Academia.eduAcademia.edu

Outline

Title
Abstract
References

Extension of sequent calculi with nonlogical rules

Profile image of Sara NegriSara Negri

1998

Abstract

Abstract In [N] the contraction-free and cut-free sequent calculus G3ip for intuitionistic p) ropositiona. l logic was extended by rules for theories of apartness an (l order. The logical content. of the axioms of these theories is expressed by the geometry of sequent calculus rules, which have only atomic formulas as active and principal. In this way also such extensions are contraction-free and cutfree. Cut. elimination permits structural proof analysis, and syntactic proofs of conservativity results.

Related papers

Investigations into a left-structural right-substructural sequent calculus
Lloyd Humberstone

Journal of Logic, Language and Information, 2007

We study a multiple-succedent sequent calculus with both of the structural rules Left Weakening and Left Contraction but neither of their counterparts on the right, for possible application to the treatment of multiplicative disjunction (fission, 'cotensor', par) against the background of intuitionistic logic. We find that, as Hirokawa dramatically showed in a 1996 paper with respect to the rules for implication, the rules for this connective render derivable some new structural rules, even though, unlike the rules for implication, these rules are what we call ipsilateral: applying such a rule does not make any (sub)formula change sides-from the left to the right of the sequent separator or vice versa. Some possibilities for a semantic characterization of the resulting logic are also explored. The paper concludes with three open questions.

View PDFchevron_right
Cut-free and Analytic Sequent Calculus of First-Order Intuitionistic Epistemic Logic
Katsuhiko Sano, Youan Su

2019

View PDFchevron_right
Permutability of proofs in intuitionistic sequent calculi
Roy Dyckhoff

Theoretical Computer Science, 1999

View PDFchevron_right
Contraction-Free Linear Depth Sequent Calculi for Intuitionistic Propositional Logic with the Subformula Property and Minimal Depth Counter-Models
Camillo Fiorentini

Journal of Automated Reasoning, 2013

Your article is protected by copyright and all rights are held exclusively by Springer Science+Business Media B.V.. This e-offprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".

View PDFchevron_right
Constructing Cut Free Sequent Systems With Context Restrictions Based on Classical or Intuitionistic Logic (extended)
Björn Lellmann

2013

We consider a general format for sequent rules for not necessarily normal modal logics based on classical or intuitionistic propositional logic and provide relatively simple local conditions ensuring cut elimination for such rule sets. The rule format encompasses e.g. rules for the boolean connectives and transitive modal logics such as S4 or its constructive version. We also adapt the method of constructing suitable rule sets by saturation to the intuitionistic setting and provide a criterium for translating axioms for intuitionistic modal logics into sequent rules. Examples include constructive modal logics and conditional logic VA.

View PDFchevron_right
Proof Theory for Intuitionistic Strong L\"ob Logic
Rosalie Iemhoff

arXiv (Cornell University), 2020

This paper introduces two sequent calculi for intuitionistic strong Löb logic iSL✷: a terminating sequent calculus G4iSL✷ based on the terminating sequent calculus G4ip for intuitionistic propositional logic IPC and an extension G3iSL✷ of the standard cutfree sequent calculus G3ip without structural rules for IPC. One of the main results is a syntactic proof of the cut-elimination theorem for G3iSL✷. In addition, equivalences between the sequent calculi and Hilbert systems for iSL✷ are established. It is known from the literature that iSL✷ is complete with respect to the class of intuitionistic modal Kripke models in which the modal relation is transitive, conversely well-founded and a subset of the intuitionistic relation. Here a constructive proof of this fact is obtained by using a countermodel construction based on a variant of G4iSL✷. The paper thus contains two proofs of cut-elimination, a semantic and a syntactic proof.

View PDFchevron_right
On sequent calculi for intuitionistic propositional logic
Vitezslav Svejdar

2006

The well-known Dyckoff’s 1992 calculus/procedure for intuitionistic propositional logic is considered and analyzed. It is shown that the calculus is Kripke complete and the procedure in fact works in polynomial space. Then a multi-conclusion intuitionistic calculus is introduced, obtained by adding one new rule to known calculi. A simple proof of Kripke completeness and polynomial-space decidability of this calculus is given. An upper bound on the depth of a Kripke counter-model is obtained.

