MATHEMATICAL MODAL LOGIC: A VIEW OF ITS EVOLUTION
MATHEMATICAL MODAL LOGIC: A VIEW OF ITS EVOLUTION MATHEMATICAL MODAL LOGIC: A VIEW OF ITS EVOLUTION
88 Robert Goldblatt[Clarke and Emerson, 1981] Edmund M. Clarke and E. Allen Emerson. Design and synthesis ofsynchronisation skeletons using branching time temporal logic. In D. Kozen, editor, Logics ofPrograms, volume 131 of Lecture Notes in Computer Science, pages 52–71. Springer-Verlag,1981.[Cook, 1971] S. A. Cook. The complexity of theorem proving procedures. In Proceedings of theThird Annual ACM Symposium on the Theory of Computing, pages 151–158, 1971.[Copeland, 1996a] B. J. Copeland, editor. Logic and Reality: Essays on the Legacy of ArthurPrior. Oxford University Press, 1996.[Copeland, 1996b] B. J. Copeland. Prior’s life and legacy. In B. J. Copeland, editor, Logic andReality: Essays on the Legacy of Arthur Prior, pages 1–40. Oxford University Press, 1996.[Copeland, 2002] B. J. Copeland. The genesis of possible worlds semantics. Journal of PhilosophicalLogic, 31(2):99–137, 2002.[Cresswell, 1967] M. J. Cresswell. A Henkin completeness theorem for T. Notre Dame Journalof Formal Logic, 8:186–190, 1967.[Cresswell, 1972] M. J. Cresswell. The completeness of S1 and some related systems. NotreDame Journal of Formal Logic, 13:485–496, 1972.[Cresswell, 1973] M. J. Cresswell. Logics and Languages. Methuen, 1973.[Cresswell, 1984] M. J. Cresswell. An incomplete decidable modal logic. The Journal of SymbolicLogic, 49:520–527, 1984.[Cresswell, 1995] M. J. Cresswell. S1 is not so simple. In Walter Sinnott-Armstrong, DianaRaffman, and Nicholas Asher, editors, Modality, Morality and Belief. Essays in Honor ofRuth Barcan Marcus, pages 29–40. Cambridge University Press, 1995.[Curry, 1950] Haskell B. Curry. A Theory of Formal Deducibility. Notre Dame MathematicalLectures, no. 6. University of Notre Dame, 1950.[Curry, 1952] Haskell B. Curry. The elimination theorem when modality is present. The Journalof Symbolic Logic, 17:249–265, 1952.[Dam, 1994] Mads Dam. CTL* and ECTL* as fragments of the modal µ-calculus. TheoreticalComputer Science, 126:77–96, 1994.[Davis, 1954] Chandler Davis. Modal operators, equivalence relations, and projective algebras.American Journal of Mathematics, 76:747–762, 1954.[de Jongh and Troelstra, 1966] D. H. J. de Jongh and A. S. Troelstra. On the connection of partiallyordered sets with some pseudo-Boolean algebras. Indagationes Mathematicae, 28:317–329, 1966.[de Jongh and van Ulsen, 1998–1999] Dick de Jongh and Paul van Ulsen. Beth’s nonclassicalvaluations. Philosophia Scientiae, 3(4):279–302, 1998–1999.[de Rijke and Venema, 1995] Maarten de Rijke and Yde Venema. Sahlqvist’s theorem forBoolean algebras with operators with an application to cylindric algebras. Studia Logica,54:61–78, 1995.[Došen, 1989] Kosta Došen. Duality between modal algebras and neighbourhood frames. StudiaLogica, 48:219–234, 1989.[Dugundji, 1940] James Dugundji. Note on a property of matrices for Lewis and Langford’scalculi of propositions. The Journal of Symbolic Logic, 5:150–151, 1940.[Dummett and Lemmon, 1959] M. A. E. Dummett and E. J. Lemmon. Modal logics betweenS4 and S5. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 5:250–264,1959.[Emerson and Clarke, 1980] E. Allen Emerson and Edmund M. Clarke. Characterizing correctnessproperties of parallel programs using fixpoints. In J. W. de Bakker and J. van Leeuwen,editors, Automata, Languages and Programming. Proceedings 1980, volume 85 of LectureNotes in Computer Science, pages 169–181. Springer-Verlag, 1980.[Emerson and Halpern, 1982] E. Allen Emerson and Joseph Y. Halpern. Decision proceduresand expressiveness in the temporal logic of branching time. In Annual ACM Symposium onTheory of Computing (STOC), pages 169–180, 1982.[Emerson and Halpern, 1983] E. Allen Emerson and Joseph Y. Halpern. “Sometimes” and “notnever” revisited: On branching versus linear time. In Proceedings of the Annual ACM Symposiumon Principles of Programming Languages, pages 127–140, 1983.[Emerson and Halpern, 1985] E. Allen Emerson and Joseph Y. Halpern. Decision proceduresand expressiveness in the temporal logic of branching time. Journal of Computer and SystemsSciences, 30:1–24, 1985.
