Supplement to Paraconsistent Logic

Bibliography Sorted by Topic

A. For Paraconsistency in general

  • Priest, Graham, Richard Routley, and Jean Norman (eds.), 1989, Paraconsistent Logic: Essays on the Inconsistent, München: Philosophia Verlag.
  • Priest, Graham, 2002, “Paraconsistent Logic”, in Handbook of Philosophical Logic, second edition, volume 6, Dov M. Gabbay and Franz Guenthner (eds.), Dordrecht: Kluwer Academic Publishers, pp. 287–393.

B. For Inconsistent but Non-Trivial Theories

  • Brown, Bryson and Graham Priest, 2004, “Chunk and Permeate: A Paraconsistent Inference Strategy. Part 1: The Infinitesimal Calculus”, Journal of Philosophical Logic, 33(4): 379–388. doi:10.1023/B:LOGI.0000036831.48866.12
  • –––, 2015, “Chunk and Permeate II: Bohr’s Hydrogen Atom”, European Journal for Philosophy of Science, 5(3): 297–314.
  • McGinnis, Nicholas D., 2013, “The Unexpected Applicability of Paraconsistent Logic: A Chomskyan Route to Dialetheism”, Foundations of Science, 18(4): 625–640. doi:10.1007/s10699-012-9294-7
  • Michael, Michaelis, 2016, “On a ‘most telling’ Argument for Paraconsistent Logic”, Synthese, 193(10): 3347–3362. doi:10.1007/s11229-015-0935-6

C. For Dialetheism

  • Priest, Graham, 1987, In Contradiction: A Study of the Transconsistent, Dordrecht: Martinus Nijhoff; second edition, Oxford: Oxford University Press, 2006.
  • Priest, Graham, J.C. Beall and Bradley Armour-Garb (eds.), 2004, The Law of Non-Contradiction, Oxford: Oxford University Press. doi:10.1093/acprof:oso/9780199265176.001.0001

D. For Automated Reasoning

  • Abe, Jair Minoro, Seiki Akama, and Kazumi Nakamatsu (eds.), 2015, Introduction to Annotated Logics: Foundations for Paracomplete and Paraconsistent Reasoning (Intelligent Systems Reference Library 88), Dordrecht: Springer. doi:10.1007/978-3-319-17912-4
  • Akama, Seiki (ed.), 2016, Towards Paraconsistent Engineering (Intelligent Systems Reference Library 110), Dordrecht: Springer. doi:10.1007/978-3-319-40418-9
  • Belnap, Nuel D., Jr., 1992, “A Useful Four-valued Logic: How a computer should think”, Entailment: The Logic of Relevance and Necessity, Volume II, Alan Ross Anderson, Nuel D. Belnap, Jr, and J. Michael Dunn, Princeton: Princeton University Press; first appeared as “A Useful Four-valued Logic”, Modern Use of Multiple-valued Logic, J. Michael Dunn and George Epstein (eds.), Dordrecht: D. Reidel, 1977: 5–37, and “How a Computer Should Think”, Contemporary Aspects of Philosophy, Gilbert Ryle (ed.), Oriel Press, 1977: 30–. doi:10.1007/978-94-010-1161-7_2
  • Besnard, Philippe and Anthony Hunter (eds.), 1998, Reasoning with Actual and Potential Contradictions, (Handbook of Defeasible Reasoning and Uncertainty Management Systems, volume 2), Dordrecht: Kluwer Academic Publishers. doi:10.1007/978-94-017-1739-7
  • Kamide, Norihiro and Heinrich Wansing, 2012, “Proof Theory of Nelson’s Paraconsistent Logic: A Uniform Perspective”, Theoretical Computer Science, 415: 1–38. doi:10.1016/j.tcs.2011.11.001

