabbay and F. Guenthner, eds, Handbook of Philosophic al Logic, vol. 3, Kluwer, 1986Google Scholar
  7. P. Blackburn and Rijke. Why combine logics? To appear.Google Scholar
  8. P. Blackburn and M. de Rijke. Zooming in, zooming out. Journal of Logic, Language and Information, to appearGoogle Scholar
  9. M. Božić and K. Došen. Models for normal intuitionistic modal logics. Studia logica, 43, 217–245,1984.CrossRefzbMATHMathSciNetGoogle Scholar
  10. R.A.Bull.A modal extension of intuitionist logic. Notre Dame Journal of Formal logic, 6, 1965Google Scholar
  11. M D’Agostino, D.M Gabbay and A.Russo.Grafting modality into substructural logics.Draft, Imperial College, 1995Google Scholar
  12. M.D’Agostino and D.M Gabbay. Fibring labelled tableaux for substructrual logics. To appear Tableaux 96 conferenceGoogle Scholar
  13. J. P. Delgrande. An approach to default reasoning based on a first order conditional logic. Artificial Intelligence, 36 63–90, 1988.CrossRefzbMATHMathSciNetGoogle Scholar
  14. J. Dörre, D. Gabbay and E. König. Fibred semantics for feature based grammar logic.To appear in Journal of Logic, Language and Information.Google Scholar
  15. K. Došen. Models for stronger normal intuitionistic modal logics. Studia Logica, 44, 39–70, 1985.CrossRefzbMATHMathSciNetGoogle Scholar
  16. A. E. Eiben, A. Janossy and A. Kurucz. Combining Logics, draft presented at Logic at Work, Amsterdam, December 1992.Google Scholar
  17. W. B. Ewald. Intuitionistic tense and modal logic. JSL,51, 166–179, 1986.zbMATHMathSciNetGoogle Scholar
  18. R. Fagin, J. Y. Halpern and M. Y. Vardi. A nonstandard approach to the logical omniscience problem in Reasoning About Knowledge, TARK 1990, R. Parikh, ed., pp. 41–55, Morgan Kaufmann, 1990.Google Scholar
  19. L. F. del Cerro and A. Herzig. Combining classical and intuitionistic logic. This volume.Google Scholar
  20. K. Fine and G. Schurz. Transfer theorems for stratified multimodal logics. To appear.Google Scholar
  21. M. Finger and D. M. Gabbay. Adding a temporal dimension to a logic. Journal of Logic, Language and Information, 1, 203–233, 1992.CrossRefzbMATHMathSciNetGoogle Scholar
  22. M. Finger and D. Gabbay. Combining temporal logic systems. To appear in Notre Dame Journal of Formal Logic.Google Scholar
  23. G. Fischer-Servi. On modal logic with an intuitionistic base. Studia Logica, 36, 1977.Google Scholar
  24. G. Fischer-Servi. Semantics for a class of intuitionistic modal calculi. In Italian Studies in the Philosophy of Science, M. L. Dalla Chiara, ed., pp. 59–71, D. Reidel, 1980.CrossRefGoogle Scholar
  25. Fischer-Servi. Axiomatizations for some intuitionistic modal logics. Rend. Sem. Mat. Univ. Politecn. Torino, 42, 179–194, 1984.zbMATHMathSciNetGoogle Scholar
  26. F. B. Fitch. Intuitionistic modal logic with quantifiers. Portugalia Mathematica, 7, 113–118, 1948.MathSciNetGoogle Scholar
  27. M. Fitting. Logics with several modal operators. Theoria, 35, 259–266, 1969.CrossRefzbMATHMathSciNetGoogle Scholar
  28. M. Fitting. Many valued modal logics. Fundamenta Informatica, 15, 235–254, 1991.zbMATHMathSciNetGoogle Scholar
  29. M. Fitting. Many valued modal logics II. Fundamenta Informatica, 17, 55–73, 1992.zbMATHMathSciNetGoogle Scholar
  30. M.Fitting.Tableaux for many valued modal logic. Report Jan 25, 1994Google Scholar
  31. J. M. Font. Modality and possibility in some intuitionistic modal logic. Notre Dame Journal of Formal Logic, 27, 533–546,1986CrossRefzbMATHMathSciNetGoogle Scholar
  32. D.M.Gabbay.Theoretical foundations for non-monotonic reasoning in expert systems. In Proceedings NATO Advanced Study Institute on Logics and Models of Concurrent Systems, (ed. K. R. Apt), pp.439–457.Springer-Verlag, Berlin, 1985CrossRefGoogle Scholar
  33. D. M. Gabbay. Fibred semantics and the weaving of logics, Part 1, Lectures given at Logic Colloquium 1992, Veszprem, Hungary, August 1992. A version of the notes is published as a Technical Report No 36, by the University of Stuttgart, Sonderforschungbereich 340, Azenbergstr 12, 70174 Stuttgart, Germany, 1993. Full version to appear in Journal of Symbolic Logic Google Scholar
