Abstract
In this introduction to the special issue “40 years of FDE”, we offer an overview of the field and put the papers included in the special issue into perspective. More specifically, we first present various semantics and proof systems for FDE, and then survey some expansions of FDE by adding various operators starting with constants. We then turn to unary and binary connectives, which are classified in a systematic manner (affirmative/negative, extensional/intensional). First-order FDE is also briefly revisited, and we conclude by listing some open problems for future research.
Article PDF
Avoid common mistakes on your manuscript.
References
Anderson, A., and N. Belnap, Tautological entailments, Philosophical Studies 13:9–24, 1962.
Anderson, A., and N. Belnap, First degree entailments, Mathematische Annalen 149:302–319, 1963.
Anderson, A., and N. Belnap, Entailment: The Logic of Relevance and Necessity. Vol. 1, Princeton University Press, 1975.
Arieli, O., and A. Avron, Reasoning with logical bilattices, Journal of Logic, Language and Information 5:25–63, 1996.
Baaz, M., Infinite-valued Gödel logic with 0-1-projections and relativisations, in P. Hájek, (ed.), Gödel’96: Logical Foundations of Mathematics, Computer Science, and Physics, vol. 6 of Lecture Notes in Logic, Springer, 1996, pp. 23–33.
Belnap, N., How a computer should think, in G. Ryle, (ed.), Contemporary aspects of philosophy, Oriel Press, 1977, pp. 30–55.
Belnap, N., A useful four-valued logic, in J.M. Dunn, and G. Epstein, (eds.), Modern Uses of Multiple-Valued Logic, D. Reidel Publishing Co., 1977, pp. 8–37.
Béziau, J.-Y., A new four-valued approach to modal logic, Logique et Analyse 54(213):109–121, 2011.
De, M., and H. Omori, Classical negation and expansions of Belnap-Dunn logic, Studia Logica 103(4):825–851, 2015.
Dunn, J. M., Intuitive semantics for first-degree entailment and “coupled trees”, Philosophical Studies 29:149–168, 1976.
Fitting, M., Bilattices are nice things, in S. A. Pedersen V. F. Hendricks, and T. Bolander, (eds.), Self-reference, CSLI Publications, Cambridge University Press, 2002, pp. 53–77.
Font, J. M., Belnap’s four-valued logic and De Morgan lattices, Logic Journal of the IGPL 5(3):413–440, 1997.
Font, J. M., and P. Hájek, On Łukasiewicz’s four-valued modal logic, Studia Logica 70(2):157–182, 2002.
Font, J. M., and M. Rius, An abstract algebraic logic approach to tetravalent modal logics, The Journal of Symbolic Logic 65(2):481–518, 2000.
Ginsberg, M. L., Multivalued logics: A uniform approach to reasoning in AI, Computer Intelligence 4:256–316, 1988.
Goble, L., Paraconsistent modal logic, Logique et Analyse 49:3–29, 2006.
Horn, L., and H. Wansing, Negation, in Edward N. Zalta, (ed.), The Stanford Encyclopedia of Philosophy, Summer 2014 edn., http://plato.stan-ford.edu/archives/sum-2015/en-tries/negation/, 2015.
Kamide, N., and H. Wansing, Proof Theory of N4-related Paraconsistent Logics, Studies in Logic, Vol. 54, College Publications, London, 2015.
Malinowski, G., Many-valued logics, in L. Goble, (ed.), The Blackwell Guide to Philosophical Logic, Blackwell Publishing, 2001, pp. 309–335.
Marcos, J., The value of the two values, in J.-Y. Béziau, and M. E. Coniglio, (eds.), Logic without Frontiers: Festschrift for Walter Alexandre Carnielli on the occasion of his 60th birthday, College Publication, 2011, pp. 277–294.
Méndez, J. M., and G. Robles, A strong and rich 4-valued modal logic without Łukasiewicz-type paradoxes, Logica Universalis 9(4):501–522, 2015.
Méndez, J. M., and G. Robles, Strengthening Brady’s paraconsistent 4-valued logic BN4 with truth-functional modal operators, Journal of Logic, Language and Information 25(2):163–189, 2016.
Odintsov, S. P., The class of extensions of Nelson paraconsistent logic, Studia Logica 80:291–320, 2005.
Odintsov, S. P., Constructive Negations and Paraconsistency, Dordrecht: Springer-Verlag, 2008.
Odintsov, S. P., and H. Wansing, Constructive predicate logic and constructive modal logic. formal duality versus semantical duality, in V. F. Hendricks et al., (ed.), First-Order Logic Revisited, Logos Verlag, Berlin, 2004, pp. 269–286.
