On the Leibniz congruences
Banach Center Publications (1993)
- Volume: 28, Issue: 1, page 17-36
- ISSN: 0137-6934
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top- [1] N. D. Belnap, Jr., A useful four-valued logic, in: Modern Uses of Multiple-Valued Logic, J. M. Dunn and G. Epstein (eds.), Reidel, Dordrecht 1977, 8-37.
- [2] W. J. Blok and D. Pigozzi, Protoalgebraic logics, Studia Logica 45 (1986), 337-369. Zbl0622.03020
- [3] W. J. Blok and D. Pigozzi, Alfred Tarski's work on general metamathematics, J. Symbolic Logic 53 (1988), 36-50. Zbl0651.03002
- [4] W. J. Blok and D. Pigozzi, Algebraizable logics, Mem. Amer. Math. Soc. 396 (1989). Zbl0664.03042
- [5] W. J. Blok and D. Pigozzi, Local deduction theorems in algebraic logic, in: Algebraic Logic, H. Andréka, J. D. Monk and I. Németi (eds.), Colloq. Math. Soc. János Bolyai 54, North-Holland, Amsterdam 1991, 75-109. Zbl0751.03036
- [6] W. J. Blok and D. Pigozzi, The deduction theorem in algebraic logic, preprint, 1991, to appear. Zbl0755.03034
- [7] W. J. Blok and D. Pigozzi, Algebraic semantics for universal Horn logic without equality, in: Universal Algebra and Quasigroups, A. Romanowska and J. D. H. Smith (eds.), Heldermann, Berlin 1992, to appear. Zbl0768.03008
- [8] S. L. Bloom, A note on Ψ-consequences, Rep. Math. Logic 8 (1977), 3-9.
- [9] S. L. Bloom and D. J. Brown, Classical abstract logics, Dissertationes Math. 102 (1973), 43-51.
- [10] D. J. Brown and R. Suszko, Abstract logics, ibid., 9-42.
- [11] S. Burris and H. P. Sankappanavar, A Course in Universal Algebra, Springer, New York 1981.
- [12] J. Czelakowski, Equivalential logics, I, II, Studia Logica 40 (1981), 227-236 and 355-372. Zbl0476.03032
- [13] J. Czelakowski and W. Dziobiak, A deduction theorem schema for deductive systems of propositional logics, Studia Logica, Special Issue on Algebraic Logic, 50 (1991), 385-390. Zbl0755.03014
- [14] J. Czelakowski and G. Malinowski, Key notions of Tarski's methodology of deductive systems, Studia Logica 44 (1985), 321-351. Zbl0615.03014
- [15] B. A. Davey and H. A. Priestley, Introduction to Lattices and Order, Cambridge Univ. Press, Cambridge 1990. Zbl0701.06001
- [16] K. Dyrda and T. Prucnal, On finitely based consequence determined by a distributive lattice, Bull. Sec. Logic Polish Acad. Sci. 9 (1980), 60-66. Zbl0435.03006
- [17] J. M. Font, On some congruence lattices of a topological Heyting lattice, in: Contributions to General Algebra 5, J. Czermak et al. (eds.), Teubner, Stuttgart 1987, 129-137.
- [18] J. M. Font and J. L. García Lapresta, Logics and Algebras motivated by cardinality restrictions in the Deduction Theorem, manuscript, 1992.
- [19] J. M. Font, F. Guzmán and V. Verdú, Characterization of the reduced matrices for the {∧,∨}-fragment of classical logic, Bull. Sec. Logic Polish Acad. Sci. 20 (1991), 124-128.
- [20] J. M. Font and R. Jansana, A general algebraic semantics for deductive systems, preprint, 1992, to appear.
- [21] J. M. Font and M. Rius, A four-valued modal logic arising from Monteiro's last algebras, in: Proc. 20th Internat. Sympos. on Multiple-Valued Logic, Charlotte 1990, 85-92.
- [22] J. M. Font and G. Rodríguez, Note on algebraic models for relevance logic, Z. Math. Logik Grundlag. Math. 36 (1990), 535-540. Zbl0696.03004
- [23] J. M. Font and G. Rodríguez, Algebraic study of system R of relevance logic, manuscript, 1992.
- [24] J. M. Font and V. Verdú, Abstract characterization of a four-valued logic, in: Proc. 18th Internat. Sympos. on Multiple-Valued Logic, Palma de Mallorca 1988, 389-396.
- [25] J. M. Font and V. Verdú, A first approach to abstract modal logics, J. Symbolic Logic 54 (1989), 1042-1062. Zbl0687.03008
- [26] J. M. Font and V. Verdú, Completeness theorems for a four-valued logic related to De Morgan lattices, Fac. Math. Preprint Ser. 57, Barcelona 1989.