E. For Belief Revision

  • Girard, Patrick and Koji Tanaka, 2016, “Paraconsistent Dynamics”, Synthese, 193(1): 1–14. doi:10.1007/s11229-015-0740-2
  • Priest, Graham, 2001, “Paraconsistent Belief Revision”, Theoria, 67(3): 214–228. doi:10.1111/j.1755-2567.2001.tb00204.x
  • Restall, Greg and John Slaney, 1995, “Realistic Belief Revision”, Proceedings of the Second World Conference in the Fundamentals of Artificial Intelligence, M. De Glas and Z. Pawlak (eds.), Paris: Angkor, pp. 367–378.
  • Tanaka, Koji, 2005, “The AGM Theory and Inconsistent Belief Change”, Logique et Analyse, 48(189–192): 113–150. [Tanaka 2005 available online]

F. For Mathematical Significance

  • Beall, Jc, 2009, Spandrels of Truth, Oxford: Oxford University Press. doi:10.1093/acprof:oso/9780199268733.001.0001
  • Brady, Ross T., 1989, “The Non-Triviality of Dialectical Set Theory”, in Paraconsistent Logic: Essays on the Inconsistent, Graham Priest, Richard Routley and Jean Norman (eds.), München: Philosophia Verlag, pp. 437–471.
  • –––, 2006, Universal Logic, Stanford, CA: CSLI Publications.
  • Libert, Thiery, 2005, “Models for a Paraconsistent Set Theory”, Journal of Applied Logic, 3(1): 15–41. doi:10.1016/j.jal.2004.07.010
  • McKubre-Jordens, Maarten and Zach Weber, 2011, “Real Analysis in Paraconsistent Logic”, Journal of Philosophical Logic, 41(5): 901–922. doi:10.1007/s10992-011-9210-6
  • Mortensen, Chris, 1995, Inconsistent Mathematics, Dordrecht: Kluwer Academic Publishers.
  • Omori, Hitoshi, 2015, “Remarks on Naive Set Theory Based on LP”, Review of Symbolic Logic, 8(2): 279–295. doi:10.1017/S1755020314000525
  • Priest, Graham, 2003, “Inconsistent Arithmetic: Issues Technical and Philosophical”, in Trends in Logic: 50 Years of Studia Logica (Studia Logica Library, volume 21), V.F. Hendricks and J. Malinowski (eds.), Dordrecht: Kluwer Academic Publishers, pp. 273–99.
  • Verdée, Peter, 2013, “Strong, Universal and Provably Non-trivial Set Theory by Means of Adaptive Logic”, Logic Journal of the IGPL, 21(1): 108–125. doi:10.1093/jigpal/jzs025
  • Weber, Zach, 2010b, “Transfinite Numbers in Paraconsistent Set Theory”, Review of Symbolic Logic, 3(1): 71–92. doi:10.1017/S1755020309990281
  • –––, 2012, “Transfinite Cardinals in Paraconsistent Set Theory”, Review of Symbolic Logic, 5(2): 269–293. doi:10.1017/S1755020312000019

G. For Vagueness

  • Hyde, Dominic, 1997, “From Heaps and Gaps to Heaps of Gluts”, Mind, 106(424): 641–660. doi:10.1093/mind/106.424.641
  • Ripley, David, 2011, “Contradictions at the Borders”, in R. Nouwen, R. van Rooij, U. Sauerland & H.-C. Schmitz (eds.), Vagueness in Communication, Dordrecht: Springer, pp. 169–188. doi:10.1007/978-3-642-18446-8_10
  • Weber, Zach, 2010a, “A Paraconsistent Model of Vagueness”, Mind, 119(476): 1025–1045. doi:10.1093/mind/fzq071

H. For a History of ex contradictione quodlibet

  • Sylvan, Richard, 2000, “A Preliminary Western History of Sociative Logics”, in Sociative Logics and Their Applications: Essays by the late Richard Sylvan, Dominic Hyde and Graham Priest (eds.), Aldershot: Ashgate Publishers.