View PDFchevron_right
On Non-eliminability of the Cut Rule and the Roles of Associativity and Distributivity in Non-commutative Substructural Logics
Takeshi Ueno

arXiv: Logic, 2009

We introduce a sequent calculus FL' for non-commutative substructural logic. It has at most one formula on the right side of sequent, and excludes three structural inference rules, i.e. contraction, weakening and exchange. (FL' is based on our investigations of the Gentzen-style natural deduction for non-commutative substructural logics.) FL' has the same proof strength as the standard sequent calculus FL (Full Lambek), which is the basic sequent calculus for all other substructural logics. For the standard FL, we use Ono's formulation. Although FL' and the standard FL are equivalent, there is a subtle difference in the left rule of implication. In the standard FL, two parameters $\Gamma_1$ and $\Gamma_2$(resp.), each of which is just an finite sequence of arbitrary formulas, appear on the left and right side (resp.) of a formula which is placed on the left side of the sequent on the upper left side of the left rule $\imply$ (which corresponds to $\imply'$ in...

View PDFchevron_right
Sequent Calculus for Intuitionistic Epistemic Logic IEL
Alexey Yatmanov

Lecture Notes in Computer Science, 2015

The formal system of intuitionistic epistemic logic IEL was proposed by S. Artemov and T. Protopopescu. It provides the formal foundation for the study of knowledge from an intuitionistic point of view based on Brouwer-Hayting-Kolmogorov semantics of intuitionism. We construct a cut-free sequent calculus for IEL and establish that polynomial space is sufficient for the proof search in it. So, we prove that IEL is PSPACEcomplete.

View PDFchevron_right
The Cut Elimination and the Nonlengthening Property for the Sequent Calculus with Equality
Franco Parlamento

2017

We show how Leibnitz’s indiscernibility principle and Gentzen’s original work lead to extensions of the sequent calculus to first order logic with equality and investigate the cut elimination property. Furthermore we discuss and improve the nonlengthening property of Lifschitz and Orevkov in [5] and [8].

View PDFchevron_right

References (273)