- [27] J. M. Font and V. Verdú, Algebraic logic for classical conjunction and disjunction, Studia Logica, Special Issue on Algebraic Logic, 50 (1991), 391-419. Zbl0753.03027
- [28] J. M. Font and V. Verdú, The lattice of distributive closure operators over an algebra, Studia Logica, to appear. Zbl0773.03039
- [29] J. M. Font and V. Verdú, Algebraic study of Belnap's four-valued logic, manuscript.
- [30] J. L. García Lapresta, Finitely deductive logics, Ph.D. dissertation, Univ. of Barcelona, 1991 (in Spanish).
- [31] A. Grzegorczyk, An approach to logical calculi, Studia Logica 30 (1972), 33-43 Zbl0286.02029
- [32] F. Guzmán and V. Verdú, On two Gentzen logifications of the variety of semilattices, manuscript, 1992.
- [33] R. Jansana, The Box fragments of modal logic K, in: Actas del VII Congreso de Lenguajes Naturales y Lenguajes Formales, Vic, Barcelona 1991, C. Martín-Vide (ed.), 409-413 (in Spanish).
- [34] R. Jansana, Abstract modal logics, preprint, 1992, to appear.
- [35] J. Łoś and R. Suszko, Remarks on sentential logics, Indag. Math. 20 (1958), 177-183. Zbl0092.24802
- [36] D. Pigozzi, Fregean algebraic logic, in: Algebraic Logic, H. Andréka, J. D. Monk and I. Németi (eds.), Colloq. Math. Soc. János Bolyai 54, North-Holland, Amsterdam 1991, 473-502. Zbl0749.03055
- [37] J. Pla and V. Verdú, Quasi-Hilbert algebras, Publ. Mat. 20 (1980), 97-99 (in Catalan).
- [38] W. A. Pogorzelski and J. Słupecki, Basic properties of deductive systems based on nonclassical logics, I, II, Studia Logica 9 (1960), 163-176 and 10 (1960), 77-95. Zbl0129.25602
- [39] M. Porębska and A. Wroński, A characterization of fragments of the intuitionistic propositional logic, Rep. Math. Logic 4 (1975), 39-42. Zbl0318.02027
- [40] H. Rasiowa, An Algebraic Approach to Non-Classical Logics, North-Holland, Amsterdam 1974. Zbl0299.02069
- [41] W. Rautenberg, Axiomatizing logics closely related to varieties, Studia Logica, Special Issue on Algebraic Logic, 50 (1991), 607-620. Zbl0749.03020
- [42] W. Rautenberg, On reduced matrices, preprint, 1992, to appear.
- [43] J. Rebagliato and V. Verdú, On the algebraization of some Gentzen systems, Fund. Inform., Special Issue on Algebra and Logic in Computer Science (1992), to appear. Zbl0788.03006
- [44] J. Rebagliato and V. Verdú, A Hilbert-style axiomatization of the {∧,∨,¬}-fragment of IPC, manuscript, 1992. Zbl0806.03010
- [45] M. Rius, Tetravalent modal logics, Ph.D. dissertation, Univ. of Barcelona, 1992 (in Catalan).
- [46] A. J. Rodríguez, A. Torrens and V. Verdú, Łukasiewicz logic and Wajsberg algebras, Bull. Sec. Logic Polish Acad. Sci. 19 (1990), 51-55. Zbl0717.03027
- [47] A. Tarski, Über einige fundamentale Begriffe der Metamathematik, C. R. Soc. Sci. Lettres Varsovie Cl. III 23 (1930), 22-29.
- [48] A. Torrens, Model theory for sequential deductive systems, preprint, 1991.
- [49] A. Torrens and V. Verdú, Abstract Łukasiewicz logics, preprint, 1990.
- [50] V. Verdú, Contribution to the study of some classes of abstract logics, Ph.D. dissertation, Univ. of Barcelona, 1978 (in Catalan).
- [51] V. Verdú, Distributive and Boolean logics, Stochastica 3 (1979), 97-108 (in Catalan). Zbl0419.03041
- [52] V. Verdú, Some algebraic structures determined by closure operators, Z. Math. Logik Grundlag. Math. 31 (1985), 275-278. Zbl0553.03041
- [53] V. Verdú, On some relations between closure operators and congruences, preprint, 1986.
- [54] V. Verdú, Logics projectively generated from [M] = (F₄,[{1}]) by a set of homomorphisms, Z. Math. Logik Grundlag. Math. 33 (1987), 235-241. Zbl0607.03020
- [55] R. Wójcicki, Lectures on Propositional Calculi, Ossolineum, Wrocław 1984. Zbl0647.03019
- [56] R. Wójcicki, Theory of Logical Calculi. Basic Theory of Consequence Operations, Synthese Library 199, Reidel, Dordrecht 1988. Zbl0682.03001