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Part of the book series: Synthese Library ((SYLI,volume 165))

Abstract

It is popular practice to borrow metaphors between different fields of thought. When it comes to evaluating modal logic it is tempting to borrow from the anthropologists who seem to agree that our civilization has lived through two great waves of change in the past, the Agricultural Revolution and the Industrial Revolution. Where we stand today, where the world is going, is difficult to say. If there is a deeper pattern fitting all that is happening today, then many of us do not see it. All we know, really, is that history is pushing on.

This chapter is the result of collaboration on the following terms. Segerberg wrote Sections 1–9, Bull Sections 10–24. Although the authors met and together planned the paper, each wrote his part independently of the other with little ex post scripto discussion.

Segerberg wishes to thank S. K. Thomason (who conveniently spent part of his sabbatical 1982 at the University of Auckland) for a number of very useful critical comments.

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References

  • Ackerman, W.: 1956, ‘Begründung einer strengen Implikation’, J. Symbolic Logic 21, 113–128.

    Article  Google Scholar 

  • Alban, M. J.: 1943, ‘Independence of the primitive symbols of Lewis’ calculi of propositions’, J. Symbolic Logic 8, 24–26.

    Article  Google Scholar 

  • Anderson, A. R. and Belnap, N. D.: 1975, Entailment: The Logic of Relevance and Necessity, Vol. 1, Princeton University Press, Princeton.

    Google Scholar 

  • Anderson, C. A.: 1980, ‘Some axioms for the logic of sense and denotation: Alternative (0)’, Noûs 14, 217–234.

    Article  Google Scholar 

  • Bayart, A.: 1959, ‘Quasi-adéquation de la logique modale du second ordre S5 et adéquation de la logique du premier ordre S5’, Logique et analyse 2, 99–121.

    Google Scholar 

  • Becker, O.: 1930, ‘Zur Logik der Modalitäten’, Jahrbuch für Philosophie und phänom-enologische Forschung 11, 496–548.

    Google Scholar 

  • Belnap, N. D.: 1981, ‘Modal and relevance logics:1977’, in E. Agazzi (ed.),Modern Logic — A Survey, Reidel, Dordrecht, pp.131–151.

    Chapter  Google Scholar 

  • Beth, E.W.: 1959, The Foundations of Mathematics: A Study in the Philosophy of Science, North-Holland, Amsterdam.

    Google Scholar 

  • Blok, W. J.: 1980, ‘The lattice of modal algebras: An algebraic investigation’, J. Symbolic Logic 45, 221–236.

    Article  Google Scholar 

  • Blok, W. J.: 1980a, ‘Pretabular varieties of modal algebras’, Studia Logica 39, 101–124.

    Article  Google Scholar 

  • Boolos, G.: 1979, The Unprovability of Consistency: An Essay in Modal Logic, Cambridge University Press, Cambridge.

    Google Scholar 

  • Bowen, K. A.: 1978, Model Theory for Modal Logic, Reidel, Dordrecht.

    Google Scholar 

  • Bull, R. A.: 1965, ‘An algebraic study of Diodorean modal systems’, J. Symbolic Logic 30, 58–64.

    Article  Google Scholar 

  • Bull, R. A.: 1965a, ‘A modal extension of intuitionistic logic’, Notre Dame J. Formal Logic 6,142–146.

    Article  Google Scholar 

  • Bull, R. A.: 1966, ‘That all normal extensions of S4.3 have the finite model property’, Zeit Math. Logik. Grund. 12, 341–344.

    Article  Google Scholar 

  • Bull, R. A.: 1966a, ‘MIPC as the formalization of an intuitionist concept of modality’, J. Symbolic Logic 31, 609–616.

    Article  Google Scholar 

  • Bull, R. A.: 1967, ‘On the extension of S4 with CLMpMLp’, Notre Dame J. Formal Logic 8, 325–329.

    Article  Google Scholar 

  • Bull, R. A.: 1969, ‘On modal logic with propositional quantifiers’, J. Symbolic Logic 34, 257–263.

    Article  Google Scholar 

  • Bull, R. A.: 1982, Review, J. Symbolic Logic 47, 440–445.

    Google Scholar 

  • Bull, R. A.: 1983, Review, J. Symbolic Logic 48, 488–495.

    Article  Google Scholar 

  • Carnap, R.: 1942, Introduction to Semantics, Harvard University Press, Cambridge, Mass.