  1. P. Cholak, C. Jockusch, and T. Slaman, The strength of Ramsey's theorem for pairs, in preparation.
  2. T. Hummel and C. Jockusch, Generalized cohesiveness, to appear in J. Symbolic Logic.
  3. C. Jockusch, Ramsey's theorem and recursion theory, J. Symbolic Logic 37 (1972), 268-280.
  4. D. Seetapun and T. Slaman, On the strength of Ramsey's theorem, Notre Dame J. For- mal Logic 36 (1995), 570-582.
  5. S. Simpson, Subsystems of second order arithmetic, to appear. -18- LC '98 Book of Abstracts References
  6. Daniel Leivant. Contracting proofs to programs. In P. Odifreddi, editor. Logic in Computer Science, Academic Press, pp 279-327.
  7. Herman Geuvers. Inductive and coinductive types with iteration and recursion. In Nordstr~m et al, editors. Preliminary Proceedings Workshop on Types for Proofs and Programs, Bdstad, June 1992, pp 193-217 (ftp://ftp. cs. chalmers. se/pub/cs-reports/baastad. 92/proc.dvi.Z). References
  8. L.D. Beklemishev. Parameter free induction and reflection. In G. Gottlob, A. Leitsch, and D. Mundici, editors, Computational Logic and Proof The- ory. Lecture Notes in Computer Science 1289. Springer-Verlag, Berlin, 1997, pp. 103-113.
  9. R. Kaye, J. Paris, and C. Dimitracopoulos. On parameter free induction schemas. Journal of Symbolic Logic, 53(4):1082-1097, 1988.
  10. C. Parsons. On a number-theoretic choice schema and its relation to induction. In A. Kino, J. Myhill, and R.E. Vessley, editors, Intuitionism and Proof Theory, pages 459-473. North Holland, Amsterdam, 1970. -25- LC '98 Book of Abstracts References
  11. A.S. Kechris, D.A. Martin and J.R. Steel (eds.), Appendix: Victoria Delfino Problems II, in: Cabal Seminar 81-85, Lecture Notes in Math. 1333 (1988), 221-224.
  12. W.H Woodin, On the Consistency Strength of Projective Uniformization, in: Logic Colloquium '81, J. Stern (ed.), North Holland (1982), 365-383.
  13. -26- LC '98 Book of Abstracts
  14. M. L. Dalla Chiara and R. Giuntini, 'Quantum logical semantics'.
  15. Levi, Isaac, 'The logic of full belief,' in The Covenant of Reason: Ratio- nality and the Commitments of Thought, CUP, 40-69, 1997.
  16. B. C. Van Fraassen, 'Fine-grained opinion, probability and the logic of full belief,' Journal of Philosophical Logic 24, 349-377, 1995 [41 Kyburg, Henry E., Jr., 'The rule of Adjunction and reasonable inference,' Journal of Philosophy, March 1997.
  17. Maher, Patrick, Betting on Theories, CUP, 1993.
  18. Moore, Robert, Logic and Representation, CSLI Lecture Notes No. 39, 1995. -34- LC '98 Book of Abstracts References
  19. Saul A. Kripke. The problem of entailment. The Journal of Symbolic Logic, 24:324, 1959. Abstract.
  20. P. Lincoln, J. Mitchell, A. Scedrov, and N. Shankar. Decision problems for propositional linear logic. Annals of Pure and Applied Logic, 56:239-311, 1992.
  21. R.K. Meyer. Topics in Modal and Many-valued Logic. PhD thesis, University of Pittsburgh, Pennsylvania, 1966.
  22. Alasdair Urquhart. The complexity of decision procedures in relevance logic. In J. Michael Dunn and Anil Gupta, editors, Truth or Consequences: Essays in honour of Nuel Belnap, pages 61-76. Kluwer, Dordrecht, 1990. -41- LC '98 Book of Abstracts References
  23. T. Arai. Proof theory for theories of ordinals, I-I1. Preprints, 1996-97
  24. W. Buchholz. Notation system for infinitary derivations. Arch. Math. Logic, 30:277-296, 1991
  25. W. Buchholz. Explaining the Gentzen-Takeuti reduction steps. Preprint, 1997
  26. G. Mints. Finite investigations of transfinite derivations. In: G. Mints, Selected Papers in Proof Theory. Bibliopolis, 1992: 17-71. Russian original: 1975
  27. G. Mints. A new reduction sequence for arithmetic. In: G. Mints, Selected Papers in Proof Theory. Bibliopolis, 1992: 77-96. Russian original: 1979
  28. M. Rathjen. Proof theoretic analysis of KPM. Arch. Math. Logic, 30:377-403, 1991