Mathematical Modal Logic: A View of its Evolution 89[Emerson and Halpern, 1986] E. Allen Emerson and Joseph Y. Halpern. “Sometimes” and “notnever” revisited: On branching versus linear time temporal logic. Journal of the Associationfor Computing Machinery, 33:151–178, 1986.[Emerson and Jutla, 1988] E. Allen Emerson and Charanjit S. Jutla. The complexity of treeautomata and logics of programs. In Proceedings of the 29th Annual IEEE Symposium onFoundations of Computer Science, pages 328–337, 1988.[Emerson and Jutla, 1999] E. Allen Emerson and Charanjit S. Jutla. The complexity of treeautomata and logics of programs. SIAM Journal on Computing, 29:132–158, 1999.[Emerson, 1990] E. Allen Emerson. Temporal and modal logic. In Jan van Leeuwen, editor,Handbook of Theoretical Computer Science, Volume B: Formal Models and Semantics, pages995–1072. Elsevier, 1990.[Erdős, 1959] Paul Erdős. Graph theory and probability. Canadian Journal of Mathematics,11:34–38, 1959.[Èsakia, 1974] L. L. Èsakia. Topological Kripke models. Soviet Mathematics Doklady, 15:147–151, 1974.[Everett and Ulam, 1946] C. J. Everett and S. Ulam. Projective algebras I. American Journalof Mathematics, 68:77–88, 1946.[Fagin et al., 1995] Ronald Fagin, Joseph Y. Halpern, Yoram Moses, and Moshe Y. Vardi. ReasoningAbout Knowledge. The MIT Press, 1995.[Fairtlough and Mendler, 1995] Matt Fairtlough and Michael Mendler. An intuitionistic modallogic with applications to the formal verification of hardware. In Leszek Pacholoski and JerzyTiuryn, editors, Computer Science Logic. Proceedings 1994, volume 933 of Lecture Notes inComputer Science, pages 354–368. Springer-Verlag, 1995.[Fairtlough and Mendler, 1997] Matt Fairtlough and Michael Mendler. Propositional lax logic.Information and Computation, 137:1–33, 1997.[Feys, 1965] Robert Feys. Modal Logics. E. Nauwelaerts, 1965.[Fine, 1971] Kit Fine. The logics containing S4.3. Zeitschrift für Mathematische Logik undGrundlagen der Mathematik, 17:371–376, 1971.[Fine, 1974] Kit Fine. An incomplete logic containing S4. Theoria, 40:23–29, 1974.[Fine, 1975a] Kit Fine. Normal forms in modal logic. Notre Dame Journal of Formal Logic,16:229–234, 1975.[Fine, 1975b] Kit Fine. Some connections between elementary and modal logic. In Stig Kanger,editor, Proceedings of the Third Scandinavian Logic Symposium, pages 15–31. North-Holland,Amsterdam, 1975.[Fischer and Ladner, 1977] Michael J. Fischer and Richard E. Ladner. Propositional modallogic of programs. In Proceedings of the Ninth Annual ACM Symposium on The Theory ofComputing, pages 286–294, 1977.[Fischer and Ladner, 1979] Michael J. Fischer and Richard E. Ladner. Propositional dynamiclogic of regular programs. Journal of Computer and Systems Sciences, 18:194–211, 1979.