MATHEMATICAL MODAL LOGIC: A VIEW OF ITS EVOLUTION
MATHEMATICAL MODAL LOGIC: A VIEW OF ITS EVOLUTION MATHEMATICAL MODAL LOGIC: A VIEW OF ITS EVOLUTION
90 Robert Goldblatt[Gerson, 1976] Martin Gerson. A neighborhood frame for T with no equivalent relational frame.Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 22:29–34, 1976.[Givant and Venema, 1999] S. Givant and Y. Venema. The preservation of Sahlqvist equationsin completions of Boolean algebras with operators. Algebra Universalis, 41:47–84, 1999.[Gödel, 1931] Kurt Gödel. Review of Becker 1930. Monatshefte für Mathematik und Physik(Literaturberichte), 38:5, 1931. English translation in Solomon Feferman et al., editors, KurtGödel, Collected Works, Volume 1, p. 217. Oxford University Press, 1986.[Gödel, 1933] Kurt Gödel. Eine interpretation des intuitionistischen aussagenkalküls. Ergebnisseeines mathematischen Kolloquiums, 4:39–40, 1933. English translation, with an introductorynote by A. S. Troelstra, in Solomon Feferman et al.,editor, Kurt Gödel, Collected Works,Volume 1, pages 296–303. Oxford University Press, 1986.[Goldblatt and Thomason, 1975] R. I. Goldblatt and S. K. Thomason. Axiomatic classes inpropositional modal logic. In J. N. Crossley, editor, Algebra and Logic, volume 450 of LectureNotes in Mathematics, pages 163–173. Springer-Verlag, 1975.[Goldblatt, et al., 2003] Robert Goldblatt, Ian Hodkinson, and Yde Venema. On canonicalmodal logics that are not elementarily determined. Logique et Analyse, 181:???–???, 2003.[Goldblatt et al., 2004] Robert Goldblatt, Ian Hodkinson, and Yde Venema. Erdős graphs resolveFine’s canonicity problem. The Bulletin of Symbolic Logic, 10(2):186–208, 2004.[Goldblatt, 1974] Robert Goldblatt. Metamathematics of Modal Logic. PhD thesis, VictoriaUniversity, Wellington, February 1974. Included in [Goldblatt, 1993].[Goldblatt, 1975a] Robert Goldblatt. First-order definability in modal logic. The Journal ofSymbolic Logic, 40(1):35–40, 1975.[Goldblatt, 1975b] Robert Goldblatt. Solution to a completeness problem of Lemmon and Scott.Notre Dame Journal of Formal Logic, 16:405–408, 1975.[Goldblatt, 1978] Rob Goldblatt. Arithmetical necessity, provability, and intuitionistic logic.Theoria, 44:38–46, 1978. Reprinted in [Goldblatt, 1993].[Goldblatt, 1980] Robert Goldblatt. Diodorean modality in Minkowski spacetime. Studia Logica,39:219–236, 1980. Reprinted in [Goldblatt, 1993].[Goldblatt, 1981] Robert Goldblatt. Grothendieck topology as geometric modality. Zeitschriftfür Mathematische Logik und Grundlagen der Mathematik, 27:495–529, 1981. Reprinted in[Goldblatt, 1993].[Goldblatt, 1986] Robert Goldblatt. Review of initial papers on dynamic logic by Pratt, Fischerand Ladner, Segerberg, Parikh and Kozen. The Journal of Symbolic Logic, 51:225–227, 1986.[Goldblatt, 1989] Robert Goldblatt. Varieties of complex algebras. Annals of Pure and AppliedLogic, 44:173–242, 1989.[Goldblatt, 1991a] Robert Goldblatt. The McKinsey axiom is not canonical. The Journal ofSymbolic Logic, 56:554–562, 1991.[Goldblatt, 1991b] Robert Goldblatt. On closure under canonical embedding algebras. InH. Andréka, J.D. Monk, and I. Németi, editors, Algebraic Logic, volume 54 of ColloquiaMathematica Societatis János Bolyai, pages 217–229. North-Holland, Amsterdam, 1991.[Goldblatt, 1993] Robert Goldblatt. Mathematics of Modality. CSLI Lecture Notes No. 43.CSLI Publications, Stanford, CA, 1993. Distributed by Chicago University Press.