    Google Scholar 

  • Carnap, R.: 1947, Meaning and Necessity: A Study in Semantics and Modal Logic, The University of Chicago Press, Chicago.

    Google Scholar 

  • Chellas, B. F.: 1980, Modal Logic: An Introduction, Cambridge University Press, Cambridge.

    Google Scholar 

  • Church, A.: 1946, ‘A formulation of the logic of sense and denotation. Abstract’, J. Symbolic Logic 11, 31.

    Google Scholar 

  • Church, A,: 1951: ‘A formulation of the logic of sense and denotation’, in P. Henle et al. (eds.), Structure, Method, and Meaning: Essays in Honor of Henry M. Scheffer, The Liberal Arts Press, New York, pp. 3–24.

    Google Scholar 

  • Church, A.: 1951a,‘The weak theory of implication’, in Menne et al. (eds.), Kontrolliertes Denken: Untersuchungen zum Logikkalkül und der Einzelwissenschaften, Kommissions-Verlag Karl Alber, Munich, pp. 22–37.

    Google Scholar 

  • Church, A.: 1973/4, ‘Outline of a revised formulation of the logic of sense and denotation’, Noûs 7, 24–33; 8, 135-156.

    Article  Google Scholar 

  • Cresswell, M.: 1967, ‘A Henkin completeness theorem for T’, Notre Dame J. Formal Logic 8, 186–190.

    Article  Google Scholar 

  • Curley, E. M.: 1975, ‘The development of Lewis’ theory of strict implication’, Notre Dame J. Formal Logic 16, 517–527.

    Article  Google Scholar 

  • Curry, H. B.: 1950, A Theory of Formal Deducibility, University of Notre Dame Press, Notre Dame, Ind.

    Google Scholar 

  • Dugundj, J.: 1940, ‘Note on a property of matrices for Lewis and Langford’s calculi of propositions’, J. Symbolic Logic 5, 150–151.

    Article  Google Scholar 

  • Dummett, M. A. E. and Lemmon, E. J.: 1959, ‘Modal logics between S4 and S5’, Zeit. Math. Logik. Grund. 3, 250–264.

    Article  Google Scholar 

  • Esakia, L. and Meskhi, V.: 1977, ‘Five critical modal systems’, Theoria 43, 52–60.

    Article  Google Scholar 

  • Feys, R.: 1965, Modal Logics, Edited with some complements by Joseph Dopp, E. Nauwelaerts, Louvain and Gauthier-Villars, Paris.

    Google Scholar 

  • Fine, K.: 1970, ‘Propositional quantifiers in modal logic’, Theoria 36, 336–346.

    Article  Google Scholar 

  • Fine, K.: 1971, ‘The logics containing S4.3’,Zeit. Math. Logik. Grund. 17, 371–376.

    Article  Google Scholar 

  • Fine, K.: 1972, ‘Logics containing S4 without the finite model property’, in W. Hodges (ed.), Conference in Mathematical Logic, London 1970, Lecture Notes in Mathematics 255, Springer-Verlag, Berlin, Heidelberg, New York, pp. 88–102.

    Google Scholar 

  • Fine, K.: 1974, ‘An incomplete logic containing S4’, Theoria 40, 23–29.

    Article  Google Scholar 

  • Fine, K.: 1974a, ‘An ascending chain of S4 logics’, Theoria 40, 110–116.

    Article  Google Scholar 

  • Fine, K.: 1974b, ‘Logics containing K4, Part I’, J. Symbolic Logic 39, 31–42.

    Article  Google Scholar 

  • Fine, K.: 1975, ‘Some connections between elementary and modal logic’, in S. Kanger (ed.), Proceedings of the Third Scandinavian Logic Symposium, North-Holland, Amsterdam, pp. 15–31.

    Chapter  Google Scholar 

  • Fine, K.: 1975a, ‘Normal forms in modal logic’, Notre Dame J. Formal Logic 16, 229–234.

    Article  Google Scholar 

  • Fine, K.: 1977, ‘Prior on the construction of possible worlds and instants’, in A. N. Prior and K. Fine (eds.), Worlds, Times and Selves, Duckworth, London, pp. 116–161.

    Google Scholar 

  • Fine, K.: 1977a, ‘Properties, propositions and sets’, J. Philosophical Logic 6, 135–191.

