Skip to main content
SpringerLink
Log in

Non-Classical Negation in the Works of Helena Rasiowa and Their Impact on the Theory of Negation

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

The paper is devoted to the contributions of Helena Rasiowa to the theory of non-classical negation. The main results of Rasiowa in this area concerns

–constructive logic with strong (Nelson) negation,

–intuitionistic negation and some of its generalizations: minimal negation of Johansson and semi-negation.

We discuss also the impact of Rasiowa works on the theory of non-classical negation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Akama, S., ‘On the proof method for constructive falsity’, Z. Math. Logik Grundlagen Math., 34 (1988), 385–392.

    Google Scholar 

  2. Akama, S., ‘Constructive predicate logic with strong negation and model theory’, Notre Dame J. Form. Logic, 29 (1989), 18–27.

    Google Scholar 

  3. Akama, S., ‘Subformula semantics for strong negation systems’, J. Phil. Logic, 19 (1990), 217–226.

    Article  Google Scholar 

  4. Akama, S., ‘Tableaux for logic programming with strong negation’, in D.Galmiche (ed.), TABLEAUX'97: Automated Reasoning with Analitic Tableaux and Related Methods, Springer, Berlin, 1997, pp. 31–42.

    Google Scholar 

  5. Akama, S., ‘On Constructive Modality’, in S. Akama (ed.), Logic, Language and Computation, Kluwer Academic Publishers, Dordrecht, 1997, pp. 143–158.

    Google Scholar 

  6. Almukdad, A., and D. Nelson, ‘Constructible Falsity and Inexact Predicates’, J. Symbolic Logic, 49 (1984), 231-233.

    Google Scholar 

  7. Arieli, O., and A. Avron, ‘Reasoning with logical bilattices’, Journal of Logic Language and Information, 5 (1996), 25–63.

    Google Scholar 

  8. Arieli, O., and A. Avron, ‘The Value of the Four Values’, newblock Artificial Intelligence, 102 (1998), 97–141.

    Google Scholar 

  9. Avron, A., ‘Natural 3-valued Logics’, Journalof Symbolic Logic, 56 (1991), 276–294.

    Google Scholar 

  10. Avron, A., ‘Negation: two points of view’, in D. Gabbay and H. Wansing (eds.), What is Negation? Applied Logic Series, vol. 13 (1999), 3–22.

  11. Avron, A., ‘On Negation, Completeness and Consistency’, in D. Gabbay and F. Guenther (eds.), Handbook of Philosophical Logic, vol. 9, Kluwer Academic Publishers, 2002, pp. 287–319.

  12. Avron, A., ‘Tableaux with four Signs as a Unified Framework’, in M.C. Mayer and F. Piri (eds.), Proceedings of TABLEAUX-2003, LNAI No 2796, Springer, 2003, pp. 4–16.

  13. Avron, A., ‘Combining Classical Logic, Paraconsistency and Ralevance’, Journal of Applied Logic, 3 (2005), 133–160.

    Google Scholar 

  14. Avron, A., ‘Non-deterministic Matrices and Modular semantics of Rules’, in J.Y. Beziau (ed.), Logica Universalis, Birkhüser Verlag, 2005, pp. 149–167.

  15. Avron, A., ‘Non-deterministic Semantics for Paraconsistent C-systems’, in L. Godo (ed.), Proceedings of 8-th ECQARU, LNAI No 3571, Springer, 2005, pp. 625–637.

  16. Avron, A., ‘A non-deterministic view of non-classical negations’, Studia Logica 80, No 2–3 (2005), 159–194.

    Google Scholar 

  17. Avron, A., and B. Konikowska, ‘Multi-valued Calculi for Logics Based on Non-determinism’, Logical Journal of the IJPL, 13 (2005), 365–387.

    Google Scholar 

  18. Belnap, N.D., ‘How Computers Should Think’. in G. Ryle (ed.) Contemporary Aspects of Philosophy, Oriel Press, Stockfield, England, 1977, pp. 30–56.