I. For Modern History of Paraconsistent Logic

  • Arruda, Ayda I., 1989, “Aspects of the Historical Development of Paraconsistent Logic”, in Paraconsistent Logic: Essays on the Inconsistent, Graham Priest, Richard Routley and Jean Norman (eds.), München: Philosophia Verlag, pp. 99–130.
  • Priest, Graham, 2007, “Paraconsistency and Dialetheism”, in Handbook of the History of Logic, Volume 8, D. Gabbay and J. Woods (eds.), Amsterdam: North Holland, pp. 129–204.

J. For the Systems of Paraconsistent Logic in general

  • Brown, Bryson, 2002, “On Paraconsistency”, in A Companion to Philosophical Logic, Dale Jacquette (ed.), Oxford: Blackwell, pp. 628–650. doI:10.1002/9780470996751.ch40

K. For Discussive Logic

  • Jaśkowski, Stanisław, 1948 [1969], “Rachunek zdań dla systemów dedukcyjnych sprzecznych”, Studia Societatis Scientiarum Torunensi (Sectio A), 1(5): 55–77; an English translation appeared as “Propositional Calculus for Contradictory Deductive Systems”, Studia Logica, 24 (1969): 143–157.
  • –––, 1949 [1999], “O koniunkcji dyskusyjnej w rachunku zdań dla systemów dedukcyjnych sprzecznych”, Studia Societatis Scientiarum Torunensis (Sectio A), 1 (8): 171–172; an English translation appeared as “On the Discussive Conjunction in the Propositional Calculus for Inconsistent Deductive Systems”, Logic and Logical Philosophy, 7(1999): 57–59.
  • da Costa, Newton C.A. and L. Dubikajtis, 1977, “On Jaśkowski’s Discussive Logic”, in Non-Classical Logics, Model Theory and Computability (Studies in Logic and the Foundations of Mathematics 89), Ayda I. Arruda, Newton C.A. da Costa and R. Chuaqui (eds.), Amsterdam: North-Holland Publishing Company, pp. 37–56. doi:10.1016/S0049-237X(08)70644-X

L. For Non-Adjunctive Systems

  • Rescher, Nicholas and Ruth Manor, 1970, “On Inference from Inconsistent Premises”, Theory and Decision, 1(2): 179–217. doi:10.1007/BF00154005

M. For Preservationism

  • Schotch, P.K. and R.E. Jennings, 1980, “Inference and Necessity”, Journal of Philosophical Logic, 9(3): 327–340. doi:10.1007/BF00248398
  • Schotch, Peter, Bryson Brown, and Raymond Jennings (eds.), 2009, On Preserving: Essays on Preservationism and Paraconsistent Logic, Toronto: University of Toronto Press.

N. For Adaptive Logics

  • Batens, Diderik, 2001, “A General Characterization of Adaptive Logics”, Logique et Analyse, 44(173–175): 45–68. [Batens 2001 available online]
  • –––, 2007, “A Universal Logic Approach to Adaptive Logics”, Logica Universalis, 1(1): 221–242. doi:10.1007/s11787-006-0012-5

O. For Logics of Formal Inconsistency

  • Carnielli, Walter A. and Marcelo Esteban Coniglio, 2016, Paraconsistent Logic: Consistency, Contradiction and Negation, Dordrecht: Springer. doi:10.1007/978-3-319-33205-5
  • Carnielli, Walter A., Marcelo E. Coniglio, and João Marcos, 2007, “Logics of Formal Inconsistency”, in Handbook of Philosophical Logic, Volume 14 (Second Edition), Dov M. Gabbay and Franz Guenthner (eds.), Berlin: Springer, pp. 15–107. doi:10.1007/978-1-4020-6324-4_1
  • da Costa, Newton C.A., 1974, “On the Theory of Inconsistent Formal Systems”, Notre Dame Journal of Formal Logic, 15(4): 497–510. doi:10.1305/ndjfl/1093891487

