Linked bibliography for the SEP article "Substructural Logics" by Greg Restall

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A comprehensive bibliography on relevant logic was put together by Robert Wolff and can be found in Anderson, Belnap and Dunn 1992. The bibliography in Restall 2000 (see Other Internet Resources) is not as comprehensive as Wolff’s, but it does include material up to the present day.

Books on Substructural Logic and Introductions to the Field

  • Anderson, A.R., and Belnap, N.D., 1975, Entailment: The Logic of Relevance and Necessity, Princeton, Princeton University Press, Volume I. (Scholar)
  • Anderson, A.R., Belnap, N.D. Jr., and Dunn, J.M., 1992, Entailment, Volume II, Princeton, Princeton University Press
    [This book and the previous one summarise the work in relevant logic in the Anderson–Belnap tradition. Some chapters in these books have other authors, such as Robert K. Meyer and Alasdair Urquhart.] (Scholar)
  • Dunn, J. M. and Restall, G., 2000, “Relevance Logic” in F. Guenthner and D. Gabbay (eds.), Handbook of Philosophical Logic second edition; Volume 6, Kluwer, pp 1–136.
    [A summary of work in relevant logic in the Anderson–Belnap tradition.] (Scholar)
  • Galatos, N., P. Jipsen, T. Kowalski, and H. Ono, 2007, Residuated Lattices: An Algebraic Glimpse at Substructural Logics (Studies in Logic: Volume 151), Amsterdam: Elsevier, 2007. (Scholar)
  • Mares, Edwin D., 2004, Relevant Logic: a philosophical interpretation Cambridge University Press.
    [An introduction to Relevant Logic, proposing an information theoretic understanding of the ternary relational semantics.] (Scholar)
  • Moortgat, Michael, 1988, Categorial Investigations: Logical Aspects of the Lambek Calculus Foris, Dordrecht.
    [Another introduction to the Lambek calculus.] (Scholar)
  • Morrill, Glyn, 1994, Type Logical Grammar: Categorial Logic of Signs Kluwer, Dordrecht
    [An introduction to the Lambek calculus.] (Scholar)
  • Paoli, Francesco, 2002, Substructural Logics: A Primer Kluwer, Dordrecht
    [A general introduction to substructural logics.] (Scholar)
  • Read, S., 1988, Relevant Logic, Oxford: Blackwell.
    [An introduction to Relevant Logic motivated by considerations in the theory of meaning. Develops a Lemmon-style proof theory for the Relevant Logic \(\mathbf{R}\).] (Scholar)
  • Restall, Greg, 2000, An Introduction to Substructural Logics, Routledge. (online précis)
    [A general introduction to the field of substructural logics.] (Scholar)
  • Routley, R., Meyer, R.K., Plumwood, V., and Brady, R., 1983, Relevant Logics and their Rivals, Volume I, Atascardero, CA: Ridgeview.
    [Another distinctive account of relevant logic, this time from an Australian philosophical perspective.] (Scholar)
  • Schroeder-Heister, Peter, and Došen, Kosta, (eds), 1993, Substructural Logics, Oxford University Press.
    [An edited collection of essays on different topics in Substructural Logics, from different traditions in the field.] (Scholar)
  • Troestra, Anne, 1992, Lectures on Linear Logic, CSLI Publications
    [A quick, easy-to-read introduction to Girard’s linear logic.] (Scholar)

Other Works Cited

  • Ackermann, Wilhelm, 1956, “Begründung Einer Strengen Implikation,” Journal of Symbolic Logic, 21: 113–128. (Scholar)
  • Avron, Arnon, 1988, “The Semantics and Proof Theory of Linear Logic,” Theoretical Computer Science, 57(2–3): 161–184. (Scholar)
  • Gianluigi Bellin, Martin Hyland, Edmund Robinson, and Christian Urban, 2006, “Categorical Proof Theory of Classical Propositional Calculus,” Theoretical Computer Science, 364: 146–165. (Scholar)
  • Church, Alonzo, 1951, “The Weak Theory of Implication,” in Kontrolliertes Denken: Untersuchungen zum Logikkalkül und zur Logik der Einzelwissenschaften, A. Menne, A. Wilhelmy and H. Angsil (eds.), Kommissions-Verlag Karl Alber, 22–37. (Scholar)
  • Curry, Haskell B., 1977, Foundations of Mathematical Logic, New York: Dover (originally published in 1963). (Scholar)
  • Dunn, J.M., 1991, “Gaggle Theory: An Abstraction of Galois Connections and Residuation with Applications to Negation and Various Logical Operations,” in Logics in AI, Proceedings European Workshop JELIA 1990 (Lecture notes in Computer Science, Volume 476), Berlin: Springer-Verlag. (Scholar)
  • Dunn, J.M., 1993, “Star and Perp,” Philosophical Perspectives, 7: 331–357. (Scholar)
  • Fine, K., 1989, “Incompleteness for Quantified Relevance Logics,” in J. Norman and R. Sylvan (eds.), Directions in Relevant Logic, Dordrecht: Kluwer, pp. 205–225. (Scholar)
  • Geach, P. T., 1955, “On Insolubilia,” Analysis, 15: 71–72. (Scholar)
  • Gentzen, Gerhard, 1935, “Untersuchungen über das logische Schließen,” Mathematische Zeitschrift, 39: 176–210 and 405–431. [An English translation is found in Gentzen 1969.] (Scholar)
  • Gentzen, Gerhard, 1969, The Collected Papers of Gerhard Gentzen, M. E. Szabo (ed.), Amsterdam: North Holland, 1969. (Scholar)
  • Goldblatt, R., and E. Mares, 2006, “An Alternative Semantics for Quantified Relevant Logic,” Journal of Symbolic Logic, 71(1): 163–187. (Scholar)
  • Girard, Jean-Yves, 1987, “Linear Logic,” Theoretical Computer Science, 50: 1–101. (Scholar)
  • Lambek, Joachim, 1958, “The Mathematics of Sentence Structure,” American Mathematical Monthly, 65: 154–170. (Scholar)
  • Lambek, Joachim, 1961, “On the Calculus of Syntactic Types, ” in Structure of Language and its Mathematical Aspects (Proceedings of Symposia in Applied Mathematics, XII), R. Jakobson (ed.), Providence, RI: American Mathematical Society. (Scholar)
  • Moh Shaw-Kwei, 1950, “The Deduction Theorems and Two New Logical Systems,” Methodos, 2: 56–75. (Scholar)
  • Moortgat, Michael, 1995, “Multimodal Linguistic Inference,” Logic Journal of the IGPL, 3: 371–401. (Scholar)
  • Ono, Hiroakira, 2003, “Substructural Logics and Residuated Lattices – an Introduction,” in V. Hendricks and J. Malinowski (eds.), Trends in Logic: 50 Years of Studia Logica, Dordrecht: Kluwer, 2003, pp. 193–228. (Scholar)
  • Routley, R., 1980. “Problems and Solutions in Semantics in Quantified Relevant Logics,” in A. Arruda, R. Chuaqui, and N.C.A. Da Costa (eds.), Mathematical Logic in Latin America, Amsterdam: North Holland, 1980, pp. 305–340. (Scholar)

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