    Google Scholar 

  19. Belnap, N.D., ‘A useful four-valued logic’. in G. Epstein and M. Dunn (eds.), Modern Use of Multiple-Valued Logic, Reidel, Dordrecht, 1977, pp. 7–37.

    Google Scholar 

  20. Bialinicki-Birula, A., and H. Rasiova, ‘On the representation of quasi-Boolean algebras’, Bull. Ac. Pol. Sci., 5 (1957), 259–261.

    Google Scholar 

  21. Bialinicki-Birula, A., and H. Rasiova, ‘On constructible falsity in constructive logic with strong negation’, Colloquium Mathematicum, 6 (1958), 287–310.

    Google Scholar 

  22. Brignole, D., and A.Monteiro, ‘Caracterisation des algèbres des Nelson par des egalitès’, I, II. Proc. Japan. Ac., 43 (1967), 279–283, 284–285.

    Article  Google Scholar 

  23. Carnieli, W.A., and J.Markos, ‘A taxonomy of C-systems’. in W. A. Carnieli, M.E. Coniglio, and I.L.M. D'Otaviano (eds.), Paraconsistency — the logical way to be inconsistent, Lecture notes in pure and applied Mathematics, Marcell Dekker, 2002, pp. 1–94.

  24. Cignoli, R., ‘The class of Kleene algebras satisfying interpolation preperty and Nelson algebras’. Algebra Universalis, 23 (1986), 262–292.

    Google Scholar 

  25. Cignioli, R., and M.S. de Gallego, ‘Dualities for some De Morgan algebras with operators and Lukasiewicz algebras’. J. Austral. Math. Soc., (Ser. A), 83 (1983), 377–393.

    Article  Google Scholar 

  26. Cleave, J.P., ‘The notion of validity in logical systems with inexact predicates’. British J. Philos. Sci., 21 (1970), 269–274.

    Google Scholar 

  27. Cleave, J.P., ‘The notion of logical consequence in the logic of inexact predicates’. Z. Mtah. Logik Grundlagen Math., 20 (1974), 307–324.

    Google Scholar 

  28. sc Cleave, J.P., ‘Logic and inexactness. Stephan Körner — Philosophical analysis and reconstruction’. Contributions to Philosophy, Nijhooff Int. Philos. Ser. 28 (1987), 137–167.

    Google Scholar 

  29. Curry, H.B., ‘A theory of formal deducibility’, Notre Dame Mathematical Lectures, 6, Notre Dame, 1950.

  30. Curry, H.B., ‘On the definition of negation by a fixed proposition in the inferential calculus’, J. Symb. Logic, 17 (1952), 98–104.

    Google Scholar 

  31. H. B. Curry, ‘The system LD’, J. Symb. Logic, 17 (1952), 35–42.

    Google Scholar 

  32. Došen, K., ‘Negative modal operators in intuitionistic logic’, Publications de L'Institu Mathematique (N.S) 35(49) (1984), 3–14.

    Google Scholar 

  33. Došen, K., ‘Negation as a modal operator’, Reports on Mathematical Logic, 20 (1986), 15–27.

    Google Scholar 

  34. Došen, K., ‘Negation and Impossibility’, in J. Perzanowski (ed.), Essays on Philisophy and Logic, Jagielonian University Press, Cracow, 1987, 85–91.

    Google Scholar 

  35. Došen, K., ‘Negation in the light of modal logic’, in D.Gabbay and H. Wansing (eds.), What is Negation?, Kluwer, Dordrecht, 1999, 77–86.

    Google Scholar 

  36. Dunn, J.M., ‘Partiality and its Dual’, Studia Logica 66, No. 1(1980), 5–40.

    Google Scholar 

  37. Dunn, J.M., ‘Gaggle Theory: An Abstraction of Galois Connections and Residuation with Applications to Negations and Various Logical Operations’, LNCS, No 478, 1990, 31–51.

  38. Dunn, J.M., ‘Generalized ortho negation’, in H. Wansing (ed.), Negation, A notion in Focus, Walter de Gruyer. Berlin. New York, 1996, pp. 3–26.