[Fitch, 1948] F. B. Fitch. Intuitionistic modal logic with quantifiers. Portugaliae Mathematicae,7:113–118, 1948.[Føllesdal, 1994] Dagfinn Føllesdal. Stig Kanger in memoriam. In Dag Prawitz, Brian Skyrms,and Dag Westerståhl, editors, Logic, Methodology and Philosophy of Science IX, pages 885–888. North-Holland, Amsterdam, 1994.[Gabbay et al., 1980] D. M. Gabbay, A. Pneuli, S. Selah, and J. Stavi. On the temporal analysisof fairness. In Proceedings of the 7th Annual ACM Symposium on Principles of ProgrammingLanguages, pages 163–173, 1980.[Gabbay et al., 1994] Dov M. Gabbay, Ian Hodkinson, and Mark Reynolds. Temporal Logic.Mathematical Foundations and Computational Aspects, volume 1. Oxford University Press,1994.[Gabbay, 1972] Dov M. Gabbay. On decidable, finitely axiomatizable, modal and tense logicswithout the finite model property, part I. Israel Journal of Mathematics, 11:478–495, 1972.[Gabbay, 1976] Dov M. Gabbay. Investigations in Modal and Tense Logics with Applicationsto Problems in Philosophy and Linguistics. D. Reidel, 1976.[Gerson, 1975a] Martin Gerson. An extension of S4 complete for the neighborhood semanticsbut incomplete for the relational semantics. Studia Logica, 34:333–342, 1975.[Gerson, 1975b] Martin Gerson. The inadequacy of the neighborhood semantics for modal logic.The Journal of Symbolic Logic, 40:141–148, 1975.
- Page 38 and 39: 38 Robert Goldblattnormal (“queer
- Page 40 and 41: 40 Robert Goldblattinterpreting for
- Page 42 and 43: 42 Robert GoldblattDiodorean interp
- Page 44 and 45: 44 Robert Goldblattthat the formula
- Page 46 and 47: 46 Robert Goldblatt6.1 Incompletene
- Page 48 and 49: 48 Robert Goldblatttions: every nor
- Page 50 and 51: 50 Robert Goldblatttrue at some poi
- Page 52 and 53: 52 Robert Goldblattof the monadic s
- Page 54 and 55: 54 Robert Goldblattversion [van Ben
- Page 56 and 57: 56 Robert Goldblatt6.5 Duality and
- Page 58 and 59: 58 Robert Goldblattfrom a suitably
- Page 60 and 61: 60 Robert GoldblattAnother way to d
- Page 62 and 63: 62 Robert Goldblattwhether a variet
- Page 64 and 65: 64 Robert Goldblattatomic commands
- Page 66 and 67: 66 Robert Goldblattmodalities 〈 i
- Page 68 and 69: 68 Robert Goldblatt[Hennessy and Li
- Page 70 and 71: 70 Robert GoldblattThe logic CTL* w
- Page 72 and 73: 72 Robert GoldblattThe meaning of
- Page 74 and 75: 74 Robert Goldblattwhich shows that
- Page 76 and 77: 76 Robert Goldblattmodal formulas s
- Page 78 and 79: 78 Robert GoldblattGrothendieck gen
- Page 80 and 81: 80 Robert GoldblattNow if Y and Z a
- Page 82 and 83: 82 Robert Goldblatt7.7 Modal Logic
- Page 84 and 85: 84 Robert GoldblattThis abstracts t
- Page 86 and 87: 86 Robert Goldblattextensions [Gold
- Page 90 and 91: 90 Robert Goldblatt[Gerson, 1976] M
- Page 92 and 93: 92 Robert Goldblatt[Hoare, 1969] C.