  29. S. Tupailo. Finitary reductions for local predicativity, I: recursively regular ordinals. Preprint, 1998 References
  30. A. Blass, Cardinal characteristics and the producht of countably many infinite cyclic groups, J. Algebra 169 (1994) pp. 512-540.
  31. M. Kada, Cofinalities of null and meager ideals and infinite games, manuscript.
  32. M. Scheepers, Lebesgue measure zero subsets of the real line and an infinite game, J. Symbolic Logic 61 (1996), pp. 246-250.
  33. M. Scheepers, Meager sets and infinite games, Contemp. Math. 192 (1996), pp. 77-89. -46- LC '98 Book of Abstracts References:
  34. A. Ku~era and S. A. Terwijn, Lowness for the class of random sets, to appear in JSL.
  35. S. A. Terwijn and D. Zambella, Algorithmic randomness and lowness, manuscript, 1997. -50- LC '98 Book of Abstracts References
  36. U. H6hle, Commutative, residuated 1-monoids, in: Non-Classical Logics and Their Applications to Fuzzy Subsets, Eds. U. H6hle, E.P. Klement, 53-106 (Kluwer, Boston, Dordrecht 1995).
  37. - , Presheaves over GL-monoids, in: Non-Classical Logics and Their Applications to Fuzzy Subsets, Eds. U. LI6hle, E.P. Klement, 127-157 (Kluwer, Boston, Dordrecht 1995). -53- LC '98 Book of Abstracts References
  38. HA'JEK, P., Metamathematics of fuzzy logic. Book in preparation, to appear at Kluwer.
  39. BELLUCE, L.P. AND CHANG, C.C., A weak completeness theorem for infinite valued first-order logic. Journal of Symbolic Logic. 28 (1963), 43-50.
  40. HAJEK, P., PARIS, J., SHEPHERDSON, J.C., Rational Pavelka predicate logic is a conservative extension of Lukasiewicz predicate logic, submitted to the Journal of Symbolic Logic, 1998. REFERENCES
  41. P. Howard and J. Rubin, Weak Forms of the Axiom of Choice, Preprint.
  42. T. Jech, The Axiom of Choice, North Holland, 1973.
  43. A. Levy, The independence of various definitions of finiteness, Fund. Math. 46 (1958), 1-13.
  44. A. Tarski, Sur les ensembles finis, Fund. Math. 6 (1924), 45-95. odlccrmath.ufl.edu, http://www.math.ufl.edu/-odlc References
  45. Beller, A., Jensen, R. B. and Welch, P., Coding the universe in a real, London Math. Soc. Lecture Note Series 47, Cambridge University Press 1982
  46. Jensen, R. B., Some remarks on El below 0 ¶, Handwritten notes, Oxford
  47. Jensen, R. B., More on El below 0 ¶, Handwritten notes, Oxford 1994
  48. Jensen, R. B., and Zeman, M. Smooth categories and global 0, submitted
  49. Schimmerling, E., Combinatorial principles in the core model for one Woodin cardinal, Annals of Pure and Applied Logic 74 (1995), 153-201
  50. Schimmerling, E., [lf< holds in L[t•], to appear
  51. Zeman, M., Doctoral Dissertation, HU Berlin
  52. Zeman, M., Global 0 below 0 ¶, in preparation -59- LC '98 Book of Abstracts References
  53. H. Becker and A. S. Kechiris, The Descriptive Set Theory of Polish Group Actions, Cambridge University press, 1996.
  54. A.S. Kechris and S. Solecki, Approximation of Analytic by Borel Sets and Definable Chain Condition, Israel Journal of Mathematics, vol 89, 1995, pp. 343-356.
  55. J. Stem, On Lusin's Restricted Continuum Problem, Annals of Mathematics, vol. 120, 1984, pp. 7- 37. -60- LC '98 Book of Abstracts References
  56. Anastasios Kamburelis and Bogdan W~glorz. Splittings. Archive for Math- ematical Logic, 35:263-277, 1996.
  57. Peter Vojtas. Series and Toeplitz Matrices (A Global Implicit Approach). Preprint 1997. -61- LC '98 Book of Abstracts REFERENCES
  58. P. J. Cameron, Oligomorphic permutation groups (1983), Cambridge University press.
  59. A. Miller, Some properties of measure and category, Transactions of the American Math- ematical Society 266, Number, 1 (July 1981), 93-114.
  60. -65- LC '98 Book of Abstracts References [11 Amitava Bagchi. Economy of Descriptions and Minimal Indices. MAC Technical Memo- randum, MIT, 1972.