    Google Scholar 

  39. Dunn, J.M., ‘A comparative study of various model-theoretic treatments of negation: a history of formal negation’, in D. Gabbay and H. Wansing (eds.), What is Negation?, Applied Logic Series 13, Kluwer Academic Publishers, Dordrecht, 1999, pp. 23–51.

    Google Scholar 

  40. Dunn, J.M., and Chunlai Zhou, ‘Negation in the Context of Gagle Theory’, Studia Logica, 80, vol. 2–3 (2005), 235–264.

    Google Scholar 

  41. Fidel, M.M., ‘An algebraic study of a propositional system of Nelson’, in Mathematical Logic, Proc. of the First Brasilian Conference, Campinas 1977, Lecture Notes in pure Appl. Math., 39 (1978), 99–117.

    Google Scholar 

  42. Fidel, M.M, ‘An algebraic study of logic with constructive negation’, Proc. of the Third Brazilian Conf. on Math. Logic, Recife 1979, 1980, pp. 119–29.

  43. Fitting, M., ‘Bilattices in logic programming’, in G. Epstein (ed.), Proc. of the 20th Int. Symp. on Multyple-Valued Logic, IEEE Press, 1990, pp. 238–246.

  44. Fitting, M., ‘Bilattices and the semantics of logic programming’, Journal of logic programming, 11 (2) (1991), 91–116.

    Google Scholar 

  45. Gabbay, D., and H. Wansing, ‘Negation in Structured Consequence Relations’, in A. Fuhrmann and H. Rott (eds.), Logic, Action and Information, de Gruyter, Berlin, 1995, pp. 328–350.

    Google Scholar 

  46. Gargov, G., ‘Knowledge, uncertainty and ignorance in logic: bilattices and beyond’, Journal of Applied Non-Classical Logics, 9 (1999), 195–283.

    Google Scholar 

  47. Gelfond, M., and V. Lifschitz, ‘Classical negation in logic programs and disjunctive databases’, New Generation Computing, 9 (1991), 365–385.

    Article  Google Scholar 

  48. Ginsberg, M. L., ‘Multiple-valued logics: a uniform approach to reasoning in AI’, Computer Intelligence, 4 (1988), 256–316.

    Google Scholar 

  49. Goldblatt, R.I, ‘Decidability of some extensions of J’, Z. für Math. Logic und Gründ. Math., 20 (1974), 203–206.

    Google Scholar 

  50. Goranko, V.F, ‘Propositional logics with strong negation and the Craig interpolation theorem’, C. R. Acad. Bulg. Sci., 38 (1985), 825–827.

    Google Scholar 

  51. Goranko, V., ‘The Craig Interpolation Theorem for Propositional Logics with StrongNegation’, Studia Logica, 44 (1985), 291–317.

    Google Scholar 

  52. Goré, R., ‘Dual intuitionistic logic revisited’, LNAI No 1847, Springer Verlag, Berlin, 2000, pp. 252–267.

    Google Scholar 

  53. Gurevich, Y, ‘Intuitionistic logic with strong negation’, Studia Logica, 36, (1–2) (1977), 49–59.

    Google Scholar 

  54. Hasuo, I., and R. Kashima, ‘Kripke completeness of first-order constructive logics with strong negation’, Logic Journal of the IGPL, 11(6) (2003), 615–646.

    Google Scholar 

  55. Herre, H., and D. Pearce, ‘Disjunctive logic programming, constructivity and strong negation’, in D. Pearce et al. (eds.), Logics in AI. European workshop JELIA'92. Berlin, Germany, September 7–10, 1992. LNCS 663, Springer, Berlin, 1992, pp. 391–410.

    Google Scholar 

  56. Jaspers, J., Calculi for Constructive Communication. ILLC Dissertation Series 1994-4, ILLC 1994.

  57. Johansson, I., ‘Der Minimalkalkül, ein reduzierter intuitionistisher Formalismus’, Compositio Math., 4 (1936).

  58. Kamide, N., ‘Sequent Calculi for Intuitionistic Linear Logic with strong Negation’, Logic Journal of the IGPL, 10 (2002), 653–678.

    Google Scholar 

  59. Kamide, N., ‘A Canonical Model Construction for Substructural Logics with strong negation’. Reports on Mathematical Logic, 36 (2002), 95–116.

