BIBLIOGRAPHY

ABBREVIATIONS for names of journals:
JSL: Journal of Symbolic Logic
NDJFL: Notre Dame Journal of Formal Logic
ZML: Zeitschrift für Mathematische Lοgik und Grundlagen der Μathematik
LA: Logique et Analyse

BECKER, O.

1930

'Zur Logik der Modalitäten' , Jahrb. f . Ρhilos. und Phenomenol. Forschung 11 (1930), 496-548.

1942

'Das Formale System der ontologischen Modalitäten', Blätter für Deutsche Philosophie 16 (1942), 287-422.

1944

'Ein "natürliches" formales System der 1οgίsch-ontologιschen Μοda1ltäten', ibid. 18 (1944), 82-93.

1952

'Untersuchungen über den Modalkalkul' Meisenheim am Glan, Anton Heim, 1952.

BETH, Ε. W.

1955

'Semantic Entailment and Formal Derivability', Mededlungen van de Koninklijke Nederlandse Akademie van Wetenschappen, Αfdeling Letterkunde N.R.18 (1955) 309-42 (reprinted in Hintikka 1969).

BULL, R. Α.

1963 

'Modal Logics with Intuitionist Ρropositional Fragments' abstract JSL 28 (1963), 262-3.

1964a 

'Α note on the Modal Calculi S4.2 and S4.3', ZML 10 (1964) 53-5

1964b

'An Axiomatϊzation of Prior's Modal Calculus', NDJFL 5 (1964), 211-14 (360).

1965 

'An Algebraic Study of Diodorean Modal Systems', JSL 30 (1965) 58-64.

1965a

'Α Modal Extension of Intuitionist Logic', NDJFL 6 (1965), 142-6.

1965b 

'Α Class of Extensions of the Modal System S4 with the Finite Model Property', ZML 11 (1965), 127-32.

1966a

'That all Normal Extensions of S4.3 have the Finite Model Property', ZML 12 (1966) 341-4.

1966b

'MIPC as the Formalization of an Intuιtionist Concept of Modality', JSL 31 (1966) 609-16.

CANTY, J. Τ.

1964 

'Α Natural Deduction System for Modal Logic', NDJFL 5 (1964), 199-210.

1965  'Systems Classically Axiomatized and properly contained in Lewis's S3', NDJFL 6 (1965). 309-18.

CHURCH, Α.

1936

'Α Note on the Entscheidungsρroblem', JSL 1 (1936), 40-1

1951

'Α Formulation of the Logic of Sense and Denotation', Structure, Method and Meaning ed. Ρ. Henle, Η. Μ. Kallen, S. Κ. Langer . New York: Liberal Arts Press 1957.

1956

Introduction to Mathematical Logic, vol. 1. Princeton, N.J. 1956. 

CRESWELL, Μ. J.

1965

'Another Basis for S4', LA 8 ( 1965) 191-5 (333).

1966a

'The Completeness of S0.5', LA 9 1966 263-6. 

1966b

'Functions of Propositions', JSL 31 (1966), 545-60. 

1967a

'Note on a System of Αqvist' JSL 32 ( 1967) 58-60.

1967b

'The Interpretation of some Lewis Systems of Modal Logic', Australasian Journal of Philosophy 45 (1967), 198-206.

1967c

'Propositional Identity', LA 10 (1967), 283-92.

1969

'The Completeness of S1 and some Related Systems' read at 1969 ASL meetings, New York), abstract to appear in JSL.

CURRY, Η. Β.

1950

Α Theory of Formal Deducibility, Νotre Dame Mathematical Lectures no.6 Notre Dame, Indiana, 1950.

1952

'The Elimination Theorem when Modality is Present' JSL 17 (1952). 249-65.

1963

Foundations οf Mathematical Logic, New York 1963. 

DUGUNDJI, J.

1940 

'Note on α Property of Matrices for Lewis and Langf ord's Calculi of Propositions', JSL 5 (1940).,150-l.

DUMMETT, Μ. Α. Ε.

