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2016 | OriginalPaper | Chapter

2. Why Paraconsistent Logics?

Authors : Seiki Akama, Newton C. A. da Costa

Published in: Towards Paraconsistent Engineering

Publisher: Springer International Publishing

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Abstract

In this chapter, we briefly review paraconsistent logics which are closely related to the topics in this book. We give an exposition of their history and formal aspects. We also address the importance of applications of paraconsistent logics to engineering.

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previous chapter Introduction

next chapter An Application of Paraconsistent Logic to Physics: Complementarity

In fact, in some systems of paraconsistent logic, like da Costa’s systems \(C_n\), the “good” propositions do satisfy this principle.

Abe, J.M.: On the Foundations of Annotated Logics (in Portuguese), Ph.D. Thesis, University of São Paulo, Brazil (1992)

Abe, J.M., Akama, S., Nakamatsu, K.: Introduction to Annotated Logics. Springer, Heidelberg (2016)MATH

Akama, S.: Resolution in constructivism. Logique et Analyse 120, 385–399 (1987)MathSciNet

Akama, S.: Constructive predicate logic with strong negation and model theory. Notre Dame J. Formal Logic 29, 18–27 (1988)MathSciNetCrossRefMATH

Akama, S.: On the proof method for constructive falsity. Zeitschrift für mathematische Logik und Grundlagen der Mathematik 34, 385–392 (1988)MathSciNetCrossRefMATH

Akama, S.: Subformula semantics for strong negation systems. J. Philos. Logic 19, 217–226 (1990)MathSciNetCrossRefMATH

Akama, S.: Constructive Falsity: Foundations and Their Applications to Computer Science, Ph.D. Thesis, Keio University, Yokohama, Japan (1990)

Akama, S.: Nelson’s paraconsistent logics. Logic Logical Philos. 7, 101–115 (1999)MathSciNetCrossRefMATH

Akama, S., Abe, J.M., Nakamatsu, K.: Constructive discursive logic with strong negation. Logique et Analyse 215, 395–408 (2011)MathSciNetMATH

10.

Almukdad, A., Nelson, D.: Constructible falsity and inexact predicates. J. Symbolic Logic 49, 231–233 (1984)MathSciNetCrossRefMATH

11.

Anderson, A., Belnap, N.: Entailment: The Logic of Relevance and Necessity I. Princeton University Press, Princeton (1976)

12.

Anderson, A., Belnap, N., Dunn, J.: Entailment: The Logic of Relevance and Necessity II. Princeton University Press, Princeton (1992)MATH

13.

Arieli, O., Avron, A.: Reasoning with logical bilattices. J. Logic Lang. Inform. 5, 25–63 (1996)MathSciNetCrossRefMATH

14.

Arieli, O., Avron, A.: The value of fur values. Artif. Intell. 102, 97–141 (1998)MathSciNetCrossRefMATH

15.

Arruda, A.I.: A survey of paraconsistent logic. In: Arruda, A., da Costa, N., Chuaqui, R. (eds.) Mathematical Logic in Latin America, pp. 1–41. North-Holland, Amsterdam (1980)

16.

Asenjo, F.G.: A calculus of antinomies. Notre Dame J. Formal Logic 7, 103–105 (1966)MathSciNetCrossRefMATH

17.

Batens, D.: Dynamic dialectical logics. In: Priest, G., Routley, R. Norman, J. (eds.) Paraconsistent Logic: Essay on the Inconsistent, pp. 187–217. Philosophia Verlag, München (1989)

18.

Batens, D.: Inconsistency-adaptive logics and the foundation of non-monotonic logics. Logique et Analyse 145, 57–94 (1994)MathSciNetMATH

19.

Batens, D.: A general characterization of adaptive logics. Logique et Analyse 173–175, 45–68 (2001)MathSciNetMATH

20.

Batens, D., Mortensen, C., Priest, G., Van Bendegem, J.-P. (eds.): Frontiers of Paraconsistent Logic. Research Studies Press, Baldock (2000)

21.

Belnap, N.D.: A useful four-valued logic. In: Dunn, J.M., Epstein, G. (eds.) Modern Uses of Multi-Valued Logic, pp. 8–37. Reidel, Dordrecht (1977)

22.

Belnap, N.D.: How a computer should think. In: Ryle, G. (ed.) Contemporary Aspects of Philosophy, pp. 30–55. Oriel Press (1977)

23.

Beziau, J.-Y., Carnielli, W., Gabbay, D. (eds.): Handbook of Paraconsistency. College Publication, London (2007)MATH

24.

Blair, H.A., Subrahmanian, V.S.: Paraconsistent logic programming. Theoret. Comput. Sci. 68, 135–154 (1989)MathSciNetCrossRefMATH

25.

Carnielli, W.A., Marcos, J.: Tableau systems for logics of formal inconsistency. In: Abrabnia, H.R. (ed.), Proceedings of the 2001 International Conference on Artificial Intelligence, vol. II, pp. 848–852. CSREA Press (2001)

26.

Carnielli, W.A., Coniglio, M.E., D’Ottaviano, I.M. (eds.): Paraconsistency: The Logical Way to the Inconsistent. Marcel Dekker, New York (2002)

27.

