Protoalgebraic gentzen systems and the cut rule

Studia Logica

Volumn 65, Issue 1, 2000, Pages 53-89

  Gil, Àngel J ^a   Rebagliato, Jordi ^b  

^a UNIVERSITAT POMPEU FABRA   (Spain)

^b UNIVERSITY OF BARCELONA   (Spain)

Author keywords

Accumulative gentzen system; Cut rule; Gentzen system; Logical rule; Many sided sequent; Protoalgebraicity; Sequent calculus; Structural rule

Indexed keywords

EID: 27744531816     PISSN: 00393215     EISSN: 15728730     Source Type: Journal    
DOI: 10.1023/A:1005243108996     Document Type: Article

References (27)

1. AVRON, A., 'Gentzen-type systems, resolution and tableaux', Journal of Automated Reasoning 10: 265-281, 1993.
2. BAAZ, M., G.G. FERMÜLLER, G. SALZER, and R. ZACH, 'Labeledcalculi and finitevalued logics', Studia Logica 61 (1): 7-33, 1998.
3. BAAZ, M., G.G. FERMÜLLER, and R. ZACH, 'Elimination of cuts in first-order finitevalued logics', Journal of Information Processing and Cybernetics. EIK 29 (6): 333-355, 1994.
4. BAAZ, M., C.G. FERMüLLER, G. SALZER, and R. ZACH, 'MUltlog 1.0: Towards an expert system for many-valued logics', in [19], pages 226-230.
5. BARWISE, J., D. GABBAY, and C. HARTONAS, 'On the logic of information flow', Bull, of the IGPL 3 (1): 7-49, 1995.
6. BLOK, W. J., and D. PIGOZZI, 'Protoalgebraic logics', Studia Logica 45: 337-369, 1986.
7. BLOK, W. J., and D. PIGOZZI, Algebraizable Logics, volume 396 of Memoirs of the American Mathematical Society, A.M.S, Providence, January 1989.
8. BLOK, W. J., and D. PIGOZZI, 'Algebraic semantics for universal Horn logic without equality', in A. Romanowska and J. D. H. Smith (eds.), Universal Algebra and Quasigroups, pages 1-56, Heldermann Verlag Berlin, 1992.
9. BLOK, W. J., and D. PIGOZZI, 'Abstract algebraic logic and the deduction theorem', The Bulletin of Symbolic Logic (to appear).
10. CZELAKOWSKI, J., 'Algebraic aspects of deduction theorems', Studio, Logica 44: 396387, 1985.
11. CZELAKOWSKI, J., Consequence Operations: Foundational Studies, Reports of the Research Project "Theories, Models, Cognitive Schemata", Institute of Philosophy and Sociology, Polish Academy of Sciences, Warszawa, 1992.
12. CZELAKOWSKI, J., Protoalgebraic Logics, Trends in Logic (Studia Logica Library), Kluwer Academic Publishers, Dordrecht (to appear).
13. CZELAKOWSKI, J., and D. PIGOZZI, 'Amalgamation and interpolation in abstract algebraic logic', in X. Caicedo and C. H. Montenegro (eds.), Models, Algebras and Proofs, volume 203 of Lecture Notes in Pure and Applied Matehraatics Series, pages 187-265, New York and Basel, 1998. Marcel Dekker.
14. FONT, J. M., and R. JANSANA, A General Algebraic Semantics for Sentential Logics, volume 7 of Lecture Notes in Logic, Springer-Verlag, 1996.
15. GIL, A. J., Sisteraes de Gentzen Multidiraensionals i logiques finitaraent valorades. Teoria i aplicacions, PhD Thesis, Facultat de Matemàtiques, Universitat de Barcelona, 1996.
16. GIL, A. J., J. REBAGLIATO, and V. VERDÚ, 'A strong completeness theorem for the Gentzen systems associated with finite algebras', Journal of Applied Non-Classical Logics 9: 9-36, 1999.
17. GIL, A.J., A. TORRENS, and V. VERDU, 'On Gentzen systems associated with the finite linear MV-algebras', Journal of Logic and Computation 7 (4): 473-500, 1997.
18. HERRMANN, B., Equivalential Logics and Definability of Truth, PhD Thesis, Freie Univ. Berlin, 1993.
19. MCROBBIE, M. A., and J. K. SLANEY (eds.), 13th Int. Conf. on Automated Deduction (CADE'96), LNCS (LNAI) 1104, Springer, 1996.
20. REBAGLIATO, J., and V. VERDÚ, 'On the algebraization of some Gentzen systems', Fundamenta Informaticae, Special Issue: Algebraic Logic and its Applications, 18: 319-338, 1993.
21. REBAGLIATO, J., and V. VERDÚ, Algebraizable Gentzen Systems and the Deduction Theorem for Gentzen Systems, Mathematics Preprint Series 175, Universitat de Barcelona, June 1995.
22. ROUSSEAU, G., 'Sequents in many valued logic I', Fundamenta Mathematicae 60: 23-33, 1967.
23. SALZER, G., 'MUltlog: an expert system for multiple-valued logics', in: Collegium Logicum: Annals of the Kurt-Gödel-Society, volume 2, pages 50-55, Springer, 1996.
24. TAKEUTI, G., Proof Theory, volume 81 of Studies in Logic, North-Holland, 2 edition, 1987.
25. WÓJCICKI, R., Theory of Logical Calculi. Basic Theory of Consequence Operations, volume 199 of Synthese Library, Reidel, Drodrecht, 1988.
26. ZACH, R., 'Proof theory of finite-valued logics', Diplomarbeit, Technische Universitat Wien, Vienna, Austria, 1993 (available as Technical Report E185.2-Z.1-93).
27. ZEMAN, J. J., Modal Logic. The Lewis-Modal Systems, Oxford University Press, 1973.