- Page 94 and 95: 94 Robert Goldblatt[̷Lukasiewicz a
- Page 96 and 97: 96 Robert Goldblatt[Prior, 1967] Ar
- Page 98: 98 Robert Goldblatt[Tarski, 1956] A
Mathematical Modal Logic: A View of its Evolution 89[Emerson and Halpern, 1986] E. Allen Emerson and Joseph Y. Halpern. “Sometimes” and “notnever” revisited: On branching versus linear time temporal logic. Journal of the Associationfor Computing Machinery, 33:151–178, 1986.[Emerson and Jutla, 1988] E. Allen Emerson and Charanjit S. Jutla. The complexity of treeautomata and logics of programs. In Proceedings of the 29th Annual IEEE Symposium onFoundations of Computer Science, pages 328–337, 1988.[Emerson and Jutla, 1999] E. Allen Emerson and Charanjit S. Jutla. The complexity of treeautomata and logics of programs. SIAM Journal on Computing, 29:132–158, 1999.[Emerson, 1990] E. Allen Emerson. Temporal and modal logic. In Jan van Leeuwen, editor,Handbook of Theoretical Computer Science, Volume B: Formal Models and Semantics, pages995–1072. Elsevier, 1990.[Erdős, 1959] Paul Erdős. Graph theory and probability. Canadian Journal of Mathematics,11:34–38, 1959.[Èsakia, 1974] L. L. Èsakia. Topological Kripke models. Soviet Mathematics Doklady, 15:147–151, 1974.[Everett and Ulam, 1946] C. J. Everett and S. Ulam. Projective algebras I. American Journalof Mathematics, 68:77–88, 1946.[Fagin et al., 1995] Ronald Fagin, Joseph Y. Halpern, Yoram Moses, and Moshe Y. Vardi. ReasoningAbout Knowledge. The MIT Press, 1995.[Fairtlough and Mendler, 1995] Matt Fairtlough and Michael Mendler. An intuitionistic modallogic with applications to the formal verification of hardware. In Leszek Pacholoski and JerzyTiuryn, editors, Computer Science Logic. Proceedings 1994, volume 933 of Lecture Notes inComputer Science, pages 354–368. Springer-Verlag, 1995.[Fairtlough and Mendler, 1997] Matt Fairtlough and Michael Mendler. Propositional lax logic.Information and Computation, 137:1–33, 1997.[Feys, 1965] Robert Feys. Modal Logics. E. Nauwelaerts, 1965.[Fine, 1971] Kit Fine. The logics containing S4.3. Zeitschrift für Mathematische Logik undGrundlagen der Mathematik, 17:371–376, 1971.[Fine, 1974] Kit Fine. An incomplete logic containing S4. Theoria, 40:23–29, 1974.[Fine, 1975a] Kit Fine. Normal forms in modal logic. Notre Dame Journal of Formal Logic,16:229–234, 1975.[Fine, 1975b] Kit Fine. Some connections between elementary and modal logic. In Stig Kanger,editor, Proceedings of the Third Scandinavian Logic Symposium, pages 15–31. North-Holland,Amsterdam, 1975.[Fischer and Ladner, 1977] Michael J. Fischer and Richard E. Ladner. Propositional modallogic of programs. In Proceedings of the Ninth Annual ACM Symposium on The Theory ofComputing, pages 286–294, 1977.[Fischer and Ladner, 1979] Michael J. Fischer and Richard E. Ladner. Propositional dynamiclogic of regular programs. Journal of Computer and Systems Sciences, 18:194–211, 1979.[Fitch, 1948] F. B. Fitch. Intuitionistic modal logic with quantifiers. Portugaliae Mathematicae,7:113–118, 1948.[Føllesdal, 1994] Dagfinn Føllesdal. Stig Kanger in memoriam. In Dag Prawitz, Brian Skyrms,and Dag Westerståhl, editors, Logic, Methodology and Philosophy of Science IX, pages 885–888. North-Holland, Amsterdam, 1994.[Gabbay et al., 1980] D. M. Gabbay, A. Pneuli, S. Selah, and J. Stavi. On the temporal analysisof fairness. In Proceedings of the 7th Annual ACM Symposium on Principles of ProgrammingLanguages, pages 163–173, 1980.[Gabbay et al., 1994] Dov M. Gabbay, Ian Hodkinson, and Mark Reynolds. Temporal Logic.Mathematical Foundations and Computational Aspects, volume 1. Oxford University Press,1994.[Gabbay, 1972] Dov M. Gabbay. On decidable, finitely axiomatizable, modal and tense logicswithout the finite model property, part I. Israel Journal of Mathematics, 11:478–495, 1972.[Gabbay, 1976] Dov M. Gabbay. Investigations in Modal and Tense Logics with Applicationsto Problems in Philosophy and Linguistics. D. Reidel, 1976.[Gerson, 1975a] Martin Gerson. An extension of S4 complete for the neighborhood semanticsbut incomplete for the relational semantics. Studia Logica, 34:333–342, 1975.[Gerson, 1975b] Martin Gerson. The inadequacy of the neighborhood semantics for modal logic.The Journal of Symbolic Logic, 40:141–148, 1975.
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