    Article  Google Scholar 

  • Fine, K.: 1978/81, ‘Model theory for modal logic’, J. Philosophical Logic 7, 125–156, 277-306, 10, 293-307.

    Google Scholar 

  • Fine, K.: 1980/81/82, ‘First-order modal theories’, I: Sets, Noûs 15, 177–205; II: Propositions, Studia Logica 34, 159-202; III: Facts, Synthese, 53, 43-122.

    Article  Google Scholar 

  • Fischer Servi, G.: 1977, ‘On modal logic with an intuitionist base’, Studia Logica 36, 141–149.

    Article  Google Scholar 

  • Fischer Servi, G.: 1981, ‘Semantics for a class of intuitionist modal calculi’, in Maria Luisa Dalla Chiara (ed.), Italian Studies in the Philosophy of Science, Reidel, Dordrecht, pp. 59–72.

    Google Scholar 

  • Fitch, F. B.: 1937, ‘Modal functions in two-valued logic’, J. Symbolic Logic 2, 125–128.

    Article  Google Scholar 

  • Fitch, F. B.: 1939, ‘Note on modal functions’, J. Symbolic Logic 4, 115–116.

    Article  Google Scholar 

  • Fitch, F. B.: 1948, ‘Intuitionistic modal logic with quantifiers’, Portugaliae Mathematica 7, 113–118.

    Google Scholar 

  • Fitch, F. B.: 1952, Symbolic Logic: An Introduction, Ronald Press, New York.

    Google Scholar 

  • Føllesdal, D.: ‘Von Wright’s modal logic’, in P. A. Schilpp (ed.), The Philosophy of Georg Henrik Von Wright, to appear.

    Google Scholar 

  • Føllesdal, D. and Hilpinen, R.: 1971, ‘Deontic logic: An introduction’, in Hilpinen [1971], pp. 1–35.

    Google Scholar 

  • Friedman, H.: 1975, ‘One hundred and two problems in mathematical logic’, J. Symbolic Logic 40, 113–129.

    Article  Google Scholar 

  • Gabbay, D. M.: 1976, Investigations in Modal and Tense Logics with Applications to Problems in Philosophy and Linguistics, Reidel, Dordrecht.

    Book  Google Scholar 

  • Gabbay, D. M.: 1981, Semantical Investigations in Heyting’s Intuitionistic Logic, Reidel, Dordrecht.

    Google Scholar 

  • Gerson, M.: 1975, ‘The inadequacy of the neighbourhood semantics for modal logic’, J. Symbolic Logic 40, 141–148.

    Article  Google Scholar 

  • Gerson, M.: 1975a, ‘An extension of S4 complete for the neighbourhood semantics but incomplete for the relational semantics’, Studia Logica 34, 333–342.

    Article  Google Scholar 

  • Gerson, M.: 1976, ‘A neighbourhood frame for T with no equivalent relational frame’, Zeit. Math. Logik. Grund. 22, 29–34.

    Article  Google Scholar 

  • Gödel, K.: 1933,.‘Eine Interpretation des intuitionistischen Aussagenkalküls’, Ergebnisse eines mathematisches Kolloquiums 4, 39–40.

    Google Scholar 

  • Goldblatt, R.I.: 1975, ‘First-order definability in modal logic’, J. Symbolic Logic 40, 3540.

    Google Scholar 

  • Goldblatt, R. I.: 1976, ‘Metamathematics of modal logic’, Reports on Mathematical Logic 6, 41–78; 7, 21-52.

    Google Scholar 

  • Goldblatt, R. I. and Thomason, S. K.: 1975, ‘Axiomatic classes in propositional modal logic’, in J. N. Crossley (ed.), Algebra and Logic, Lecture Notes in Mathematics 450. Springer-Verlag, Berlin, Heidelberg, New York, pp. 163–173.

    Chapter  Google Scholar 

  • Grzegorczyk, A.: 1981, ‘Individualistic formal approach to deontic logic’, Studia Logica 40, 99–102.

    Article  Google Scholar 

  • Guillaume, M.: 1958, ‘Rapports entre calculs propositionnels modaux et topologie impliqués par certaines extensions de la méthode de tableaux sémantiques’, Comptes rendus hebdomaires des séances de l’Académie des Sciences 246, 1140–1142, 2207-2210; 247, 1281-1283, Gauthiers-Villars, Paris.

