5 Model theory of modal logic

Studies in Logic and Practical Reasoning

Volumn 3, Issue , 2007, Pages 249-329

  Goranko, Valentin ^a   Otto, Martin ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 40849118428     PISSN: 15702464     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1570-2464(07)80008-5     Document Type: Article

References (139)

1. Andreka H., van Benthem J., and Nemeti I. Modal languages and bounded fragments of predicate logic. Journal of Philosophical Logic 27 (1998) 217-274
2. Arnold A., and Niwinski D. Rudiments of μ-Calculus (2001), North-Holland
3. Beeri C., Fagin R., Maier D., and Yannakakis M. On the desirability of acyclic database schemes. Journal of the ACM 30 (1983) 479-513
4. Berge C. Graphs and Hypergraphs (1973), North-Holland
5. Blackburn P., de Rijke M., and Venema Y. Modal Logic (2001), Cambridge Univ. Press
6. Boolos G., and Sambin G. An incomplete system of modal logic. Journal of Philosophical Logic 14 (1985) 351-358
7. R. Bull and K. Segerberg. Basic modal logic. In Gabbay and Guenthner [33], pages 1-88.
8. Carnap R. Logical Foundations of Probability (1950), Univ. of Chicago Press, Chicago
9. Chagrov A., Wolter F., and Zakharyaschev M. Advanced modal logic. Handbook of Philosophical Logic. second edition vol 3 (2001), Kluwer Academic Publishers 83-266
10. Chagrov A., and Zakharyaschev M. Modal Logic (1997), Oxford University Press, Oxford
11. Chagrova L. An undecidable problem in correspondence theory. Journal of Symbolic Logic 56 (1991) 1261-1272
12. Chang C., and Keisler H. Model Theory (1973), North-Holland, Amsterdam
13. Conradie W. Definability and changing perspectives. The Beth property for three extensions of modal logic. Technical Report MoL-2002-03 (2002), ILLC Publications, Master of Logic Series
14. Conradie W., Goranko V., and Vakarelov D. Elementary canonical formulae: a survey on syntactic, algorithmic, and model-theoretic aspects. In: Reynolds M., et al. (Ed). Advances in Modal Logic volume 5 (2005), Kings College Publ., London 17-51
15. ILLC Dissertation Series DS-1998-04. D'Agostino G. Modal Logic and Non-Well-Founded Set Theory: Translation, Bisimulation, Inter- polation. PhD thesis (1998), University of Amsterdam
16. D'Agostino G., and Hollenberg M. Logical questions concerning the μ-calculus: interpolation, Lyndon and oś-Tarski. Journal of Symbolic Logic 65 (2000) 310-332
17. Dawar A., and Otto M. Modal characterisation theorems over special classes of frames. Proc. of LICS'2005 (2005), IEEE Press 21-30
18. de Rijke M. Extending Modal Logic. PhD thesis (1993), ILLC, University of Amsterdam
19. M. de Rijke. A Lindström theorem for modal logic. In Ponse et al. [109], pages 217-230.
20. de Rijke M. Modal model theory. Technical Report CS-R9517 (1995), CWI, Amsterdam
21. de Rijke M. A note on graded modal logic. Studia Logica 64 2 (2000) 271-283
22. de Rijke M., and Sturm H. Global definability in basic modal logic. In: Wansing H. (Ed). Essays on Non-Classical Logic (2001), World Scientific Publishers 111-135
23. Doets K. Basic Model Theory (1996), CSLI Publications, Stanford, California
24. Doets K., and van Benthem J. Higher-order logic. In: Gabbay D., and Guenthner F. (Eds). Handbook of Philosophical Logic vol. 1 (1983), Reidel, Dordrecht 275-329