1959 

'Α Proρositional Calculus with Denumerable Matrix' JSL 24 (1959). 97-106.

DUMMETT, Μ. Α. Ε. and LEMMON, Ε. J.

1959 

'Modal Logics between S4 and S5', ZML 3 ( 1959) 250-δ4. 

FEYS, R.

1937 

'Les logiques nouvelles de modalités', Revue Neoscolastique de Philosophie 40 ( 1937), 517-33 and 41 ( 1938), 214-52.

1950 

'Les systèmes formalisés des modalités aristotéliciennes' Revue Philosophique de Louvain 48 ( 1950) 478-509.

1951 

'Oudere en nieuwe modaliteiten logica' Handelingen van XIXe Vlaamse Filοlοgencongres, Brussels, 1951, 284-9.

1952 

'Les logiques modales (Thémes de discussion)', Theoria ( Madrid) 1 (1952),163-6.

1953 

'Α Simplified Proof of the Reduction of all Modalities to 42 in S3' Boletin de la Soc. Mathematica Mexicana 10 (1953), 53-7.

1955 'Expression modale du "devoir-être"' (Abstract), JSL 20 (1955), 91-2.
1961  'Modèles à variable de différentes sortes pour les 1οgiques modales Μ' ou S5' in The Concept and the Role οf the Model in Mathematics and Natural and Social Sciences ed. Β. Κ. Kazemier and D. Vuysje . Dordrecht, 1961, 58-72.
1965  Modal Logics. Louvain, Ε. Nauwelaerts, 1965
FREGE, G.
1879  'Begriffsschrift', in From Frege to Gödel ed. Jean van Heijenoort,  Harvard, Mass., 1961, 1-82.
GENTZEN, G.
1934  'Untersuchungen iiber das 1οgische Schliessen', Mathematische Zeitschrift 39 (1934), 176-210, 405-31.
GÖDEL, Κ.
1933  'Eine Interpretation des intuitionistischen Aussagenkalkuls', Εrgebnisse eines mathematischen Κοllοquiums 4 (1933), 34-50 (tr. in Hintikka 1969). 
HALLDEN, S.
1948a  'Α Note concerning the Paradoxes of Strict Implication and Lewis's System S1', JSL 13 (1948), 138-9.
1948b  'Α Question concerning a Logical Calculus Related to Lewis's System of Strict Implication, which is of Special Interest for the Study of Entailment', Theoria 4 (1948), 265-9.
1949a  'Results concerning the Decision Problem of Lewis's Calculi S3 and S6', JSL 14 (1949), 230-6.
1949b  'On the Decision Problem of Lewis's Calculus SS', Norsk Mathematisk Tidsskrift 31 (1949), 89-94.
1949c  'Α Reduction of the Primitive Symbols of the Lewis's Calculi', Portugaliae Mathematica 8 (1949, publ.1950), 85-8.
1951  'On the Semantic Non-Completeness of certain Lewis Calculi', JSL 16 (1951), 127-9.
1963  'Α Pragmatic Approach to Modal Theory', Acta Philosophica Fennica 16 (1963)ι 53-64.
ΗΙΝΤΙΚΚΑ, Κ. J. J.
1954  'An Application of Logic to Algebra', Mathematica Scandinavica 2 (1954),243-6.
1951a  'Modality as Referential Multiplicity', Αjatus (Helsinki) 20 (1957), 49-δ4. 
1957b  'Necessity, Universality and Time in Aristotle', ibid. 64-90.
1957c  'Quantifiers in Deontic Logic', Societas Scientiarum Fennica, Commentationes Humanarum Litterarum, 23 (1957), 2-23.
1961  'Modality and Quantification', Theoria 27 (1961), 110-28.
1963  'The Modes of Modality', Acta Philosophica Fennica (1963) Modal and Many-Valued Logics 65-81.
1967  'Individuals, Possible Worlds, and Εpistemic Logic', Nous 1 (1967), 33-62. 
1969  (ed.) The Philosophy οf Mathematics, Oxford, 1969.