  61. Manuel Blum. On the size of machines. Information and Control, 11, 257-265, 1967.
  62. Albert R. Meyer. Program Size in Restricted Programming Languages. Information and Control, 21, 382-394, 1972.
  63. David Pager. On the Problem of Finding Minimal Programs for Tables. Information and Control, 14, 550-554, 1969. -69- LC '98 Book of Abstracts References
  64. Allen Van Gelder. Propositional search with k-clause introduction can be polynomially sim- ulated by resolution. In Fifth International Symposium on Artificial Intelligence and Mathe- matics, January 1998. WWW: http://rutcor.rutgers.edu/.amai/.
  65. Oliver Kulmann. Methods for 3-SAT-decision in less than 20"9"n steps. The Bulletin of Symbolic Logic, 1(1):96-97, 1995. Abstracts of contributed papers of the Logic Colloquium' 93, Keele, England, July 20 -29, 1993.
  66. Oliver Kullmann. On a generalization of extended resolution. To appear in Discrete Applied Mathematics (special edition on the satisfiability problem), 1996.
  67. Oliver Kullmann. Some remarks on extended resolution. volume 3 of The Bulletin of Symbolic Logic, page 267. Association for Symbolic Logic, June 1997. Abstracts of contributed talks of the Logic Colloquium' 96, Donostia-San Sebastian, Spain, July 9 -15, 1996.
  68. Oliver Kullmann. Worst-case analysis, 3-SAT decision and lower bounds: Approaches for im- proved SAT algorithms, volume 35 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pages 261-313. American Mathematical Society, 1997.
  69. Oliver Kullmann. New methods for 3-SAT decision and worst-case analysis. Theoretical Com- puter Science, 1998. To appear; first version announced in [2].
  70. G.S. Tseitin. On the complexity of derivation in propositional calculus. In Seminars in Math- ematics, volume 8. V.A. Steklov Mathematical Institute, Leningrad, 1968. English translation: Studies in mathematics and mathematical logic, Part II (A.O. Slisenko, editor), 1970, pages 115-125. -73- LC '98 Book of Abstracts References
  71. S. Bellantoni and S. Cook. A new recursion-theoretic characterization of the polytime functions. computational complexity, 2:97-110, 1992.
  72. Daniel Leivant. Intrinsic Theories and Computational Complexity. Logic and Computational Complexity, (Ed. D. Leivant), pages 177-194, 1995.
  73. R.W.Ritchie. Classes of predictably computable functions. Transactions of the American Mathematical Society, 106:139, 1963. -74- LC '98 Book of Abstracts References
  74. T.Plotkin, B.Plotkin, "Algebraic logic in the problem of databases equivalence", Logic Colloquium Logic'94, Clermont -Ferrand, 1994, p. 1 0 4 .
  75. P.Halmos, " Algebraic Logic", Chelcea, N.Y., 1962.
  76. B.Plotkin, "Universal algebra, algebraic logic and databases", Kluwer, 1994, 438pp. -75- LC '98 Book of Abstracts References
  77. K. Nakatogawa and T. Ueno, On structural inference rules for Gentzen-style natural deduction, Part I, Proceedings of the Sixth Asian Logic Conference, Beijing 1996, C. Chong, M. Yasugi et al. eds., World Scientific, 1998.
  78. Jaap van Oosten, Basic Category Theory, BRICS Lecture Series, LS-95-1, University of Aarhus, 1995. -77- LC '98 Book of Abstracts References
  79. D.E.Pal'chunov. On the undeciability of theories of Boolean algebras with a distinguished Ideal (Russian) Algebra i Logika 25 (1986), no.3, 326-346,364.
  80. D.E.Pal'chunov. Finitely axiomatizable. Boolean algebras with a distinguished Ideal (Rus- sian) Algebra i Logika 26 (1987), no.4, 435-455,525. 'Supported by the siberian Division of the Russian Academy of Science, grant N 3 on mathematics for youth scientific groups. -78- LC '98 Book of Abstracts References
  81. Wolfgang J. Paul, Ernst J. Prauss, Rudiger Reischuk: On Alternation. Acta Informatica 14: 243-255 (1980)