25. Ebbinghaus H.-D., and Flum J. Finite Model Theory. Perspectives in Mathematical Logic (1995), Springer, Berlin
26. Ebbinghaus H.-D., Flum J., and Thomas W. Mathematical Logic (1984), Springer, Berlin
27. Fagin R. Probabilities on finite models. Journal of Symbolic Logic 41 (1976) 50-58
28. K. Fine. Some connections between elementary and modal logic. In Kanger [81], pages 15-31.
29. Fischer M., and Ladner R. Propsitional dynamic logic of regular programs. Journal of Computer and System Sciences 18 (1979) 194-211
30. December. Flum J. On the (infinite) model theory of fixed-point logics. Preprint, Inst, für Math. Logik und Grundl. der Math (1995), Albert-Ludwigs-Universität Freiburg
31. Gabbay D. Selective filtration in modal logic. Theoria 30 (1970) 323-330
32. Gabbay D. Investigations in Modal and Tense Logics with Applications to Problems in Philosophy and Linguistics (1976), Reidel, Dordrecht
33. In: Gabbay D., and Guenthner F. (Eds). Handbook of Philosophical Logic vol. 2 (1984), Reidel, Dordrecht
34. Gabbay D., Hodkinson I., and Reynolds M. Temporal Logic: Mathematical Foundations and Com- putational Aspects (1994), Oxford University Press
35. Gabbay D., Kurucz A., Wolter F., and Zakharyaschev M. Many-dimensional modal logics: theory and applications. Studies in Logic 148 (2003), Elsevier Science
36. Gabbay D., and Maksimova L. Interpolation and Definability. Modal and Intuitionistic Logic. Oxford Logic Guides 46 (2005), Oxford Univ. Press
37. Gaifman H. Concerning measures in first-order calculi. Israel J. of Math. 2 (1964) 1-18
38. Gaifman H. On local and nonlocal properties. In: Stern J. (Ed). Logic Colloquium '81 (1982), North Holland 105-135
39. Ghilardi S., and Zawadowski M. Sheaves, Games, and Model Completions. Trends in Logic (2002), Kluwer 14
40. Glebskii Y., Kogan D., Liogonki M., and Talanov V. Range and degree of realizability of formulas in the restricted predicate calculus. Cybernetics 5 (1969) 142-154
41. Goguadze G., Piazza C., and Venema Y. Simulating polyadic modal logics by monadic ones. Journal of Symbolic Logic 68 (2003) 419-462
42. Goldblatt R. First-order definability in modal logic. Journal of Symbolic Logic 40 (1975) 35-40
43. Goldblatt R. Metamathematics of modal logic I. Reports on Mathematical Logic 6 (1976) 41-78
44. Goldblatt R. Metamathematics of modal logic II. Reports on Mathematical Logic 7 (1976) 21-52
45. Goldblatt R. Varieties of complex algebras. Annals of Pure and Applied Logic 38 (1989) 173-241
46. Goldblatt R. Logics of Time and Computation. Number 7 in CSLI Lecture Notes. 2nd edition (1992), CSLI, Stanford
47. Goldblatt R. Mathematics of Modality, volume 43 of CSLI Lecture Notes. Center for the Study of Language and Information (1993), Stanford University