[Goldblatt, 1995] Robert Goldblatt. Elementary generation and canonicity for varieties ofBoolean algebras with operators. Algebra Universalis, 34:551–607, 1995.[Goldblatt, 1999] Robert Goldblatt. Reflections on a proof of elementarity. In Jelle Gerbrandy,Maarten Marx, Maarten de Rijke, and Yde Venema, editors, JFAK. Essays Dedicated toJohan van Benthem on the Occasion of his 50th Birthday, Vossiuspers. Amsterdam UniversityPress, 1999. ISBN 90 5629 104 1.[Goldblatt, 2000] Robert Goldblatt. Algebraic polymodal logic: A survey. Logic Journal of theIGPL, Special Issue on Algebraic Logic edited by István Németi and Ildikó Sain, 8(4):393–450,July 2000. Electronically available at: www3.oup.co.uk/igpl.[Goldblatt, 2001a] Robert Goldblatt. Quasi-modal equivalence of canonical structures. TheJournal of Symbolic Logic, 66:497–508, 2001.[Goldblatt, 2001b] Robert Goldblatt. What is the coalgebraic analogue of Birkhoff’s varietytheorem? Theoretical Computer Science, 266:853–886, 2001.[Goldblatt, 2003a] Robert Goldblatt. Enlargements of polynomial coalgebras. In Rod Downeyet al., editor, Proceedings of the 7th and 8th Asian Logic Conferences, pages 152–192. WorldScientific, 2003.
Mathematical Modal Logic: A View of its Evolution 91[Goldblatt, 2003b] Robert Goldblatt. Equational logic of polynomial coalgebras. In PhilippeBalbiani, Nobu-Yuki Suzuki, Frank Wolter, and Michael Zakharyaschev, editors, Advances inModal Logic, Volume 4, pages 149–184. King’s College Publications, King’s College London,2003. www.aiml.net.[Goldblatt, 2003c] Robert Goldblatt. Mathematical modal logic: A view of its evolution. Journalof Applied Logic, 1(5–6):309–392, 2003.[Goldblatt, 2003d] Robert Goldblatt. Observational ultraproducts of polynomial coalgebras.Annals of Pure and Applied Logic, 123:235–290, 2003.[Goldblatt, 2004] Robert Goldblatt. Final coalgebras and the Hennessy-Milner property. Annalsof Pure and Applied Logic, 2004. To appear.[Grzegorczyk, 1967] Andrzej Grzegorczyk. Some relational systems and the associated topologicalspaces. Fundamenta Mathematicae, 60:223–231, 1967.[Gumm, 1999] H. Peter Gumm. Elements of the general theory of coalgebras. LUATCS’99, RandAfricaans University, Johannesburg, South Africa, 60 pp. www.Mathematik.uni-marburg.de/~gumm/Papers/publ.html, 1999.[Halmos, 1962] P. R. Halmos. Algebraic Logic. Chelsea, New York, 1962.[Halpern and Moses, 1985] Joseph Y. Halpern and Yoram Moses. A guide to the modal logicsof knowledge and belief: Preliminary draft. In Proceedings of the Ninth International JointConference on Artificial Intelligence, pages 480–490, 1985.[Halpern and Moses, 1992] Joseph Y. Halpern and Yoram Moses. A guide to completeness andcomplexity for modal logics of knowledge and belief. Artificial Intelligence, 54:319–379, 1992.[Harel et al., 1982] David Harel, Dexter Kozen, and Rohit Parikh. Process logic: Expressiveness,decidability, completeness. Journal of Computer and Systems Sciences, 25:144–170, 1982.[Harel et al., 1983] D. Harel, A. Pnueli, and J. Stavi. Propositional dynamic logic of nonregularprograms. Journal of Computer and Systems Sciences, 26:222–243, 1983.[Harel, 1979] David Harel. First-Order Dynamic Logic, volume 68 of Lecture Notes in ComputerScience. Springer-Verlag, 1979.[Harel, 1984] David Harel. Dynamic logic. In D. Gabbay and F. Guenthner, editors, Handbookof Philosophical Logic, Volume II: Extensions of Classical Logic, pages 497–604. D. Reidel,1984.