Nelson's paraconsistent logics
DOI:
https://doi.org/10.12775/LLP.1999.009Abstrakt
. David Nelson’s constructive logics with strong negation may be viewed as alternative paraconsistent logic. These logics have been developed before da Costa’s works. We address some philosophical aspects of Nelson’s logics and give technical results concerning Kripke models and tableau calculi. We also suggest possible applications of paraconsistent constructive logics.Bibliografia
Akama, S. (1987): Resolution in constructivism, Logique et Analyse 120, 385–399.
Akama, S. (1988a): On the proof method for constructive falsity, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 34, 385–392.
Akama, S. (1988b): Constructive predicate logic with strong negation and model theory, Notre Dame Journal of Formal Logic 29, 18–27.
Akama, S. (1989): Constructive Falsity: Foundations and Their Applications to Computer Science, Ph.D. dissertation, Department of Administration Engineering, Keio University, Yokohama, Japan.
Akama, S. (1990): Subformula semantics for strong negation systems, The Journal of Philosophical Logic 19, 217–226.
Akama, S. (1995): Three-valued constructive logic and logic programs, Proc. of the IEEE 25th International Symposium on Multiple-Valued Logic, 276–281, Bloomington, USA, May.
Akama, S. (1996): Curry’s paradox in contractionless constructive logic, The Journal of Philosophical Logic 25, 217–226.
Akama, S. (1997): Tableaux for logic programming with strong negation, D. Galmiche (ed.), TABLEAUX’97: Automated Reasoning with Analytic Tableaux and Related Methods, 31–42, Springer, Berlin.
Almukdad, A., and D. Nelson (1984): Constructible falsity and inexact predicates, The Journal of Symbolic Logic 49, 8–37, 231–233.
da Costa, N.C.A.: (1974): On the theory of inconsistent formal system, Notre Dame Journal of Formal Logic 15, 497–510.
Fitch, F. (1952): Symbolic Logic, Ronald Press, New York.
Fitting, M. (1969): Intuitionistic Logic, Model Theory and Forcing, North-Holland, Amsterdam.
Gurevich, Y. (1977): Intuitionistic logic with strong negation, Studia Logica 36, 49–59.
Jaśkowski, S. (1948): Un calcul des propositions pour les systems deductifs contradictories, Studia Sicietatis Scientiarum Torunensis, Sect. A, 1, 57–77.
Markov, A.A. (1950): Constructive logic (in Russian), Uspekhi Mathematičekih Nauk 5, 187–188.
Nelson, D. (1949): Constructible falsity, The Journal of Symbolic Logic 14, 16–26.
Nelson, D. (1959): Negation and separation of concepts in constructive systems, A. Heyting (ed.), Constructivity in Mathematics, 208–225, North-Holland, Amsterdam.
Pearce, D., and G. Wagner (1990): Reasoning with negative information I: Strong negation in logic programs, Acta Philosophica Fennica 49, 430–453.
Pearce, D., and G. Wagner (1991): Logic programming with strong negation, P. Schroeder-Heister (ed.), Extensions in Logic Programming, 311–326, Springer, Berlin.
Prawitz, D. (1965): Natural Deduction: A Proof-Theoretical Study, Almqvist and Wiksell, Stockholm.
Rautenberg,W. (1979): Klassische und Nichtklassische Aussagenlogik, Vieweg, Wiesbaden.
Smullyan, R. (1968): First-Order Logic, Springer, Berlin.
Thomason, R.H. (1969): A semantical study of constructible falsity, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 15, 247–257.
Wagner, G. (1991): Logic programming with strong negation and inexact predicates, Journal of Logic and Computation 1, 835–859.
Wagner, G. (1992): Vivid Logic: Knoweldge-Based Reasoning with Two Kinds of Negation, Ph.D. dissertation, Freien Universitat Berlin, also published as Lecture Notes in Aritificial Intelligence 764, Springer, Berlin, 1994.
Wansing, H. (1992): The Logic of Information Structures, Ph.D. dissertation, Freien Universitat Berlin, also published as Lecture Notes in Aritificial Intelligence 681, Springer, Berlin, 1993.
Wansing, H. (1995): Semantics-based nonmonotonic inference, Notre Dame Journal of Formal Logic 36, 44–54.
Zaslavskii, I. (1978): Symmetric Constructive Logics (in Russian), Erevan.
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