48. R. Goldblatt. Saturation and the Hennessy-Milner property. In Ponse et al. [109], pages 107-129.
49. Goldblatt R. Mathematical modal logic: A view of its evolution. Journal of Applied Logic 1 (2003) 309-392
50. Goldblatt R., Hodkinson I., and Venema Y. Erdös graphs resolve Fine's canonicity problem. Bulletin of Symbolic Logic 10 (2004) 186-208
51. Goldblatt R., and Thomason S. Axiomatic classes in propositional modal logic. In: Crossley J. (Ed). Algebra and Logic (1974), Springer 163-173
52. Goranko V. Axiomatizations with context rules of inference in modal logic. Studia Logica 61 (1998) 179-197
53. Goranko V., and Kapron B. The modal logic of the countable random frame. Archive for Mathematical Logic 42 (2003) 221-243
54. Goranko V., and Passy S. Using the universal modality: Gains and questions. Journal of Logic and Computation 2 (1992) 5-30
55. Goranko V., and Vakarelov D. Elementary canonical formulae.Extending Sahlqvist's theorem. Annals of Pure and Applied Logic 141 (2005) 180-217
56. Grädel E. On the restraining power of guards. Journal of Symbolic Logic 64 (1999) 1719-1742
57. Grädel E. Why are modal logics so robustly decidable?. Bulletin of the EATCS 68 (1999) 90-103
58. Grädel E., Hirsch C., and Otto M. Back and forth between guarded and modal logics. ACM Transactions on Computational Logics 3 3 (2002) 418-463
59. Grädel E., Kolaitis P., and Vardi M. On the Decision Problem for Two-Variable First-Order Logic. Bulletin of Symbolic Logic 3 (1997) 53-69
60. Grädel E., and Otto M. On Logics with Two Variables. Theoretical Computer Science 224 (1999) 73-113
61. Grädel E., Otto M., and Rosen E. Undecidability Results on Two-Variable Logics. Archive for Mathematical Logic 38 (1999) 213-354
62. Grädel E., and Walukiewicz I. Guarded Fixed Point Logic. Proceedings of 14th IEEE Symposium on Logic in Computer Science LICS '99, Trento (1999) 45-54
63. Grandjean E. Complexity of the first-order theory of almost all structures. Information and Com-putation 52 (1983) 180-204
64. Gurevich Y. Zero-one laws: The logic in computer science column. Bulletin of the European Asso-ciation for Theoretical Computer Science 46 (1992) 90-106
65. Hafer T., and Thomas W. Computation tree logic CTL* and path quantifiers in the monadic theory of the binary tree. Proceedings of ICALP 1987 (1987) 269-279
66. Halpern J., and Kapron B. Zero-one laws for modal logic. Annals of Pure and Applied Logic 69 (1994) 157-193
67. Herwig B., and Lascar D. Extending partial isomorphisms and the profinite topology on free groups. Transactions of the AMS 352 (2000) 1985-2021
68. Hodges W. Model Theory (1993), Cambridge University Press, Cambridge
69. Hodkinson I. Loosely guarded fragment of first-order logic has the finite model property. Studia Logica 70 (2002) 205-240
70. Hodkinson I., and Otto M. Finite conformai hypergraph covers and Gaifman cliques in finite struc-tures. The Bulletin of Symbolic Logic 9 (2003) 387-405
71. M. Hollenberg. Hennessy-Milner classes and process algebra. In Ponse et al. [109], pages 187-216.
72. Hollenberg M. Safety for bisimulation in general modal logic. Proceedings 10th Amsterdam Colloquium (1996) 359-376
73. ILLC Dissertation Series DS-2001-05. Hoogland E. Definability and Interpolation: Model-theoretic investigations. PhD thesis (2001), University of Amsterdam
74. Hughes G. Every world can see a reflexive world. Studia Logica 49 (1990) 175-181
75. Hughes G., and Cresswell M. A New Introduction to Modal Logic (1996), Routledge, London
76. Immerman N. Languages that capture complexity classes. SIAM Journal of Computing 16 (1987) 760-778
77. Janin D., and Walukiewicz I. On the expressive completeness of the propositional μ-calculus w.r.t. monadic second-order logic. Proceedings CONCUR '96 (1996) 263-277
78. Jónsson B., and Tarski A. Boolean algebras with operators, Part I. American Journal of Mathematics 73 (1952) 891-939
79. Jónsson J., and Tarski A. Boolean algebras with operators, Part II. American Journal of Mathemat-ics 74 (1952) 127-162
80. Kamp H. Tense Logic and the Theory of Linear Order. PhD thesis (1968), University of California, Los Angeles
