Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-26T15:22:31.263Z Has data issue: false hasContentIssue false
  • English
  • Français

The pure calculus of entailment1

Published online by Cambridge University Press:  12 March 2014

Alan Ross Anderson  and
Nuel D. Belnap Jr.
Alan Ross Anderson
Affiliation:
Yale University
Nuel D. Belnap Jr.
Affiliation:
Yale University
Get access Rights & Permissions [Opens in a new window]

Extract

The “implicational paradoxes” are treated by most contemporary logicians somewhat as follows:

“The two-valued prepositional calculus sanctions as valid many of the obvious and satisfactory inferences which we recognize intuitively as valid, such as

(A→.B→C)→.A→B→.A→C,2

and

A→B→.B→C→.A→C;

it consequently suggests itself as a candidate for a formal analysis of implication.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 27 , Issue 1 , March 1962 , pp. 19 - 52
Copyright
Copyright © Association for Symbolic Logic 1962

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

1

This research was supported in part by the Office of Naval Research, Group Psychology Branch, Contract No. SAR/Nonr-609(16). Permission is granted for reproduction, translation, publication, and disposal in whole or in part by or for the U. S. Government.

References

Ackermann, Wilhelm, Begründung einer strengen Implikation, this Journal, vol. 21 (1956), pp. 113–128.Google Scholar
Anderson, Alan Ross, Completeness theorems for the systems E of entailment and EQ of entailment with quantification, Technical report no. 6, Office of Naval Research Contract no. SAR/Nonr-609(16), New Haven, 1959. (Also forthcoming in the Zeitschrift für mathematische Logik und Grundlagen der Mathematik.)Google Scholar
Anderson, Alan Ross and Belnap, Nuel D. Jr., A modification of Ackermann's “rigorous implication,” [abstract], this Journal, vol. 23 (1958), pp. 457–458.Google Scholar
Anderson, Alan Ross and Belnap, Nuel D. Jr., Modalities in Ackermann's “rigorous implication,” this Journal, vol. 24 (1959), pp. 107–111.Google Scholar
Anderson, Alan Ross, Belnap, Nuel D. Jr., and Wallace, John R., Independent axiom schemata for the pure theory of entailment, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 6 (1960), pp. 93–95.CrossRefGoogle Scholar
Marcus, Ruth Barcan, The deduction theorem in a functional calculus of first order based on strict implication, this Journal, vol. 11 (1946), pp. 115–118.Google Scholar
Marcus, Ruth Barcan, Strict implication, deducibility, and the deduction theorem, this Journal, vol. 18 (1953), pp. 234–236.Google Scholar
Baylis, Charles A., Implication and subsumption, Monist, vol. 41 (1931), pp. 392–399.CrossRefGoogle Scholar
Belnap, Nuel D. Jr., Entailment and relevance, forthcoming in this Journal (1959).Google Scholar
Belnap, Nuel D. Jr., Pure rigorous implication as a sequenzen-kalkül [abstract], this Journal, vol. 24 (1959a), pp. 282–283.Google Scholar
Belnap, Nuel D. Jr., Tautological entailments, [abstract], forthcoming in this Journal (1959b).Google Scholar
Belnap, Nuel D. Jr., A formal analysis of entailment, Technical report no. 7, Office of Naval Research Contract no. SAR/Nonr-609(16), New Haven, 1960.CrossRefGoogle Scholar
Bennett, Jonathan F., Meaning and implication, Mind, n.s. vol. 63 (1954), pp. 451–463.CrossRefGoogle Scholar
Blanshard, Brand, The nature of thought, London, 1939.Google Scholar
Boehner, Philotheus, Medieval logic, Manchester, 1952.Google Scholar
Church, Alonzo, The weak theory of implication, Kontrolliertes Denken (Festgabe zum 60 Geburtstag von Prof. W. Britzelmayr), Munich, 1951.Google Scholar
Curry, Haskell B., The interpretation of formalized implication, Theoria, vol. 25 (1959), pp. 1–26.CrossRefGoogle Scholar
Duncan-Jones, Austin E., Is strict implication the same as entailment? Analysis, vol. 2 (1935), pp. 70–78.CrossRefGoogle Scholar
Feys, Robert, Les logiques nouvelles des modalités, Revue néoscolastique de philosophie, vol. 40 (1937), pp. 517–553, and vol. 41 (1938), pp. 217–252.CrossRefGoogle Scholar
Fitch, Frederic B., Symbolic logic, New York, 1952.Google Scholar
Heyting, Arend, Die formalen Regeln der intuitionistischen Logik, Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse (1930), pp. 42–56, 57–71, 158–169.Google Scholar
Jaśkowski, Stanislaw, Trois contributions au calcul des propositions bivalent, Studia Societatis Scientlarum Torunensls, sectio A, vol. 1 no. 1 (1948), pp. 1–15.Google Scholar
Joseph, H. W. B., An introduction to logic, London, 1925.Google Scholar
Kneale, William, Truths of logic, Proceedings of the Aristotelian Society, vol. 64 (1946), pp. 207–234.CrossRefGoogle Scholar
Kripke, Saul A., The problem of entailment, [abstract], forthcoming in this Journal.Google Scholar
Lemmon, E. J., Meredith, C. A., Meredith, D., Prior, A. N., and Thomas, I., Calculi of pure strict implication (mimeographed), 1956.Google Scholar
Lewis, C. I. and Langford, C. H., Symbolic logic, New York, 1932.Google Scholar
Łukasiewicz, Jan, Elementy logiki matematycznej, mimeographed Warsaw 1929, printed Warsaw 1958.Google Scholar
Moore, G. E., External and internal relations, Proceedings of the Aristotelian Society, n.s. vol. 20 (1920), pp. 40–62.CrossRefGoogle Scholar
Shaw-Kwei, Moh, The deduction theorems and two new logical systems, Methodos, vol. 2 (1950), pp. 56–75.Google Scholar
Myhill, John, On the interpretation of the sign “⊃”, this Journal, vol. 18 (1953), pp. 60–62.Google Scholar
Nelson, E. J., Intensional relations, Mind, n.s. vol. 39 (1930), pp. 440–453.CrossRefGoogle Scholar
Smiley, T. J., Entailment and deducibility, Proceedings of the Aristotelian Society, vol. 59 (1959), pp. 233–254.CrossRefGoogle Scholar
Strawson, P. F., Introduction to logical theory, London, 1952.Google Scholar
Sugihara, Takeo, Strict implication free from implicational paradoxes, Memoirs of the Faculty of Liberal Arts, Fukui University, Series I (1955), pp. 55–59.Google Scholar
von Wright, Georg H., An essay in modal logic, Amsterdam, 1951.Google Scholar
von Wright, Georg H., Logical studies, London, 1957.Google Scholar