HUGHES, G. Ε., and CRESSWELL, Μ. Ι.
1968  An Introduction to Modal Logic, London, 1968
KANGER, S. G.
1957 'Provability in Logic', Acta Universitatis Stockholmiensis, Stockholm Studies in Philosophy 1, Stockholm, 1957.
1951a  'The Morning Star Paradox' Theoria (Lund) 23 (1957), 1-11
1957b  'Α Note on Quantification and Modalities', ibid. 133-4.
1957c ' On the Characterization of Modalities', ibid. 152-5.
ΚΕΤΟΝΕΝ, O.
1944  'Untersuchungen zum Prädikatenkalkul' Annales Academiae Scientiiarum Fennicae, ser. Α, 1. Mathematica-ρhysica 23, Helsinki, 71 pp.
KLEENE, S. C.
1952  Introduction to Metamathematics. Princeton N.J.: Van Nostrand, 1952.
KÖNIG, D.
1926  'Sur les corresρondances multivoques des ensembles', Fundamenta Mathematica 8 (1926), 114-34.
KRIPKE, S. Α.
1959  'Α Completeness Theorem in Modal Logic', JSL 24 (1959), 1-14.
1962  'The Undecidability of Monadic Modal Quantification Theory', ΖΜL 8 (1962),113-16.
1963 'Semantical Analysis of Modal Logic I, Normal Proρositional Calculi',  ZML 9 (1963), 67-96.
1963a  'Semantical Considerations on Modal Logics', Acta Philosoρhica Fennica (1963) Modal and Many-Valued Logics, 83-94.
1965a  'Semantical Analysis of Modal Logic II, Non-Normal Modal Proροsitional Calculi', The Theory οf Models ed. J. W. Addison, L. Henkin, Α. Tarski, Amsterdam, 1965, 206-20. 
LEMMON, Ε. J.
1956  'Alternative Postulate Sets for Lewis's S5' JSL 21 1956 347-9. 
1957  'New Foundations for Lewis Modal Systems', JSL 22 (1957), 186-96 . 
1957a  'Quantifiers and Modal Operators', Proceedings οf the Aristotelian Society 58 (1956-8), 244-68.
1959  'Is there only one Correct System of Modal Logic?', Aristotelian Society Suppl. 33 1959), 23-50.
1960a  'An Extension Algebra and the Modal System Τ', NDJFL 1 (1960), 2-12 . 
1960b  'Quantified S4 and the Barcan Formula' (Abstract), JSL 24 (1960), 391-2. 
1963  'Α Theory of Attributes Based on Modal Logic', Αcta Philosophica Fennica (1963) Modal and Many-Valued Logics, 95-122.
1965  'Some Results on Finite Axiomatizability in Modal Logic', NDJFL 6 (1965), 301-7.
1965a  'Deontιc Logic and the Logic of Imperatiνes', LA 29 (1965), 39-40 (350)
1966a 'Algebraic Semantics for Modal Logics I', JSL 31 (1966), 46-65.
1966b  'Algebraic Semantics for Modal Logics ΙΙ', ibid. 191-218
LΕΜΜΟΝ, Ε.J., and GJERSTEN, 1959,174.
.See PRIOR, Α. Ν., Formal Logic 2nd ed., Oxford, 1962, 312. ,
LEWIS, C. Ι.
1912  'Implication and the Algebra of Logic', Mind N.S., 21 (1912), 522-31.
1914a  'Α New Algebra of Strict Implication', Mind N.S., 23 (1914), 240-1.
1914  'The Matrix Algebra for Implication', Journal οf Philosophy 11 (1914), 589-600.
1918  Α Survey of Symbolic Logic, Berkeley, Cal., 1918.
1920  'Strict Implication. An Emendation', Journal of Philosophy 17 (1920), 300-2.
LEWIS, C. I., and LANGFORD, C. H.
1932  Symbolic Logic, 2nd ed., New York, 1959.
ŁUKASIEWICZ, J.
1929  Elementy Logiki Matematycznej, Warsaw, 1929. 
1951  First ed. of Łukasiewicz 1957.
1953a  'Α System of Modal Logic', The Journal ο Computing Systems 1 (1953), 111-49.