81. In: Kanger S. (Ed). Proceedings of the Third Scandinavian Logic Symposium. Uppsala 1973 (1975), North-Holland, Amster- dam
82. Karp C. Languages with Expressions of Infinite Length (1964), North-Holland, Amsterdam
83. Keisler H. Model Theory for Infinitary Logic (1971), North-Holland, Amsterdam
84. Kracht M. Tools and Techniques in Modal Logic, volume 142 of Studies in Logic (1999), Elsevier, Amster- dam
85. Kracht M., and Wolter F. Simulation and transfer results in modal logic: a survey. Studia Logica 59 (1997) 149-177
86. Kripke S. A completeness theorem in modal logic. Journal of Symbolic Logic 24 (1959) 1-14
87. Kripke S. Semantical analysis of modal logic I.Normal modal propositional calculi. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 9 (1963) 67-96
88. Kurtonina N., and de Rijke M. Expressiveness of concept expressions in first-order description logics. Artificial Intelligence 107 2 (1999) 303-333
89. Lachlan A. A note on Thomason's refined structures for tense logics. Theoria 40 (1970) 117-120
90. Le Bars J.-M. Zero-one law fails for frame satisfiability in propositional modal logic. Proceedings of LICS'2002 (2002), IEEE Computer Society Press 225-234
91. Lemmon E., and Scott D. An Introduction to Modal Logic (1977), Blackwell, Oxford
92. Lewis D. Intensional logics without iterative axioms. Journal of Philisophical Logic 3 (1974) 457-466
93. Libkin L. Elements of Finite Model Theory (2004), Springer
94. Lisitsa A., and Sazonov V. Linear ordering on graphs, anti-founded sets and polynomial time com-putability. Theoretical Computer Science 224 (1999) 173-213
95. Lopez-Escobar E. On defining well-orderings. Fundamenta Mathematicae 59 (1966) 299-300
96. Lutz C., Sattler U., and Wolter F. Modal logic and the two-variable fragment. Proceedings of 15th International Workshop on Computer Science Logic, volume 2142 of LNCS (2001) 247-261
97. Makinson D. A generalization of the concept of relational model. Theoria (1970) 331-335
98. Maksimova L. Definability and interpolation in classical modal logics. Contemporary Mathematics 131 3 (1992) 583-599
99. May. Marx M. Complexity of modal logics of relations. Technical Report ML-97-02 (1997), Institute for Logic, Language and Computation, University of Amsterdam
100. Marx M. Xpath and modal logics of finite DAG's. Automated Reasoning with Analytic Tableaux and Related Methods, LNCS 2796 (2003) 150-164
101. Möller F., and Rabinovich A. On the expressive power of CTL*. Proceedings of the 14th IEEE Symposium on Logic in Computer Science (1999) 360-369
102. Mortimer M. On languages with two variables. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 21 (1975) 135-140
103. Nonnengart A., and Szalas A. A fixpoint approach to second-order quantifier elimination with ap- plications to correspondence theory. In: Orlowska E. (Ed). Logic at Work, Essays dedicated to the memory of Helena Rasiowa (1998) 89-108
104. Otto M. Bisimulation-invariant Ptime and higher-dimensional mu-calculus. Theoretical Computer Science 224 (1999) 237-265
105. Otto M. Elementary proof of the van Benthem-Rosen characterisation theorem. Technical Report 2342 (2004), Fachbereich Mathematik, Technische Universität Darmstadt, Springer Physica-Verlag
106. Otto M. Modal and guarded characterisation theorems over finite transition systems. Annals of Pure and Applied Logic 130 (2004) 173-205
107. to appear. Otto M. Bisimulation invariance and finite models. Logic Colloquium 02. Lecture Notes in Logic (2005)
108. Poizat B. A Course in Model Theory (2000), Universitext. Springer
109. In: Ponse A., de Rijke M., and Venema Y. (Eds). Modal Logic and Process Algebra. A Bisimulation Perspective., volume 53 of CSLI Lecture Notes (1995), Stanford University
110. Radev S. Infinitary propositional normal modal logic. Studia Logica 46 (1987) 291-309
111. Reynolds M. An axiomatization of full computation tree logic. Journal of Symbolic Logic 66 (2001) 1011-1057
112. Rosen E. Modal logic over finite structures. Journal of Logic, Language and Information 6 (1997) 427-439
113. H. Sahlqvist. Completeness and correspondence in the first and second order semantics for modal logic. In Kanger [81], pages 110-143.