    Google Scholar 

  60. Kamide, N., ‘A note on dual intuitionistic logic’, Mathematical Logic Quarterly, 49 (2003), 519–524.

    Google Scholar 

  61. Kamide, N., ‘Quantized linear logic, involving quantales and strong negation’, Studia Logica, 77 (2004), 355–384.

    Google Scholar 

  62. Kamide, N., ‘A relationship between Rauszer's H-B Logic and Nelson's Constructive Logic’, Bulletin of the Section of Logic, 33(4) (2004), 237–249.

    Google Scholar 

  63. Kamide, N., ‘Gentzen -Type Methods for Bilattice Negation’, Studia Logica, 80, No 2–3 (2005), 265–289.

    Google Scholar 

  64. Klunder, B, ‘Topos based semantics for constructive logics with strong negation’, Z. Math. Logik Grundlagen Math. 38, No.5–6 (1992), 509–519.

    Google Scholar 

  65. Kracht, M., ‘On extensions of intermediate logics by strong negation’, Journal of Philosophical Logic, 27 (1998), 49–73.

    Google Scholar 

  66. Lopez-Escobar, E.G.K, ‘Refutability and Elementary Number Theory’, Indag. Math. 34 (1972), 362–374.

    Google Scholar 

  67. Maximova, L., Interpolation and Definability in Extensions of the Minimal Logic. Algebra and Logic, vol. 44, No 6, November 2005, 407–421.

    Google Scholar 

  68. Markov, A.A., ‘Constructive Logic’(in Russian), Uspekhi Matematicheskih Nauk 5 (1950), 187–188.

    Google Scholar 

  69. Monteiro, A., ‘Les Algébres de Nelson semi-simple’, Notas de Logica Matematica, Inst. de Mat. Universidad Nacional del Sur, Bahia Blanca.

  70. Monteiro, A., ‘Construction des algébres de Nelson finies’, Bull.Ac.Pol. Sc. Cl. III, 11 (1963), 359–362.

    Google Scholar 

  71. Nelson, D., ‘Constructible falsity’, Journal of Symbolic Logic, 14 (1949), 16–26.

    Google Scholar 

  72. Nelson, D., ‘Negation and separation of Concepts in Constructive Systems’, in A. Heyting (ed.), Constructivityin Mathematics, North-Holland, Amsterdam, 1959, pp. 208–225.

    Google Scholar 

  73. Odintsov, S. P., ‘Maximal paraconsistent extension of Johansson logic’, Logique et Analyse, 161–162–163(1998), 107–120.

    Google Scholar 

  74. Odintsov, S. P., ‘Representation of j-algebras and Segerberg's logics’, Logique et analyse, 165/166 (1999), 81–106.

    Google Scholar 

  75. Odintsov, S. C., ‘Logic of classical refutability and class of extensions of minimal logic’, Logic and Logical Philosophy, 9 (2001), 91–107.

    Google Scholar 

  76. Odintsov, S. P., ‘Algebraic semantics for paraconsistent Nelson's Logic’, Journal of Logic and Computation, 13(4) (2003), 453–468.

    Google Scholar 

  77. Odintsov, S. C., ‘Reductio ad absurdum and Lukasiewicz modalities’, Logic and Logical Philosophy, 11/12 (2003), 149–166.

    Google Scholar 

  78. Odintsov, S. P., ‘On the Representation of N4-Lattices’, Studia Logica, vol. 76, 3 (2004), 385–405.

    Google Scholar 

  79. Odintsov, S. P., ‘The class of extensions of Nelson's paraconsistent logic’, Studia Logica, 80, No 2–3 (2005), 291–320.

    Google Scholar 

  80. Odintsov, S. P., and D. Pearce, ‘Routley Semantics for Answer Sets’, Proceedings LPNMR05, Springer LNAI, forthcoming 2005.

  81. Odintsov, S. P., and H. Wansing, Inconsistency-tolerant Description Logic: Motivation and Basic Systems, in V.F. Hendricks and J. Malinowski (eds.), Trends in Logic: 50 Years of Studia Logica, Kluwer Academic Publishers, Dordrecht, 2003, pp. 301–335.

