Abstract
Two logics L1 and L2 are negatively equivalent if for any set of formulas X and any negated formula ¬ϕ, ¬ϕ can be deduced from the set of hypotheses X in L1 if and only if it can be done in L2. This article is devoted to the investigation of negative equivalence relation in the class of extensions of minimal logic.
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References
Burris S., and H. P. Sankappanavar, A course in universal algebra, Springer-Verlag, 1981.
Curry H. B., Foundations of mathematical logic. McGrow-Hill Book Company, New York, 1963.
Jankov V. A., ‘The relationship between deducibility in the intuitionistic propositional calculus and finite implicational structures’, Soviet Math. Dokl. 4:1203–1204, 1963.
Jankov V. A., ‘Constructing a sequence of strongly independent superintuitionistic propositional calculi’, Soviet Math. Dokl. 9:806–807, 1968.
Johansson I., ‘Der Minimalkalkül, ein reduzierter intuitionistischer Formalismus’, Compositio Mathematika, 4:119–136, 1937.
Maksimova L. L., ‘On maximal intermediate logics with the disjunction property’, Studia Logica 45:69–75, 1986.
McKay C. M., ‘On finite logics’, Indagationes Mathematicae 29:363–365, 1967.
Odintsov S. P., ‘Maximal paraconsistent extension of Johansson logic’, Logique at Analyse 161/163:107–120, 1998.
Odintsov S. P., ‘Logic of classical refutability and class of extensions of minimal logic’, Logic and Logical Philosophy 9:91–107, 2002.
Odintsov S. P., ‘Algebraic semantics and Kripke semantics for extensions of minimal logic’, Logical investigations (electronic journal) No.2, 1999 [in Russian] (http://www.logic.ru/LogStud/02/No2-06.html).
Odintsov S. P., ‘Negatively equivalent extensions of minimal logic and theirs logics of contradictions’, Logical investigations 7, Moscow, 117–129, 2000 [in Russian].
Odintsov S. P., ‘Representation of j-Algebras and Segerberg’s Logics’, Logique et Analyse 165/166:81–106, 1999.
Ono H., ‘Kripke models and intermediate logics’, Publications of Research Institute for Mathematical Sciences, Kyoto University 6:461–476, 1970.
Rasiowa H., An algebraic approach to non-classical logics, North-Holland, 1974.
Rautenberg W., Klassische und nichtclassische Aussagenlogik, Vieweg, 1979.
Segerberg K. ‘Propositional logics related to Heyting’s and Johansson’s’, Theoria 34:26–61, 1968.
Suzuki N.-Y., ‘Constructing a continuum of predicate extensions of each intermediate propositional logic’, Studia logica 54:173–198, 1995.
Woodruff P. W., ‘A note on JP’, Theoria 36:183–184, 1970.
Wroński A., ‘The degree of completeness of some fragments of the intuitionistic propositional logic’, Reports on Mathematical Logic 2:55–62, 1974.
Wroński A., ‘On the cardinalities of matrices strongly adequate for the intuitionistic propositional logic’, Reports on Mathematical Logic 3:67–72, 1974.
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The author acknowledges support by the Alexander von Humboldt-Stiftung
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Odintsov, S.P. Negative Equivalence of Extensions of Minimal Logic. Stud Logica 78, 417–442 (2004). https://doi.org/10.1007/s11225-004-6043-0
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DOI: https://doi.org/10.1007/s11225-004-6043-0