  34. D. M. Gabbay. Labelled Deductive Systems, Part I. Oxford University Press, 1995. First draft 1989. Preprint, Department of Computing, Imperial College, London SW7 2BZ, UK. Current draft February 1991, 265 pp. Published as CIS - Bericht-90–92, Centrum für Informations und Srachverabeitunt, Universität München, Germany. Third intermediate draft, Max Planck Institute, Saarbrucken, Technical Report, MPI-94–223, 460 pp, 1994Google Scholar
  35. D. M. Gabbay. Fibred semantics and the weaving of logics, part 2. In Logic Colloquium 92, L. Czermak, D. Gabbay and M. de Rijke, editors, pp. 95–113. SILLI/CUP, 1995Google Scholar
  36. D. M. Gabbay. Fibred semantics and the weaving of logic, part 3. How to make your logic fuzzy, draft, Imperial College, 1995Google Scholar
  37. D. Gabbay. Fibred semantics and the weaving of logics, part 4: Self-fibring of predicate logic. Draft, Imperial College, 1995Google Scholar
  38. D. M. Gabbay. Classical vs non-classical logic, Handbook of Logic in AI, volume 2, Oxford d University Press, 1994Google Scholar
  39. D. M. Gabbay. Conditional implication and nonmonotonic consequence. In Views on Conditionals, ed. L.F. del Cerro et al., pp. 347–369, COUP, 1995.Google Scholar
  40. V. Goranko and S. Passy. Using the Universal Modality: Gains and Questions. Journal of Logic and Computation, 2, 5–30, 1992CrossRefzbMATHMathSciNetGoogle Scholar
  41. A. J. I. Jones. Towards a formal theory of defeasible deontic conditionals. To appear in Annals of Mathematics and Artificial Intelligence.Google Scholar
  42. A.J.I.Jones and I.Pörn. Ideality, subideality and deontic logic.Synthese,65, 1985Google Scholar
  43. A. J. I. Jones and I. Pörn. ‘Ought’ and ‘must’. Synthese 66 1986Google Scholar
  44. S. Kepser and K. Schulz. Combination of constraint systems II: Rational amalgamation. To appear in Proc. CP-96 Google Scholar
  45. M. Kracht and F. Wolter. Properties of independently axiomatizable bimodal logics. Journal of Symbolic Logic, 56 1469–1485, 1991.CrossRefzbMATHMathSciNetGoogle Scholar
  46. S. Kraus, D. Lehmann, and M. Magidor. Nonmonotonic reasoning, preferential models and cumulative logics, Artificial Intelligence, 44, 167–208, 1990CrossRefzbMATHMathSciNetGoogle Scholar
  47. K. Lambert and Bas C. van Fraassen. Derivation and Counterexample, Dickinson Publishing Co, 1972.Google Scholar
  48. R. E. Meyer and E. D. Mares. Semantics of Entailment 0. In K. Dosen and P. Schroeder-Heister, eds, Substructural Logics, pp. 239–258, Oxford University Press, 1993.Google Scholar
  49. H Ono. On some intuitionistic modal logic. Publications Research Institute of Mathematical Science, 13, 687–722, 1977.CrossRefzbMATHGoogle Scholar
  50. H. Ono. Some problems in intermediate predicate logics. Reports on Mathematical Logic, 21, 55–68, 1987.zbMATHGoogle Scholar
  51. J. Pfalzgraf. A note on simplexes as geometric configurations. Archiv der Mathematik, 49, 134–140,1987.CrossRefzbMATHMathSciNetGoogle Scholar
  52. J. Pfalzgraf. Logical fiberings and polycontextural systems. In Fundamentals of Artificial Intelligence Resarch, Ph. Jorrand and J. Kelemen, eds. LNCS 535, Springer-Verlag, 1991Google Scholar
  53. J. Pfalzgraf and K. Stokkermans. On robotics scenarios and modeling with fibered structures. In Springer series texts and Monographs in Symbolic Computation, Automated Practical Reasoning: Algebraic Approaches, ed. J. Pfalzgraf and D. Wang. Springer-Verlag, 1994Google Scholar
  54. A. K. Simpson. Proof theory and semantics of intuitionistic modal logic, Technical report CTS-114-94, Univ of Edinburgh, 1994.Google Scholar
  55. N. Y. Suzuki. An algebraic aporach to intuitionistic modal logics in connection with intermediate predicate logics. Studia Logica, 48, 141–155, 1988CrossRefGoogle Scholar
  56. N.Y.Suzuki. Kripke bundles for intermediate predicate logics and Kripke frames for intuitionistic modal logics. Studia Logica, 49, 289–306, 1990CrossRefzbMATHMathSciNetGoogle Scholar
  57. D.Wijesekera.Constructive modal logic 1, Annals of Pure and Applied Logic, 50, 271–301, 1990CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  1. 1.Department of ComputingImperial CollegeLondonGreat Britain

Personalised recommendations