1953  'Arithmetic and Modal Logic'. ibid. 213-19.
1954  'On a Controversial Problem of Aristotle's Modal Syllogistic'. Dominican Studies 7 (1954), 114-23.
1957  Aristotle's Syllogistic from the Standpoint of Modern Formal Logic, 2nd ed. enlarged, Oxford, 1957.
MCKINSEY, J. C. C.
1934  'Α Reduction in the Number of Postulates for C. Ι. Lewis' System of Strict Implication'. Bulletin of the American Mathematical Society 40 (1934) , 425-527.
1934a  'Α Note on Bronstein's and Tarter's Definition of Strict Implication, Philosophical Review 43 (1934), 518-20.
1939  'Proof of the Independence of the Primitive Symbols of Heyting's Calculus of Propositions', JSL 4 (1939), 155-8.
1940  'Proof that there are Infinitely many Modalities in Lewis' System S2', JSL 5 (1940), 110-12.
1941  'Α Solution of the Decision Problem for the Lewis Systems S2 and S4 with an Application to Topology', JSL 6 (1941), 117-34.
1944  'On the Number of Complete Extensions of the Lewis Systems of Sentential Calculus' JSL 9 (1944), 41-5.
1945  'On the Syntactical Construction of Systems of Modal Logic', JSL 10 (1945), 83-96.
1953  'Systems of Modal Logic which are not Unreasonable in the Sense of Hallden', JSL 18 (1953), 109-13.
MCKINSEY,  J. C. C, and TARSKI, Α.
1944  'The Algebra of Topology', Annals of Mathematics 45 (1944), 141-91.
1948  'Some Theorems about the Sentential Calculi of Lewis and Heyting', JSL 13 (1948), 1-15. 
MATSUMOTO, Κ.
1950a  'Sur 1α\a structure concernant la logique moderne', Journal of the Osaka Institute of Science and Technology, The Kinki University, Part 1, Math. and Phys. 2 (1950), 67-78.
1950b  'On α Lattice Relating to the Intuitionistic Logic', ibid. 97-107.
1955  'Reduction Theorem in Lewis's Sentential Calculi', Mathematica Japonicae 3 (1955),133-5.
1960 'Decision Procedure for Modal Sentential Calculus S3' Osaka Mathematical Journal 12 (1960), 167-75.
OHNISHI, Μ.
1961  'Gentzen Decision Procedures for Lewis's Systems S2 and S3', Osaka Mathematical Journal 13 1961,125-37.
1961a  'Von Wright-Anderson's Decision Procedures for Lewis's Systems S2-S3', ' ibid. 139-42.
OHNISHI, Μ., and MATSUMOTO, Κ.
1957  Gentzen Method in Modal Calculi I', ibid. 9 (1957), 113-30.
1959 'Gentzen Method in Modal Calculi II', ibid. 11 (1959), 115-20.
964  1'Α System for Strict Implication', Annals of the Japanese Association for Philosophy of Science 2 (1964), 183-8.
PARRY, W. Τ.
1934  'The Postulates for "Strict Implication",  Mind 43 (1934), 78-80.
1939  'Modalities in the Survey System of Strict Implication'. JSL 4 (1939), 131-54.
PEIRCE, C. S.
1885  'Α Contribution to the Philosophy of Notation', Collected Papers, 8 vols., ed. Charles Hartshorne, Paul Weiss, Arthur W. Burks, 1931-58, 3.359-403Μ. Much of Peirce's writing on modal logic is contained in his work on the 'Existential Graphs', 4.372-584.
PRIOR, Α. Ν.
1952a 'In what Sense is Modal Logic Many-Valued?', Analysis (Oxford) 12 (1952),138-43.
1952b Modality de dicto and Modality de re'. Theoria (Lund) 18 (1952), 174-80.