  82. Anatoly P. Beltiukov: Machine description and hierarchy of initial Grzegorczyk classes. Zapiski nauchnykh seminarov LOMI, 1979, v. 88, p. 3 0 -46 .
  83. Peter Clote: Nondeterministic Stack Register Machines. TCS 178(1-2): 37-76 (1997) -81- LC '98 Book of Abstracts References
  84. J. Barwise, Admissible Sets and Structures, Springer-Verlag, 1975.
  85. J. Barwise and YN. Moschovakis. Global inductive definability. Journal of Symbolic Logic, 43:521-534, 1978.
  86. H.-D. Ebbinghaus and J. Flum, Finite Model Theory, Springer, 1995.
  87. TJ. Grilliot. Inductive definitions and computability. Transactions of the American Mathematical Society, 158: 309- 317, 1971.
  88. Y.N. Moschovakis. Elementary Induction on Abstract Structures, North-Holland, 1974.
  89. Y.N. Moschovakis, On nonmonotone inductive definability. Fundamenta Mathematicae, 82:39-83, 1974. -82- LC '98 Book of Abstracts References
  90. GARDENFORS, P -MAKINSON, D: Nonmonotonic inference based on expecta- tions. Artificial Intelligence 65 (1994) 197-245.
  91. FARINAS DEL CERRO et al.: From ordering-based nonmonotonic reasoning to conditional logics. Artificial Intelligence 66 (1994) 375-393.
  92. STALNACKER, R1 A theory of conditionals. In N. Rescher (ed.) Studies in Logi- cal Theory. American Philosophical Quarterly Monograph Series, no. 2, Blackwell, Oxford 1968. REFERENCES
  93. Douglas K. Brown, Mariagnese Giusto, and Stephen G. Simpson, Vitali's theorem and WWKL, preprint, 17 pages, October 1996, to appear.
  94. Mariagnese Giusto, Topology and Analysis in Reverse Mathematics, Ph.D. thesis, Universit•. di Torino, 1998.
  95. Stephen G. Simpson, Perspectives in Mathematical Logic, Springer-Verlag, in preparation.
  96. Xiaokang Yu and Stephen .G. Simpson, Measure theory and weak K5nig's lemma, Archive for Mathematical Logic 30 (1990), 171-180.
  97. E-mail address: giustoedm.unito .it, mariagnesefsavonaonline .it DIP. DI MATEMATICA -UNIVERSITA DI TORINO -VIA CARLO ALBERTO 10 -10123 TORINO - ITALY -88- LC '98 Book of Abstracts REFERENCES
  98. S. R. Buss. Polynomial size proofs of the propositional pigeonhole principle. Journal of Symbolic Logic, 52:916-927, 1987.
  99. P. Clote. Sequential machine independent characterizations of the parallel complexity classes AlogTIME, ACk, NCk, and NC. In Feasible Mathematics: A Mathematical Sciences Institute Workshop held in Ithaca, New York, June 1989, pages 49-69. Birkhiuser, 1990.
  100. Stephen A. Cook and Robert A. Reckhow. The relative efficiency of propositional proof systems. Journal of Symbolic Logic, 44:36-50, 1979.
  101. J.-L. Lee. Count and tree in uniform NC'. PhD thesis, Department of Mathematics, University of Illinois at Urbana-Champaign, 1997.
  102. S. B. Buss. The undecidability of k-provability. Annals of Pure and Applied Logic, 53:72-102, 1991.
  103. A. Carbone. Turning cycles into spirals, 1998. Annals of Pure and Applied Logics, submitted.
  104. D. Hilbert and P. Bernays. Grundlagen der Mathematik 2. Springer Verlag, 1970.
  105. G. Mints. Epsilon substitution method for the theory of heredittarily finite sets (russian). In Proc. Eston. Acad. of Sci. Fiz.-Math., pages 154-164, 1989.
  106. W. W. Tait. The substitution method. The Journal of Symbolic Logic, 30 (2):175- 192, 1965.
  107. V. P. Orevkov. Lower bounds for increasing complexity of derivations after cut elimination. Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matem- aticheskogo Instituta, 88:137-161, 1979.
  108. Norbert Preining. Sketch-as-proof, a proof-theoretic analysis of axiomatic projec- tive geometry. Master's thesis, University of Technology, Vienna, Austria, 1996. http://mm.logic. at/people/preining/publications/sketch-as-proof .ps.