Odintsov, S. P., and H. Wansing, Modal logics with Belnapian truth values, Journal of Applied Non-Classical Logics 20:279–301, 2010.
Omori, H., A simple connexive extension of the basic relevant logic BD, IfCoLog Journal of Logics and their Applications 3(3):467–478, 2016.
Omori, H., From paraconsistent logic to dialetheic logic, in H. Andreas, and P. Verdée, (eds.), Logical Studies of Paraconsistent Reasoning in Science and Mathematics, Springer, 2016, pp. 111–134.
Omori, H., and K. Sano, da Costa meets Belnap and Nelson, in R. Ciuni, H. Wansing, and C. Willkommen, (eds.), Recent Trends in Philosophical Logic, Berlin, Springer, 2014, pp. 145–166.
Omori, H., and K. Sano, Generalizing functional completeness in Belnap-Dunn logic, Studia Logica 103(5):883–917, 2015.
Pietz, A., and U. Rivieccio, Nothing but the truth, Journal of Philosophical Logic 42:125–135, 2013.
Priest, G., The logic of paradox, Journal of Philosophical Logic 8:219–241, 1979.
Priest, G., Paraconsistent Logic, in D. Gabbay, and F. Guenthner, (eds.), Handbook of Philosphical Logic, vol. 6, 2 edn., Kluwer Academic Publishers, 2002, pp. 287–393.
Priest, G., An Introduction to Non-Classical Logic: From If to Is, 2 edn., Cambridge University Press, 2008.
Priest, G., Towards non-being, Oxford University Press, 2016.
Priest, G., and R. Sylvan, Simplified Semantics for Basic Relevant Logic, Journal of Philosophical Logic 21(1):217–232, 1992.
Přenosil, A., The lattice of super-Belnap logics, The Review of Symbolic Logic (Forthcoming).
Pynko, A. P., Characterizing Belnap’s logic via De Morgan’s laws, Mathematical Logic Quarterly 41(4):442–454, 1995.
Rivieccio, U., An infinity of super-Belnap logics, Journal of Applied Non-Classical Logics 22(4):319–335, 2012.
Rivieccio, U., A. Jung, and R. Jansana, Four-valued modal logic: Kripke semantics and duality, Journal of Logic Computation 27(1):155–199, 2017.
Ruet, P., Complete set of connectives and complete sequent calculus for Belnap’s logic, Tech. rep., Ecole Normale Superieure, 1996. Logic Colloquium 96, Document LIENS-96-28.
Sano, K., and H. Omori, An expansion of first-order Belnap–Dunn logic, Logic Journal of the IGPL 22(3):458–481, 2014.
Shramko, Y., and H. Wansing, Truth and Falsehood. An Inquiry into Generalized Logical Values, Trends in Logic. Vol. 36, Springer, Berlin, 2011.
Słupecki, J., A criterion of fullness of many-valued systems of propositional logic, Studia Logica 30:153–157, 1972.
van Dalen, D., Logic and Structure, 4 edn., Springer, Berlin, 2004.
Wansing, H., The Logic of Information Structures, Springer Lecture Notes in AI 681, Springer, Berlin, 1993.
Wansing, H., Negation, in L. Goble, (ed.), The Blackwell Guide to Philosophical Logic, Basil Blackwell Publishers, Cambridge/MA, 2001, pp. 415–436.
Wansing, H., Connexive Modal Logic, in R. Schmidt, I. Pratt-Hartmann, M. Reynolds, and H. Wansing, (eds.), Advances in Modal Logic. Volume 5, King’s College Publications, 2005, pp. 367–383.
Wansing, H., Constructive negation, implication, and co-implication, Journal of Applied Non-Classical Logics 18(2–3):341–364, 2008.
Wansing, H., Connexive logic, in E. N. Zalta, (ed.), The Stanford Encyclopedia of Philosophy, Spring 2016 edn., https://plato.stan-ford.edu/-archives/spr2016/entries/logic-connexive/, 2014.
Wintein, S., and R. Muskens, A Gentzen calculus for nothing but the truth, Journal of Philosophical Logic 45:451–465, 2016.
Author information
Authors and Affiliations
Corresponding author
Additional information
Edited by Hitoshi Omori and Heinrich Wansing
Rights and permissions
About this article
Cite this article
Omori, H., Wansing, H. 40 years of FDE: An Introductory Overview. Stud Logica 105, 1021–1049 (2017). https://doi.org/10.1007/s11225-017-9748-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11225-017-9748-6