    Google Scholar 

  • Halldén, S.: 1949, ‘Results concerning the decision problem of Lewis’s calculi S3 and S6’, J. Symbolic Logic 14, 230–236.

    Google Scholar 

  • Hansson, B. and Gärdenfors, P.: 1973, ‘A guide to intensional semantics’, in Modality, Morality and Other Problems of Sense and Nonsense: Essays Dedicated to Soren Halldén, Gleerup, Lund, pp. 151–167.

    Google Scholar 

  • Hilpinen, R.: 1971, Deontic Logic: Introductory and Systematic Readings, Reidel, Dordrecht.

    Google Scholar 

  • Hintikka, J.: 1955, Form and content in quantification theory. Acta Philosophica Fennica 8, 11–55.

    Google Scholar 

  • Hintikka, J.: 1957, Quantifiers in Deontic Logic, Societas Scientiarum Fennica, Com-mentationes humanarum litterarum 23: 4. Helsingfors.

    Google Scholar 

  • Hintikka, J.: 1961, ‘Modality and quantification’, Theoria 27, 119–128. Revised version reprinted in Hintikka [1969].

    Article  Google Scholar 

  • Hintikka, J.: 1962, Knowledge and Belief: An Introduction to the Logic of the Two Notions, Cornell University Press, Ithaca, N.Y.

    Google Scholar 

  • Hintikka, J.: 1963, ‘The modes of modality’, Acta Philosophica Fennica 16, 65–82. Reprinted in Hintikka [1969].

    Google Scholar 

  • Hintikka, J.: 1969, Models for Modalities: Selected Essays, Reidel, Dordrecht.

    Google Scholar 

  • Hintikka, J.: 1969a, Review. J. Symbolic Logic 34, 305–306.

    Google Scholar 

  • Hintikka, J.: 1975, ‘Carnap’s heritage in logical semantics’, In J. Hintikka (ed.), Rudolf Carnap, Logical Empiricist: Materials and Perspectives, Reidel, Dordrecht, pp. 217–242.

    Google Scholar 

  • Hofstadter, A. and McKinsey, J. C. C.: 1939, ‘On the logic of imperatives.’ Philosophy of Sciences 6, 446–457.

    Article  Google Scholar 

  • Hughes, G. E. and Cresswell, M. J.: 1968, An Introduction to Modal Logic, Methuen, London, 1968. Second edition 1972.

    Google Scholar 

  • Jeffrey, R. C.: 1967, Formal Logic: Its Scope and Limits, McGraw-Hill, New York.

    Google Scholar 

  • Jónsson, B.: 1967, ‘Algebras whose congruence lattices are distributive’, Mathematica Scandinavica 21, 110–121.

    Google Scholar 

  • Jónsson, E. and Tarski, A.: 1951, ‘Boolean algebras with operators. Part I’, Am. J. Math. 73, 891–939.

    Article  Google Scholar 

  • Kamp, J. A. W.: 1968, ‘On tense logic and the theory of order’, PhD dissertation, UCLA.

    Google Scholar 

  • Kanger, S.: 1957,Provability in logic, Dissertation, Stockholm.

    Google Scholar 

  • Kanger, S.: 1957a, New Foundations for Ethical Theory, Stockholm. Reprinted in Hilpinen[1971].

    Google Scholar 

  • Kanger, S.: 1957b, ‘The Morning Star Paradox’, Theoria 23, 1–11.

    Article  Google Scholar 

  • Kanger, S.: 1957c, ‘A note on quantification and modalities’, Theoria 23, 131–134.

    Google Scholar 

  • Kaplan, D.: 1966, Review, J. Symbolic Logic 31, 120–122.

    Google Scholar 

  • Kaplan, D.: 1970, ‘S5 with quantifiable propositional variables, Abstract’, J. Symbolic Logic 35, 355.

    Google Scholar 

  • Kneale, W. and Kneale, M.: 1962, The Development of Logic, Clarendon Press, Oxford.

    Google Scholar 

  • Kripke, S.A.: 1959, ‘A completeness theorem in modal logic’, J. Symbolic Logic 24, 1–14.

    Article  Google Scholar 

  • Kripke, S.A.: 1963, ‘Semantical considerations on modal logic’, Acta Philosophica Fennica 16, 83–94.

    Google Scholar 

  • Kripke, S.A.: 1963a, ‘Semantical analysis of modal logic I: Normal propositional calculi’, Zeit. Math. Logik. Grund. 9, 67–96.