114. Sambin G., and Vaccaro V. Topology and duality in modal logic. Annals of Pure and Applied Logic 37 (1988) 249-296
115. Sambin G., and Vaccaro V. A topological proof of Sahlqvist's theorem. Journal of Symbolic Logic 54 (1989) 992-999
116. Scott D. A decision method for validity of sentences in two variables. Journal of Symbolic Logic 27 (1962) 477
117. Segerberg K. An Essay in Classical Modal Logic (1971), Filosofiska Studier 13. University of Uppsala
118. Streett R., and Emerson E. An automata theoretic decision procedure for the propositional mu-calculus. Information and Computation 81 (1989) 249-264
119. W1W. PhD thesis (1997), CIS, University of Munich
120. W1. Notre Dame Journal of Formal Logic 39 (1998) 190-211
121. to appear. ten Cate B. Expressivity of second-order propositional modal logic. Journal of Philosophical Logic (2005)
122. ILLC Dissertation Series DS-2005-01. ten Cate B. Model theory for extended modal languages. PhD thesis (2005), University of Amsterdam
123. Thomason S. An incompleteness theorem in modal logic. Theoria 40 (1974) 150-158
124. Thomason S. Reduction of second-order logic to modal logic. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 21 (1975) 107-114
125. van Benthem J. Modal Correspondence Theory. PhD thesis (1976), Mathematisch Instituut & Instituut voor Grondslagenonderzoek, University of Amsterdam
126. van Benthem J. Canonical modal logics and ultrafilter extensions. Journal of Symbolic Logic 44 (1980) 1-8
127. van Benthem J. Modal Logic and Classical Logic (1983), Bibliopolis, Naples
128. J. van Benthem. Correspondence theory. In Gabbay and Guenthner [33], pages 167-247.
129. van Benthem J. Notes on modal definability. Notre Dame Journal of Formal Logic 39 (1989) 20-39
130. van Benthem J. Exploring Logical Dynamics. Studies in Logic, Language and Information (1996), CSLI Publications, Stanford
131. van Benthem J. Modality, bisimulation and interpolation in infinitary logic. Technical Report ML- 97-06 (1997), Institute for Logic, Language and Computation, University of Amsterdam
132. van Benthem J. Minimal predicates, fixed points, and definability. Journal of Symbolic Logic 70 (2005) 696-712
133. van Benthem J. A new Lindström theorem for modal logic. ILLC Publication Series Report PP- 2006-06 (2006)
134. Vardi M. The complexity of relational query languages. Proceedings of 14th ACM Symposium on Theory of Computing (1982) 137-146
135. Vardi M. Why is modal logic so robustly decidable?. In: Immerman N., and Kolaitis P. (Eds). Descriptive Complexity and Finite Models, volume 31 of DIMACS Series in Discrete Mathematics (1997), AMS 149-184
136. Vardi M. Reasoning about the past with two-way automata. Proceedings of 25th Symposium on Automata, Language and Programming, volume 1443 of LNCS (1998) 628-641
137. Venema Y. Derivation rules as anti-axioms in modal logic. Journal of Symbolic Logic 58 (1993) 1003-1034
138. Venema Y. Modal definability, purely modal. In: Gerbrandy J., et al. (Ed). Essays Dedicated to Johan van Benthem on the Occasion of his 50th Birthday (1999)
139. Visser A. Bisimulations, model descriptions and propositional quantifiers. Technical Report 161 (1996), Department of Philosophy, Utrecht University