P. For Many-Valued Logics

  • Asenjo, F.G., 1966, “A Calculus of Antinomies”, Notre Dame Journal of Formal Logic, 7(1): 103–105. doi:10.1305/ndjfl/1093958482
  • Dunn, J. Michael, 1976, “Intuitive Semantics for First Degree Entailment and ‘Coupled Trees’”, Philosophicl Studies, 29(3): 149–68. doi:10.1007/BF00373152
  • Priest, Graham, 1979, “The Logic of Paradox”, Journal of Philosophical Logic, 8(1): 219–241. doi:10.1007/BF00258428

Q. For Relevant Logics

  • Anderson, Alan Ross and Nuel D. Belnap, 1975, Entailment: The Logic of Relevance and Necessity, Volume 1, Princeton: Princeton University Press.
  • Anderson, Alan Ross, Nuel D. Belnap, and J. Michael Dunn, 1992, Entailment: The Logic of Relevance and Necessity, Volume 2, Princeton: Princeton University Press.
  • Brady, Ross T. (ed.), 2003, Relevant Logics and Their Rivals, Volume 2, Aldershot: Ashgate.
  • Dunn, J. Michael and Greg Restall, 2002, “Relevance Logic”, Handbook of Philosophical Logic, Volume 6, second edition, Dov M. Gabbay and Franz Guenthner (eds.), Dordrecht: Kluwer Academic Publishers, pp. 1–136.
  • Routley, Richard, Val Plumwood, Robert K. Meyer, and Ross T. Brady, 1982, Relevant Logics and Their Rivals, Volume 1, Ridgeview: Atascadero.

R. World Congress of Paraconsistency Volumes

  • [First Congress] Batens, Diderik, Chris Mortensen, Graham Priest, and Jean-Paul van Bendegem (eds.), 2000, Frontiers of Paraconsistent Logic (Studies in Logic and Computation 8), Baldock, England: Research Studies Press.
  • [Second Congress] Carnielli, Walter A., M. Coniglio, and Itala Maria Lof D’ottaviano (eds.), 2002, Paraconsistency: the Logical Way to the Inconsistent (Lecture Notes in Pure and Applied Mathematics: Volume 228), Boca Raton: CRC Press.
  • [Third Congress] Beziau, Jean-Yves, Walter A. Carnielli, and Dov M. Gabbay (eds.), 2007, Handbook of Paraconsistency (Studies in Logic 9), London: College Publications.
  • [Fourth Congress] Tanaka, Koji, Francesco Berto, Edwin Mares, and Francesco Paoli (eds.), 2013, Paraconsistency: Logic and Applications (Logic, Epistemology, and the Unity of Science 26), Dordrecht: Springer. doi:10.1007/978-94-007-4438-7
  • [Fifth Congress] Beziau, Jean-Yves, Mihir Chakraborty, and Soma Dutta (eds.), 2015, New Directions in Paraconsistent Logic, Dordrecht: Springer. doi:10.1007/978-81-322-2719-9