[Harrop, 1958] R. Harrop. On the existence of finite models and decision procedures for propositionalcalculi. Proceedings of the Cambridge Philosophical Society, 54:1–13, 1958.[Hasle and Øhrstrøm, 2004] Peter Hasle and Peter Øhrstrøm. The flow of time into logic – andcomputer science. Bulletin of the European Association for Theoretical Computer Science,82:191–226, February 2004.[Henkin et al., 1971] Leon Henkin, J. Donald Monk, and Alfred Tarski. Cylindric Algebras I.North-Holland, Amsterdam, 1971.[Henkin, 1949] Leon Henkin. The completeness of the first-order functional calculus. The Journalof Symbolic Logic, 14:159–166, 1949.[Henkin, 1950] Leon Henkin. Completeness in the theory of types. The Journal of SymbolicLogic, 15:81–91, 1950.[Hennessy and Liu, 1995] M. Hennessy and X. Liu. A modal logic for message passing processes.Acta Informatica, 32:375–393, 1995.[Hennessy and Milner, 1980] Matthew Hennessy and Robin Milner. On observing nondeterminismand concurrency. In J. W. de Bakker and J. van Leeuwen, editors, Automata, Languagesand Programming. Proceedings 1980, volume 85 of Lecture Notes in Computer Science, pages299–309. Springer-Verlag, 1980.[Hennessy and Milner, 1985] Matthew Hennessy and Robin Milner. Algebraic laws for nondeterminismand concurrency. Journal of the Association for Computing Machinery, 32:137–161,1985.[Hilbert and Bernays, 1939] David Hilbert and Paul Bernays. Grundlagen der Mathematik.Springer, 1939.[Hintikka, 1957] K. J. J. Hintikka. Quantifiers in deontic logic. Societas Scientiarum Fennica,Commentationes Humanarum Litterarum, 23(4), 1957.[Hintikka, 1961] K. J. J. Hintikka. Modality and quantification. Theoria, 27:119–128, 1961.[Hintikka, 1969] K. J. J. Hintikka. Review of “The morning star paradox” by Stig Kanger. TheJournal of Symbolic Logic, 34:305–306, 1969.
- 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
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- 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
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- Page 92 and 93: 92 Robert Goldblatt[Hoare, 1969] C.
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- Page 96 and 97: 96 Robert Goldblatt[Prior, 1967] Ar
- Page 98: 98 Robert Goldblatt[Tarski, 1956] A
90 Robert Goldblatt[Gerson, 1976] Martin Gerson. A neighborhood frame for T with no equivalent relational frame.Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 22:29–34, 1976.[Givant and Venema, 1999] S. Givant and Y. Venema. The preservation of Sahlqvist equationsin completions of Boolean algebras with operators. Algebra Universalis, 41:47–84, 1999.[Gödel, 1931] Kurt Gödel. Review of Becker 1930. Monatshefte für Mathematik und Physik(Literaturberichte), 38:5, 1931. English translation in Solomon Feferman et al., editors, KurtGödel, Collected Works, Volume 1, p. 217. Oxford University Press, 1986.[Gödel, 1933] Kurt Gödel. Eine interpretation des intuitionistischen aussagenkalküls. Ergebnisseeines mathematischen Kolloquiums, 4:39–40, 1933. English translation, with an introductorynote by A. S. Troelstra, in Solomon Feferman et al.,editor, Kurt Gödel, Collected Works,Volume 1, pages 296–303. Oxford University Press, 1986.[Goldblatt and Thomason, 1975] R. I. Goldblatt and S. K. Thomason. Axiomatic classes inpropositional modal logic. In J. N. Crossley, editor, Algebra and Logic, volume 450 of LectureNotes in Mathematics, pages 163–173. Springer-Verlag, 1975.