    Article  Google Scholar 

  • Kripke, S.A.: 1965, ‘Semantical analysis of modal logic II: Non-normal modal propositional calculi’, in J. W. Addison et al. (eds.), The Theory of Models, North-Holland, Amsterdam, pp. 206–220.

    Google Scholar 

  • Kuhn, S. T.: 1977, Many-sorted Modal Logics, Philosophical studies published by the Philosophical Society and the Department of Philosophy, University of Uppsala, Vol. 35, Uppsala.

    Google Scholar 

  • Leivant, D.: 1981, ‘On the proof theory of the modal logic for arithmetic provability’, J. Symbolic Logic 46, 531–538.

    Article  Google Scholar 

  • Lemmon, E. J.: 1957, ‘New foundations for Lewis modal systems’, J. Symbolic Logic 22, 176–186.

    Article  Google Scholar 

  • Lemmon, E. J.: 1966, ‘Algebraic semantics for modal logics’, J. Symbolic Logic 31, 46–65, 191-218.

    Article  Google Scholar 

  • Lemmon, E. J.: 1977, An Introduction to Modal Logic, in collaboration with D. Scott, Blackwell, Oxford.

    Google Scholar 

  • Lewis, C. I.: 1912, ‘Implication and the algebra of logic’, Mind, n.s., 21, 522–531.

    Article  Google Scholar 

  • Lewis, C. I.: 1918, A Survey of Symbolic Logic, University of California Press, Berkeley.

    Google Scholar 

  • Lewis, C. I. and Langford, C. H.: 1932, Symbolic Logic. The Century Co., New York, London, 1932. Second edn, Dover, New York, 1959.

    Google Scholar 

  • Lewis, D.: 1973, Counterfactuals. Harvard University Press, Cambridge, Mass.

    Google Scholar 

  • Łukasiewicz, J.: 1953, ‘A system of modal logic’, J. Computing Systems 1, 111–149.

    Google Scholar 

  • Łukasiewicz, J.: 1970, Selected Works, L. Borkowski (ed.), North-Holland, Amsterdam.

    Google Scholar 

  • McCall, S.: 1967, Polish Logic 1920–1939, Clarendon Press, Oxford.

    Google Scholar 

  • McKinsey, J. C. C.: 1941, ‘A solution of the decision problem for the Lewis systems S2 and S4 with an application to topology’, J. Symbolic Logic 6, 117–134.

    Article  Google Scholar 

  • McKinsey, J. C. C.: 1945, ‘On the syntactical construction of modal logic’, J. Symbolic Logic 10, 83–96.

    Article  Google Scholar 

  • McKinsey, J. C. C. and Tarski, A.: 1944, ‘The algebra of topology’, Annals of mathematics 45, 141–191.

    Article  Google Scholar 

  • McKinsey, J. C. C. and Tarski, A.: 1948, ‘Some theorems about the sentenital calculi of Lewis and Hey ting’, J. Symbolic Logic 13, 1–15.

    Article  Google Scholar 

  • Makinson, D.: 1966, ‘On some completeness theorems in modal logic’, Zeit. Math. Logik. Grund. 12, 379–384.

    Article  Google Scholar 

  • Makinson, D.: 1969, ‘A normal modal calculus between ? and S4 without the finite model property’, J. Symbolic Logic 34, 35–38.

    Article  Google Scholar 

  • Makinson, D.: 1970, ‘A generalisation of the concept of a relational model for modal logic’, Theoria 36, 331–335.

    Article  Google Scholar 

  • Makinson, D.: 1971, Aspectos de la logica modal, Instituto de matematica, Universidad Nacional del Sur, Bahia Bianca.

    Google Scholar 

  • Makinson, D.: 1971a, ‘Some embedding theorems for modal logic’, Notre Dame J. Formal Logic 12, 252–254.

    Article  Google Scholar 

  • Maksimova, L. L.: 1975, [Pretabular extensions of Lewis’ S4.], Algebra i logika 14, 28–55.

    Google Scholar 

  • Malinowski, G.: 1977, ‘Historical note’, in R. Wójcicki (ed.), Selected Papers on Lukasiewicz Sentential Calculi, Polish Academy of Sciences, Wrocław, pp. 177–187.

    Google Scholar 

  • Mally, E.: 1926, Grundgesetze des Sollens: Elemente der Logik des Willens, Lenscher amp; Lugensky, Graz.