1952a 'On Propositions neither Necessary nor Impossible', JSL 18 (1953) 105-8.
1953b  'Three-Valued Logic and Future Contingents', The Philosophical Quarterly 3 (1953), 317-26.
1954a  'The Paradoxes of Derived Obligation', Mind N.S.. 63 (1954), 64-5.
1954b  'Many-Valued Modal Systems. An Intuitive Approach', The Philosophical Review 63 (1954), 626-30.
1954c 'The Interpretation of Two Systems of Modal Logic, The Journal of Computing Systems 4 (1954), 201-8.
1955  'Diodorian Modalities', The Philosophical Quarterly 5 (1955), 205-13.
1955a  'Modality and Quantification in S5', JSL 21 (1955), 60-2.
1957  Time and Modality, London, 1957.
1957a  'The Necessary and the Possible. The First of Three Talks on "The Logic Game"', The Listener 57 (1957), 627-8.
1958  'Diodorus and Modal Logic, Α Correction', The Philosophical Quarterly 8 (1958), 226-30 (a correction to 'Diodoran Modalities', 1955).
1958a  'The Syntax of Time-Distinctions', Franciscan Studies 18 (1958), 105-20.
1959  'Notes on α Group of Modal Systems', LA 2 (1959), 122-7.
1961  'Some Axiom-Pairs for Material and Strict Implication, ZML 7 (1961), 61-5.
1962  Formal Logic, 2nd ed., Oxford, 1962.
1962a  'Quantification and Modality', NDJFL 3 (1962), 142-7.
1962b ' Possible Worlds', The Philosophical Quarterly 12 (1962), 36-43.
1962c  'Tense-Logic and the Continuity of Time', Studia Logίca 13 (1962), 133-51.
1962d  'The Formalities of Omniscience', Philosophy 37 (1962), 114-29.
1963a  'The Theory of Implication', ZML 9 (1963), 1-6.
1963b  'Is the Concept of Referential Opacity really Necessary?', Acta Philosophica Fennica (1963) Modal and Many-Valued Logίcs, 189-98.
1963c  'Oratio Obliqua', Aristotelian Society Suppl. 37 (1963), 115-26.
1964  'ΚΙ, Κ2, and Related Modal Systems' NDJFL 5 (1964), 299-304 (282).
1964a  'Axiomatizatίons of the Modal Calculus Q', ibid. 215-17 (361).
1967  Past, Present, and Future, Oxford, 1967.
1968  Time and Tense, Oxford, 1968.
ROSSER, J. Β.
1953  Logic for Mathematicians, New York, 1953. 
SCHUMM, G. F.
1969  'On Some Open Questions of Β. Sobociniski', NDJFL 10 (1969), 261-2.
SCROGGS, S. J.
1951 ' Extensions of the Lewis System SS', JSL 16 (1951), 112-20.
SEGERBERG, Κ.
1967  'Some Modal Lo ics based on α Three-Valued Logic', Theoria 33 (1965), 53-71 (363).
1968a  'Results in Non-Classical Propositional Logic (monograph). Berlinska Boktyckeriet Lund,1968.
1968b 'Decidability of S4.1' Theoria 34 (1968) 7-20.
1968c ' Decidability of Four Modal Logics', ibid., 21-5.
1968d  'Propositional Logics Related to Heyting's and Johansson's', ibid,. 26-61.
1970  'Some Logics of Commitment and Obligation', Deontic Logic: Introductory and Systematic Readings ed. Risto Hilρinen, Dordrecht, 1970, 148-58.
SHUKLA, Α.
1970  'Decision Procedures for Lewis System S1 and Related Modal Systems' NDJFL 11 (1970),141-80.
SIMONS, L.
1953  'New Axiomatizations of S3 and S4' JSL 18 (1953), 309-16.
1962  'Α Reduction in the Number of Independent Axiom Schemata for S4' NDJFL 3 (1962), 256-8.
SOBOCINSKI, Β.