[Goldblatt, et al., 2003] Robert Goldblatt, Ian Hodkinson, and Yde Venema. On canonicalmodal logics that are not elementarily determined. Logique et Analyse, 181:???–???, 2003.[Goldblatt et al., 2004] Robert Goldblatt, Ian Hodkinson, and Yde Venema. Erdős graphs resolveFine’s canonicity problem. The Bulletin of Symbolic Logic, 10(2):186–208, 2004.[Goldblatt, 1974] Robert Goldblatt. Metamathematics of Modal Logic. PhD thesis, VictoriaUniversity, Wellington, February 1974. Included in [Goldblatt, 1993].[Goldblatt, 1975a] Robert Goldblatt. First-order definability in modal logic. The Journal ofSymbolic Logic, 40(1):35–40, 1975.[Goldblatt, 1975b] Robert Goldblatt. Solution to a completeness problem of Lemmon and Scott.Notre Dame Journal of Formal Logic, 16:405–408, 1975.[Goldblatt, 1978] Rob Goldblatt. Arithmetical necessity, provability, and intuitionistic logic.Theoria, 44:38–46, 1978. Reprinted in [Goldblatt, 1993].[Goldblatt, 1980] Robert Goldblatt. Diodorean modality in Minkowski spacetime. Studia Logica,39:219–236, 1980. Reprinted in [Goldblatt, 1993].[Goldblatt, 1981] Robert Goldblatt. Grothendieck topology as geometric modality. Zeitschriftfür Mathematische Logik und Grundlagen der Mathematik, 27:495–529, 1981. Reprinted in[Goldblatt, 1993].[Goldblatt, 1986] Robert Goldblatt. Review of initial papers on dynamic logic by Pratt, Fischerand Ladner, Segerberg, Parikh and Kozen. The Journal of Symbolic Logic, 51:225–227, 1986.[Goldblatt, 1989] Robert Goldblatt. Varieties of complex algebras. Annals of Pure and AppliedLogic, 44:173–242, 1989.[Goldblatt, 1991a] Robert Goldblatt. The McKinsey axiom is not canonical. The Journal ofSymbolic Logic, 56:554–562, 1991.[Goldblatt, 1991b] Robert Goldblatt. On closure under canonical embedding algebras. InH. Andréka, J.D. Monk, and I. Németi, editors, Algebraic Logic, volume 54 of ColloquiaMathematica Societatis János Bolyai, pages 217–229. North-Holland, Amsterdam, 1991.[Goldblatt, 1993] Robert Goldblatt. Mathematics of Modality. CSLI Lecture Notes No. 43.CSLI Publications, Stanford, CA, 1993. Distributed by Chicago University Press.[Goldblatt, 1995] Robert Goldblatt. Elementary generation and canonicity for varieties ofBoolean algebras with operators. Algebra Universalis, 34:551–607, 1995.[Goldblatt, 1999] Robert Goldblatt. Reflections on a proof of elementarity. In Jelle Gerbrandy,Maarten Marx, Maarten de Rijke, and Yde Venema, editors, JFAK. Essays Dedicated toJohan van Benthem on the Occasion of his 50th Birthday, Vossiuspers. Amsterdam UniversityPress, 1999. ISBN 90 5629 104 1.[Goldblatt, 2000] Robert Goldblatt. Algebraic polymodal logic: A survey. Logic Journal of theIGPL, Special Issue on Algebraic Logic edited by István Németi and Ildikó Sain, 8(4):393–450,July 2000. Electronically available at: www3.oup.co.uk/igpl.[Goldblatt, 2001a] Robert Goldblatt. Quasi-modal equivalence of canonical structures. TheJournal of Symbolic Logic, 66:497–508, 2001.[Goldblatt, 2001b] Robert Goldblatt. What is the coalgebraic analogue of Birkhoff’s varietytheorem? Theoretical Computer Science, 266:853–886, 2001.[Goldblatt, 2003a] Robert Goldblatt. Enlargements of polynomial coalgebras. In Rod Downeyet al., editor, Proceedings of the 7th and 8th Asian Logic Conferences, pages 152–192. WorldScientific, 2003.
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