    Google Scholar 

  • Montague, R.: 1963, ‘Syntactical treatments of modality, with corollaries on reflexion principles and finite axiomatizability’, Acta Philosophica Fennica 16, 153–167. Reprinted in Montague [1974].

    Google Scholar 

  • Montague, R.: 1968, ‘Pragmatics’, in R. Klibansky (ed.), Contemporary Philosophy. A Survey, Vol. 1, La Nuova Editrice, Florence, pp. 102–122. Reprinted in Montague [1974].

    Google Scholar 

  • Montague, R.: 1974, Formal Philosophy: Selected Papers of Richard Montague’, Edited with an introduction by Richmond H. Thomason, Yale University Press, New Haven, London.

    Google Scholar 

  • Morgan, C.: 1979, ‘Modality, analogy, and ideal experiments according to C. S. Pierce’, Synthese 41, 65–83.

    Article  Google Scholar 

  • Mortimer, M.: 1974, ‘Some results in modal model theory’, J. Symbolic Logic 39, 496–508.

    Article  Google Scholar 

  • Ohnishi, M. and Matsumoto, K.: 1957/59, ‘Gentzen method in modal calculi’, Osaka Mathematical Journal 9, 113–130; 11, 115-120.

    Google Scholar 

  • Parry, W. T.: 1934, ‘The postulates for “strict implication”’ Mind, n.s., 43, 78–80.

    Article  Google Scholar 

  • Parsons, C.: ‘Intensional logic in extensional language’, J. Symbolic Logic 47, 289–328.

    Google Scholar 

  • Pratt, V.R.: 1980, ‘Application of modal logic to programming’, Studia Logica 34, 257–274.

    Article  Google Scholar 

  • Prawitz, D.: 1965, Natural Deduction; a Proof-theoretic Study (Stockhohn Studies in Philosophy, 3), Almqvist and Wiksell, Stockholm.

    Google Scholar 

  • Prior, A. N.: 1955, Formal Logic, Clarendon Press, Oxford. Second edition 1962.

    Google Scholar 

  • Prior, A. N.: 1957, Time and Modality, Clarendon Press, Oxford.

    Google Scholar 

  • Prior, A. N.: 1967, Past, Present and Future, Clarendon Press, Oxford.

    Google Scholar 

  • Rasiowa, H. and Sikorski, R.: 1963, The Mathematics of Metamathematics, Państwowe Wydawnictwo, Naukowe.

    Google Scholar 

  • Rautenberg, W.: 1979, Klassische und nicht klassische Aussagenlogik, Vieweg, Brauns chweig, Wiesbaden.

    Google Scholar 

  • Rescher, N. and Urquhart, A.: 1971, Temporal Logic, Springer-Verlag, New York and Vienna.

    Google Scholar 

  • Ridder, J.: 1955, ‘Die Gentzensschen Schlussverfahren in modalen Aussagenlogiken I’, Indagationes mathematicae 17, 163–276.

    Google Scholar 

  • Sahlqvist, H.: 1975, ‘Completeness and correspondence in the first and second order semantics for modal logic’, in Stig Kanger (ed.), Proceedings of the Third Scandinavian Logic Symposium, North-Holland, Amsterdam, pp. 110–143.

    Chapter  Google Scholar 

  • Schumm, G. F.: 1981, ‘Bounded properties in modal logic’, Zeit. Math. Logik. Grund. 27, 197–200.

    Article  Google Scholar 

  • Schütte, K.: 1968, Vollständige Systeme modaler und intuitionistischer Logik, Springer-Verlag, Berlin, Heidelberg and New York.

    Google Scholar 

  • Scott, D.: 1971, ‘On engendering an illusion of understanding’, J. Philosophy 68, 787–807.

    Article  Google Scholar 

  • Scroggs, S. J.: 1951, ‘Extensions of the Lewis system S5’, J. Symbolic Logic 16, 112–120.

    Article  Google Scholar 

  • Segerberg, K.: 1968, Decidability of S4.1, Theoria 34, 7–20.

    Article  Google Scholar 

  • Segerberg, K.: 1970, ‘Modal logics with linear alternative relations’, Theoria 36, 301–322.

    Article  Google Scholar 

  • Segerberg, K.: 1971, An Essay in Classical Modal Logic, Philosophical studies published by the Philosophical Society and the Department of Philosophy, University of Uppsala, Vol. 13, Uppsala.