Carnielli, W.A., Coniglio, M.E, Marcos, J.: Logics of formal inconsistency. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. 14, 2nd edn, pp. 1–93. Springer, Heidelberg (2007)

28.

da Costa, N.C.A.: On the theory of inconsistent formal systems. Notre Dame J. Formal Logic 15, 497–510 (1974)MathSciNetCrossRefMATH

29.

da Costa, N.C.A., Alves, E.H.: A semantical analysis of the calculi \(C_n\). Notre Dame J. Formal Logic 18, 621–630 (1977)MathSciNetCrossRefMATH

30.

da Costa, N.C.A., Abe, J.M., Subrahmanian, V.S.: Remarks on annotated logic. Zeitschrift für mathematische Logik und Grundlagen der Mathematik 37, 561–570 (1991)MathSciNetCrossRefMATH

31.

da Costa, N.C.A., Subrahmanian, V.S., Vago, C.: The paraconsistent logic \(P{\cal T}\). Zeitschrift für mathematische Logik und Grundlagen der Mathematik 37, 139–148 (1991)

32.

Dunn, J.M.: Relevance logic and entailment. In: Gabbay, D., Gunthner, F. (eds.) Handbook of Philosophical Logic, vol. III, pp. 117–224. Reidel, Dordrecht (1986)

33.

Fitting, M.: Bilattices and the semantics of logic programming. J. Logic Program. 11, 91–116 (1991)MathSciNetCrossRefMATH

34.

Fitting, M.: A theory of truth that prefers falsehood. J. Philos. Logic 26, 477–500 (1997)MathSciNetCrossRefMATH

35.

Ginsberg, M.: Multivalued logics. In: Proceedings of AAAI’86, pp. 243–247. Morgan Kaufman, Los Altos (1986)

36.

Ginsberg, M.: Multivalued logics: a uniform approach to reasoning in AI. Comput. Intell. 4, 256–316 (1988)

37.

Jaśkowski, S.: Propositional calculus for contradictory deductive systems (in Polish). Studia Societatis Scientiarun Torunesis, Sectio A 1, 55–77 (1948)

38.

Jaśkowski, S.: On the discursive conjunction in the propositional calculus for inconsistent deductive systems (in Polish). Studia Societatis Scientiarun Torunesis, Sectio A 8, 171–172 (1949)

39.

Kleene, S.: Introduction to Metamathematics. North-Holland, Amsterdam (1952)MATH

40.

Kripke, S.: Outline of a theory of truth. J. Philos. 72, 690–716 (1975)CrossRefMATH

41.

Kifer, M., Subrahmanian, V.S.: On the expressive power of annotated logic programs. In: Proceedings of the 1989 North American Conference on Logic Programming, pp. 1069–1089 (1989)

42.

Kotas, J.: The axiomatization of S. Jaskowski’s discursive logic. Studia Logica 33, 195–200 (1974)

43.

Łukasiewicz, J.: On 3-valued logic. In: McCall, S. (ed.) Polish Logic, pp. 16–18, Oxford University Press, Oxford, 1967

44.

Nelson, D.: Constructible falsity. J. Symbolic Logic 14, 16–26 (1949)MathSciNetCrossRefMATH

45.

Nelson, D.: Negation and separation of concepts in constructive systems. In: Heyting, A. (ed.) Constructivity in Mathematics, pp. 208–225. North-Holland, Amsterdam (1959)

46.

Priest, G.: Logic of paradox. J. Philos. Logic 8, 219–241 (1979)MathSciNetCrossRefMATH

47.

Priest, G.: Paraconsistent logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, 2nd edn, pp. 287–393. Kluwer, Dordrecht (2002)

48.

Priest, G.: In Contradiction: A Study of the Transconsistent, 2nd edn. Oxford University Press, Oxford (2006)

49.

Priest, G., Routley, R., Norman, J. (eds.): Paraconsistent Logic: Essays on the Inconsistent. Philosophia Verlag, München (1989)MATH

50.

Rico, G.O.: The annotated logics \(OP_{\rm BL}\). In: Carnielli, W., Coniglio, M., D’Ottaviano, I. (eds.) Paraconsistency: The Logical Way to the Inconsistent, pp. 411–433. Marcel Dekker, New York (2002)

51.

Routley, R., Plumwood, V., Meyer, R.K., Brady, R: Relevant Logics and Their Rivals, vol. 1. Ridgeview, Atascadero (1982)

52.

Subrahmanian, V.: On the semantics of quantitative logic programs. In: Proceeding of the 4th IEEE Symposium on Logic Programming, pp. 173–182 (1987)

53.

van Fraassen, B.C.: Facts and tautological entailment. J. Philos. 66, 477–487 (1069)CrossRef

54.

Vasil’ev, N.A.: Imaginary Logic (in Russian). Nauka, Moscow (1989)

55.

Wansing, H.: The Logic of Information Structures. Springer, Berlin (1993)CrossRefMATH

Title: Why Paraconsistent Logics?
Authors: Seiki Akama
Newton C. A. da Costa
Publisher: Springer International Publishing
Book: Towards Paraconsistent Engineering
Print ISBN: 978-3-319-40417-2

Electronic ISBN: 978-3-319-40418-9

Copyright Year: 2016
DOI: https://doi.org/10.1007/978-3-319-40418-9_2

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