    Google Scholar 

  82. Odintsov, S. P., and H. Wansing, ‘Constructive Predicate Logic and Constructive Modal logic. Formal Duality versus Semantical Duality’, in V.F. Hendricks et al. (eds.), First-Order Logic Revisited, Logos Verlag, Berlin, 2004, pp. 263–280.

    Google Scholar 

  83. Pagliani P., ‘Rough sets and Nelson algebras’, Fundamenta Informaticae, 23. (2–3) (1996), 205–219.

    Google Scholar 

  84. Patterson A., ‘A symmetric model theory for constructible falsity’, Bulletin of the asasociation of Symbolic Logic, 1996.

  85. Patterson A., Implicite Programming and the Logic of Constructible Duality, Ph.D. thesis, B.S.Washington University, 1997.

  86. Pearce, D., ‘Answer Sets and Constructive Logic. Part II: extended logic programs and related nonmonotonic formalisms’, in L. M. Periera and A. Nerode (eds.), Logic Programming and Non-monotonic Reasoning. MIT press, 1993, pp. 457–475.

  87. Pearce, D, ‘A new logical characterization of stable models and answer sets’, in Proc. of NMELP 96, LNCS 1216, Springer, 1997, pp. 57–70.

  88. Pearce, D, ‘From here to there: Stable negation in logic programming’, in Dov Gabbay and Heinrich Wansing (eds.), What is Negation?. Kluwer Academic Pub., 1999, pp. 161–181.

  89. Pearce, D., and A. Valverde, ‘A First Order Non-monotonic Extension of Constructive Logic’, Studia Logica, 80 (2005), 321–346.

    Google Scholar 

  90. Pearce, D., and G. Wagner, ‘Reasoning with negative information, I: Strong negation in logic programs’, in Language, Knowledge and Intensionality (Acta Filosophica Fenica), Helsinki, 49 (1990), 405–439. .

    Google Scholar 

  91. Pearce, D., and G. Wagner, ‘Logic programming with strong negation’, in P. Schroeder-Heister (ed.). Extensions of Logic Programming, Lecture Notes in Artificial Intelligence, No 475, Springer-Verlag, Berlin, 1991, pp. 311–326.

    Google Scholar 

  92. Porte, J, ‘Lukasiewicz's L-modal system and classical refutability’, Logique Anal. Now. Ser., 27 (1984), 87–92.

    Google Scholar 

  93. Pynko, A.P., ‘Functional completeness and axiomatizability within Belnap's four-valued logic and its expansions’, Journal of Applied Non-Classical Logics, 9 (1999), 61–105.

    Google Scholar 

  94. Rasiowa, H., ‘Algebraische Charakterisierung der intuitionischen Logik mit starker Negation’, Constructivity in Mathematics, Proc. of the Coll. held at Amsterdam 1957, Studies in Logic and the Foundations of Mathematics, 1959, 234–240.

  95. Rasiowa, H., ‘N-lattices and constructive logic with strong negation’, Fundamenta Mathematicae, 46 (1958), 61–80.

    Google Scholar 

  96. Rasiowa, H., An algebraic approachto non-classical logic, North-Holland Publishing Company, Amsterdam, London, 1974.

    Google Scholar 

  97. Rasiowa, H., Algebraic Models of Logics Warsaw, 2001.

  98. Rasiowa, H., and R. Sikorski, ‘Algebraic treatment of the notion of satisfiability’, Fund. Math. 40 (1953), 62–95.

    Google Scholar 

  99. Rasiowa, H., and R. Sikorski, The Mathematics of Metamathematcs, Warsawa 1963.

  100. Rauszer, C., ‘Representation theorem for semi-boolean algebras’. I (and II). Bul. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phis., 19 (1971), I: 881–887; II: 889–899.