1953  'Note on a Modal System of Feys-Von Wright', The Journal of Computing Systems 1 (1953), 171-8.
1962  'Α Contribution to the Axiomatization of Lewis's System S5' NDJFL 3 (1962), 51-60.
1962a  'Α Note on the Regular and Irregular Modal Systems of Lewis' ibid. 109-13.
1962b  'On the Generalized Brouwerian Axioms', ibid. 132-8.
1963  'Α Note on Modal Systems', NDJFL 4 (1963), 155-7. 
1964a  'Modal System S4.4' NDJFL 5 (1964), 305-12.
1964b  'Family Κ of the Non-Lewis Modal Systems,' ibid. 313-18.
1964c  'Remarks about the Axiomatizations of Certain Modal Systems', ibid. 71-80.
1970  'Certain Extensions of Modal System S4' NDJFL 11 (1970), 347-68.
THOMAS, Ι.
1962  'Solutions of Five Modal Problems of Sobocinski', NDJFL 3 (1962), 199-200.
1963a  'S1° and Brouwerian Axioms', NDJFL 4 (1963) 151-2.
1963b  'Sl° and Generalized S5-Axioms', ibid. 153-4.
1963c  'Α Final Note on S1° and the Brouwerian Axioms', ibid. 231-2.
1964  'Modal Systems in the Neighbourhood of Τ', NDJFL 5 (1964) 59-61.
1964a  'Ten Modal Models' JSL 29 (1964) 125-8.
1964b  'Decision Procedures for S2° and Τ°' NDJFL 5 (1964) 319-20.
1968  'Replacement in Some Modal Systems', JSL 33 (1968), 569-70.
WAJSBERG, Μ.
1936  'Metalogische Beiträge', Wiadomosci Mat. 43 (1936), 131-68.
WHITEHEAD, A. N, and RUSSELL, B.
1910  Principia Mathematica, 3 vols., Cambridge, 1910-62. 
VON WRIGHT, G. Η.
1945  'Ueber Wahrscheinlichkeit, Eine logische and philosophische Untersuchung' (Acta Societatis Scientiarum Fennicae, N.S. Α, vol. 3 no. 11), Helsingfors, 1945.
1951a  An Essay in Modal Logic, Amsterdam, 1951. 
1951b  'Deontic Logic', Mind 60 (1951), 1-15.
1952a  'Interpretations of Modal Logic', Mind 61 (1952), 165-77.
1952b  'On the Logic of some Axiological and Epistemological Concepts', Ajatus 17 (1952), 213-34.
1953a  'Α New System of Modal Logic', Actes du ΧΙe Congres International de Philosophie, Brussels, 1953, Amsterdam, 1953, 5.59-63.
1953b  'Review of Becker's "Untersuchungen uber den Modalkalkul"', JSL 18 (1953), 327.
1959  'On the Logic of Negation', Societas Scientiarum Fennica Commentationes Physico-Mathematicae, ΧΧΙΙ, 4, 1959. .
ΖΕΜΑΝ, J. J.
1963  'Bases for S4 and S4.2 without Added Axioms', NDJFL 4 (1963), 227-30.
1964  The Graphical Logic of C. S. Peirce, doctoral dissertation, The University of Chicago, 1964.
1967a  'Α System of Implicit Quantification', JSL 32 (1967), 480-504.
1967b ' The Deduction Theorem in S4, S4.2, and S4', NDJFL 8 (1967), 56-60.
1968a  'Some Calculi with Strong Negation Primitive', JSL 33 (1968), 97-100.
1968b  'Lemmon-Style Bases for the Systems S1°-S4°', ibid. 458-61.
1968c 'The Semisubstitutivity of Strict Implication', ibid. 462-4.
1968d  'The Propositional Calculus MC and its Modal Analog', NDJFL 9 (1968), 294-8.
1969  'Decision Procedures for S3° and S4°', Archiv für mathematische Logik und Grundlagenforschung 12 (1969), 155-8.
1969a  'Modal Systems in which Necessity is "Factorable"', NDJFL 10 (1969), 247-56.
1971  'Α Study of some Systems in the Neighborhood of S4.4', NDJFL 12 (1971), 341-57.