S. Other Works Cited

  • Andreas, Holger and Peter Verdée, 2016, Logical Studies of Paraconsistent Reasoning in Science and Mathematics (Trends in Logic 45), Dordrecht: Springer. doi:10.1007/978-3-319-40220-8
  • Arruda, Ayda I., 1977, “On the Imaginary Logic of N.A. Vasil’év”, in Non-Classical Logic, Model Theory and Computability (Studies in Logic and the Foundations of Mathematics 89), Ayda I. Arruda, Newton da Costa and R. Chuaqui (eds.), Amsterdam: North Holland, pp. 3–24. doi:10.1016/S0049-237X(08)70642-6
  • Asmus, Conrad, 2012, “Paraconsistency on the Rocks of Dialetheism”, Logique et Analyse, 55(217): 3–21. [Asmus 2012]
  • Avron, Arnon and Iddo Lev, 2005, “Non-deterministic Multi-valued Structures”, Journal of Logic and Computation, 15(3): 241–261.
  • Chomsky, Noam, 1995, The Minimalist Program, Cambridge, MA: MIT Press.
  • da Costa, Newton C.A. and E.H. Alves, 1977, “Semantical Analysis of the Calculi \({\bf C}_{n}\)”, Notre Dame Journal of Formal Logic, 18(4): 621–630. doi:10.1305/ndjfl/1093888132
  • da Costa, Newton C.A., V.S. Subrahmanian, and Carlo Vago, 1997, “The Paraconsistent Logics \(\mathrm{P}\mathcal{T}\)”, Zeitschrift für Mathematische Logic und Grundlangen der Mathematik, 37(9–12): 139–148. doi:10.1002/malq.19910370903
  • Dunne, John D., 2004, Foundations of Dharmakīrti’s Philosophy, Boston: Wisdom Publications.
  • Fine, Kit, 1974, “Models for Entailment”, Journal of Philosophical Logic, 3(4): 347–372. doi:10.1007/BF00257480
  • Halldén, Sören, 1949, The Logic of Nonsense, Uppsala: A.-B. Lundequistska Bokhandeln.
  • Loparic, A., 1977, “Une étude semantique de quelques calculs propositionnels”, Comptes Rendus Hebdomadaires des Séances de l’Academie des Sciences, 284: 835–838.
  • Łukasiewicz, Jan, 1951, Aristotle’s Syllogistic: From the Standpoint of Modern Formal Logic, Oxford: Oxford University Press.
  • Mares, Edwin D., 2004, “‘Four-Valued’ Semantics for the Relevant Logic R”, Journal of Philosophical Logic, 33(3): 327–341. doi:10.1023/B:LOGI.0000031375.18295.30
  • Martin, Christopher J., 1986, “William’s Machine”, Journal of Philosophy, 83(10): 564–572. doi:10.2307/2026432
  • –––, 1987, “Embarrassing Arguments and Surprising Conclusions in the Development Theories of the Conditional in the Twelfth Century”, Gilbert De Poitiers Et Ses Contemporains, J. Jolivet, A. De Libera (eds.), Naples: Bibliopolis, pp. 377–401.
  • –––, 1996, “Impossible Positio as the Foundation of Metaphysics or, Logic on the Scotist Plan?”, Vestigia, Imagines, Verba: Semiotics and Logic in Medieval Theological Texts, C. Marmo (ed.), Turnhout: Brepols, pp. 255–276.
  • Priest, Graham and Richard Sylvan, 1992, “Simplified Semantics for Basic Relevant Logics”, Journal of Philosophical Logic, 21(2): 217–232. doi:10.1007/BF00248640
  • Restall, Greg, 1993, “Simplified Semantics for Relevant Logics (and some of their rivals)”, Journal of Philosophical Logic, 22(5): 481–511. doi:10.1007/BF01349561
  • –––, 1995, “Four-Valued Semantics for Relevant Logics (and some of their rivals)”, Journal of Philosophical Logic, 24(2): 139–160. doi:10.1007/BF01048529
  • Routley, Richard and Robert K. Meyer, 1993, “Semantics of Entailment”, Truth, Syntax and Modality, H. Leblanc (ed.), Amsterdam: North Holland, pp. 194–243.
  • Routley, R. and V. Routley, 1972, “Semantics of First Degree Entailment”, Noûs, 6(4): 335–359. doi:10.2307/2214309
  • Tanaka, Koji, 2003, “Three Schools of Paraconsistency”, The Australasian Journal of Logic, 1: 28–42.
  • Tillemans, Tom J.F., 1999, Scripture, Logic, Language: Essays on Dharmakīrti and His Tibetan Successors, Boston: Wisdom Publications.
  • Urquhart, Alasdair, 1972, “Semantics for Relevant Logics”, Journal of Symbolic Logic, 37(1): 159–169. doi:10.2307/2272559

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