    Google Scholar 

  • Segerberg, K.: 1982, Classical Propositional Operators: An Exercise in the Foundations of Logic, Clarendon Press, Oxford.

    Google Scholar 

  • Segerberg, K.: [*], ‘Von Wright’s tense-logic’, in P. A. Schilpp (ed.) The Philosophy of Georg Henrik von Wright, to appear.

    Google Scholar 

  • Shoesmith, D. J. and Smiley, T. J.: 1978, Multiple-Conclusion Logic, Cambridge University Press, Cambridge.

    Book  Google Scholar 

  • Smullyan, R. M.: 1968, First-order Logic, Springer-Verlag, New York, Heidelberg and Berlin.

    Google Scholar 

  • Snyder, D. P.: 1971, Modal Logic and its Applications, Van Nostrand Reinhold, New York.

    Google Scholar 

  • Sobinciński, B.: 1964, ‘Family K of the non-Lewis modal systems’, Notre Dame J. Formal Logic 5, 313–318.

    Article  Google Scholar 

  • Solovay, R. S. M.: 1976, Provability interpretations of modal logic. Israel journal of mathematics 25, 287–304.

    Article  Google Scholar 

  • Stalnaker, R.: 1968, ‘A theory of conditionals’, in N. Rescher (ed.), Studies in Logical Theory, Blackwell, Oxford, pp. 98–112.

    Google Scholar 

  • Thomason, S. K.: 1972, ‘Semantic analysis of tense logics’, J. Symbolic Logic 37, 150–158.

    Article  Google Scholar 

  • Thomason, S. K.: 1972a, ‘Noncompactness in propositional modal logic’, J. Symbolic Logic 37, 716–720.

    Article  Google Scholar 

  • Thomason, S. K.: 1974, ‘An incompleteness theorem in modal logic’, Theoria 40, 30–34.

    Article  Google Scholar 

  • Thomason, S. K.: 1975, ‘Categories of frames for modal logic’, J. Symbolic Logic 40, 439–442.

    Article  Google Scholar 

  • Van Benthem, J. F. A. K.: 1975, ‘A note on modal formulae and relational properties’, J. Symbolic Logic 40, 55–58.

    Article  Google Scholar 

  • Van Benthem, J. F. A. K.: 1976, ‘Modal formulas are either elementary or not ΣΔ-elementary’, J. Symbolic Logic 41, 436–438.

    Article  Google Scholar 

  • Van Benthem, J. F. A. K.: 1978, ‘Two simple incomplete modal logics’, Theoria 44, 25–37.

    Article  Google Scholar 

  • Van Benthem, J. F. A. K.: 1979, ‘Canonical modal logics and ultrafilter extensions’, J. Symbolic Logic 44, 1–8.

    Article  Google Scholar 

  • Van Benthem, J. F. A. K.: 1979a, ‘Syntactic aspects of modal incompleteness theorems’, Theoria 45, 67–81.

    Google Scholar 

  • Van Benthem, J. F. A. K. and Blok, W. J.: 1978, ‘Transitivity follows from Dummett’s axiom’, Theoria 44, 117–118.

    Article  Google Scholar 

  • Von Wright, G. H.: 1951, An Essay in Modal Logic, North-Holland, Amsterdam.

    Google Scholar 

  • Von Wright, G. H.: 1951a, ‘Deontic logic’, Mind, n.s., 60, 1–15.

    Article  Google Scholar 

  • Von Wright, G. H.: 1968, ‘An essay in deontic logic and general theory of action with a bibliography of deontic and imperative logic’, Acta Philosophica Fennica 21.

    Google Scholar 

  • Von Wright, G. H.: 1981, ‘Problems and prospects of deontic logic: A Survey’, in Evandro Agazzi (ed.), Modern Logic —A Survey, Reidel, Dordrecht, pp. 299–423.

    Google Scholar 

  • Zeman, J. J.: 1973, Modal Logic: The Lewis-Modal Systems, Clarendon Press, Oxford.

    Google Scholar 

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Bull, R., Segerberg, K. (1984). Basic Modal Logic. In: Gabbay, D., Guenthner, F. (eds) Handbook of Philosophical Logic. Synthese Library, vol 165. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6259-0_1

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  • DOI: https://doi.org/10.1007/978-94-009-6259-0_1

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