    Google Scholar 

  101. Rauszer, C., ‘A formalization of propositional calculus of H-B logic’, Studia Logica, 33 (1974), 24–34.

    Google Scholar 

  102. Rauszer, C., S‘emi-boolean algebras and their applications to intuitionistic logic with dual operations’, Fund. Math., 85 (1974), 219–249

    Google Scholar 

  103. Rauszer, C., ‘On the strong semantical completeness of H-B predicate calculus’, Bul. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phis., 24 (1976), 81–87.

    Google Scholar 

  104. Rauszer, C., ‘An algebraic approach to Heyting-Brouwer predicate calculus’, Fund. Math., 96 (1977), 127–135.

    Google Scholar 

  105. Rauszer, C., ‘Applications of Kripke models to Heyting-Brouwer logic’, Studia Logica, 36 (1977), 61–72.

    Google Scholar 

  106. Rauszer, C., ‘An algebraic and Kripke-style approach to a certain extension of intuitionistic logic’, Disertationes Math., 157 (1980), 1–62.

    Google Scholar 

  107. Routley, R., ‘Semantical Analyses of Propositional Systems of Fitch and Nelson’, Studia Logica 33, (3)(1974), 283–298.

    Google Scholar 

  108. Segerberg, K., ‘Propositional logics related to Heyting's and Johansson's’, Theoria, 34 (1968), 26–61.

    Google Scholar 

  109. Sendlewski, A., ‘Topological duality for Nelson algebras and its applications’, Bull. Sect. Logic, Pol. Acad. Sci., 13 (1984), 215–221.

    Google Scholar 

  110. Sendlewski, A., ‘Some investigations of varieties of N-lattices’, Studia Logica, 43 (1984), 257–280.

    Google Scholar 

  111. Sendlewski, A., ‘Nelson algebras through Heyting ones’, Studia Logica, 49 (1990), 106–126.

    Google Scholar 

  112. Sendlewski, A, ‘Axiomatic extensions of the constructive logic with strong negation and disjunction property’, Studia Logica, 55 (1995), 377–388.

    Google Scholar 

  113. Shramko, Y., ‘Semantics for constructive negations’, in H. Wansing (ed.), Essays on Non-Classical Logic, World Scientiphic, New Jersey-London-Singapore-Hong Kong, 2001, pp. 187–217.

    Google Scholar 

  114. Shramko, Y., ‘Dual Intuitionistic Logic and a Variety of Negations: The Logic of Scientiphic Research’, Studia Logica, 80 (2005), 347–367.

    Google Scholar 

  115. Shramko, Y., J.M. Dunn, and T. Tanaka, ‘The trilattice of constructive truth values’, Journal of Logic and Computation, 11 (2001), 761–788.

    Google Scholar 

  116. Thomason, R.H., ‘A Semantical Study of Constructible Falsity’, Zeitschrift fur Mathematische Logik 15 (1969), 247–257.

    Google Scholar 

  117. Vakarelov, D., ‘Ekstensional Logics’ (in Russian), Doklady BAN, 25 (1972), 1609–1612.

    Google Scholar 

  118. Vakarelov, D., ‘Representation theorem for semi-Boolean algebras and semantics for HB-predicate logic’, Acad. Polon. Sci. Ser. Math. Phis., 22 (1974), 1087–1095.

    Google Scholar 

  119. Vakarelov, D., ‘Models for constructive logic with strong negation’, V Balkan Mathematical Congress, Abstracts, Beograd, 1974, p. 298.

  120. Vakarelov, D., ‘Generalized Nelson Lattices’, IVth Allunion Conference on Mathematical Logic, Abstracts, Kishinev, 1976.

  121. Vakarelov, D., ‘Theory of Negation in Certain Logical Systems. Algebraic and Semantical Approach’, Ph.D. dissertation, University of Warsaw, 1976.

  122. Vakarelov, D., ‘Notes on N-lattices and constructive logic with strong negation’, Studia Logica 36 (1977), 109–125.

    Google Scholar 

  123. Vakarelov, D., ‘Intuitive Semantics for Some Three-valued Logics Connected with Information, Contrariety and Subcontrariety’, Studia Logica, XLVIII, 4 (1989), 565–575.

    Google Scholar 

  124. Vakarelov, D., ‘Consistency, Completeness and Negation’, in Gr. Priest, R. Routley, and J. Norman (eds.), Paraconsistent Logic. Essays on the Inconsistent. Analiytica, Philosophia Verlag, Munhen, 1989, 328–363.

    Google Scholar 

  125. Vakarelov, D., ‘Constructive Negation on the Base of Weaker Versions of Intuitionistc Negation’, Studia Logica, 80, No 2–3 (2005), 393–430.

    Google Scholar 

  126. Vorob'ev, N. N., ‘Constructive propositional calculus with strong negation’ (in Russian), Doklady Academii Nauk SSSR, 85 (1952), 456–468.

    Google Scholar 

  127. Vorob'ev, N.N, ‘The problem of deducibility in constructive propositional calculus withstrongnegation’ (in Russian). Doklady Akademii Nauk SSR, 85 (1952), 689–692.

    Google Scholar 

  128. Vorob'ev, N. N., ‘Constructive propositional calculus with strong negation’ (in Russian), Transactions of Steklov's institute, 72 (1964), 195–227.

    Google Scholar 

  129. Wagner, G., ‘Logic programming with strong negation and inexact predicates’, J. Log. Comput., 1, No.6 (1991), 635–659.

    Google Scholar 

  130. Wagner, G., Vivid Logic. Knowledge-Based reasoning with Two Kinds of Negation Springer LNAI 764, 1994.

  131. Wansing, H., The Logic of Information Structures Springer LNAI 681, 1993.

  132. Wansing, H., Informational Intererpretation of substructural Propositional Logics, Journal of logic Language and Information, 2 (1993), 285–308.

    Google Scholar 

  133. Wansing, H., ‘Semantics-based nonmonotonic inference’. Notre Dame Journal of Formal Logic, 36 (1995), 44–54.

    Google Scholar 

  134. Wansing, H., ‘Displaying in the modal logic of consistency’, Journal of Symbolic Logic, 64 (1999), 1573–1590, 68 (2003), 712.

    Google Scholar 

  135. Wansing, H., ‘Negation as Falsity: a Reply to Tennant’, in D. Gabbay and H. Wansing (eds.), What is Negation? Kluwer Academic Publishers, Dorderecht, 1999, pp. 223–238.

    Google Scholar 

  136. Wansing, H., ‘Higher-arity Gentzen Systems for Nelson's Logic’, in J. Nida-Rümelin (ed.), Rationalität, Realismus, Revision (GAP3), de Gruyter, Berlin, 1999, pp. 105–109.

    Google Scholar 

  137. Wansing, H., ‘The Idea of Proof-theoretic Semantics’, Studia Logica, 64 (2000), 3–20.

    Google Scholar 

  138. Wansing, H., ‘Negation’, in L. Goble (ed.), The Balackwell Guide to Philosophical Logic, Basil Blackwell Publishers, Cambridge/MA, 2001, pp. 415–436.

    Google Scholar 

  139. Wansing, H., ‘Logical connectives for constructive modal logic’, Synthese, 2005, to appear.

  140. Wansing, H., ‘Connexive Modal Logic’, in R. Schmidt et al. (eds.), Advances in Modal Logic, vol. 5, King's Colleage Publications, London, 2005, pp. 367–383.

    Google Scholar 

  141. Wolski M., ‘Complete Orders, Categories and Lattices of Approximations’, Fundamenta Informaticae, 2006, to appear.

  142. Zaslawskij, I.D., Symmetrical Constructive Logic (in Russian), Erevan, 1978.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Logic Faculty of Mathematics and Informatics Sofia University, Sofia, Bulgaria

    Dimiter Vakarelov

Authors
  1. Dimiter Vakarelov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dimiter Vakarelov.

Additional information

A lecture presented at the International Conference Trends in Logic III : A. Mostowski, H. Rasiowa and C. Rauszer in memoriam, Warsaw, Ruciane-Nida September 23-26, 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vakarelov, D. Non-Classical Negation in the Works of Helena Rasiowa and Their Impact on the Theory of Negation. Stud Logica 84, 105–127 (2006). https://doi.org/10.1007/s11225-006-9004-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-006-9004-y

Keywords

Search

Navigation