  109. Norbert Preining. Sketch-as-proof. In G. Gottlob, A. Leitsch, and D. Mundici, editors, Computational Logic and Proof Theory, Proc. 5a Kurt G1del Colloquium KGC'97, Lecture Notes in Computer Science 1289, pages 264-277, Vienna, Aus- tria, 1997. Springer. http://ww.logic.at/people/preining/publications/kgc97.ps.
  110. Julia Robinson. Undecidability in the arithmetic of integers and rationals and in the theory of fields. Journal of Symbolic Logic, 14:77, 1949.
  111. R. Statman. Lower bounds on Herbrand's theorem. Proc. of the Amer. Math. Soc., 75:104-107, 1979.
  112. • Supported by the Austrian Research Fund (FWF Projekt P11934-MAT)
  113. -91- LC '98 Book of Abstracts References
  114. M. Ardeshir, W. Ruitenburg, Basic Propositional Calculus, I, to ap- pear in MLQ.
  115. A. Visser, Uniform Interpolation and Layered Bisimulation, in: G6del's 96, Springer, 1996, pp. 139-164.
  116. -93- LC '98 Book of Abstracts References
  117. M. Baaz and A. Leitsch. Cut normal forms and proof complexity. Ann. Pure Appl. Logic, 1998. To appear.
  118. M. Baaz and A. Leitsch. Fast Cut-Elimination by Projection. In Proc. of the CSL'96. Springer Lecture Notes in Computer Science 1258, 18-33 (1997) *Supported by the Austrian Research Fund (FWF Projekt P11934-MAT)
  119. -94- LC '98 Book of Abstracts References
  120. M. Baaz, C. G Fermueller, and R. Zach. Elimination of cuts in first-order finite-valued logics. Journal of Information Processing and Cybernetics. EIK, 29(6):333-355, 1994.
  121. W.J. Blok and D. Pigozzi. Protoalgebraic logics. Studia Logica, 45:337-369, 1986.
  122. A.J. Gil and J. Rebagliato. Protoalgebraic Gentzen systems and the cut rule. Mathematics preprint series 245, Universitat de Barcelona, December 1997.
  123. G. Rousseau. Sequents in many valued logic I. Fundamenta Mathematicae, 60:23-33, 1967. • Universitat Pompeu Fabra, Barcelona. angel. gil~econ. upf. es.
  124. Carnielli, W. A., Systematization of finite many-valued logics through the method of tableaux, Journal of Symbolic Logic 52, no 2, pp. 473-93 (1987).
  125. Carnielli, W. A., On sequents and tableaux for many-valued logics , Journal of Non-Classical Logic 8 , no 1, pp. 59-76 (1991).
  126. Hiihnle, R., Automated Deduction in Multiple-Valued Logics, International Series of Monographs on Computer Science, vol. 10, Oxford Univ. Press, 1993.
  127. Hf.hnle, R., Many-valued logics and mixed integer programming, Annals of Mathematics and Artificial Intelligence 12 no 3,4, pp. 231-264 (1994).
  128. Hiihnle, R., Proof theory of many-valued logic -linear optimization -logic design: connections and interactions, Soft Computing 01, pp. 107-119 (1997).
  129. -96- LC '98 Book of Abstracts J. M. DAVOREN, On Continuous Dynamics and Modal Logics.
  130. CFIS, 626 Rhodes Hall, Cornell University, Ithaca, NY 14853-3801, USA.
  131. E-mail: davoren~hybrid. cornell. edu An abstract transition system is'a structure T = (X, {-}aeAct), where X 5 0 is the state space and for each a E Act, -4 is a binary relation on X. Such structures are used in many areas of computer science to model dynamic changes of state. They provide a Kripke semantics for propositional modal languages with box modalities [a] for a E Act. Given an assignment ý of a subset of X to each atomic proposition, extend the valuation to all formulas by interpreting the propositional connectives by their set-theoretic counterparts, and each modality [a] by the universal pre-image operator ra(A) -{x E X I (Vy E X)x-+y =v y E A}, for A E 'P(X). A formula ýp is true in a model ('X, ý) iff II•PWo = X, and valid in a structure T iff it is true for all valuations ý for T. The Hilbert-style proof system for such a minimal modal action logic AL has a normality axiom scheme K[a] and a rule of [a]-necessitation for each a E Act; AL is just the base of the modal i-calculus L, (see [
  132. My interest is in the topological notions of continuity for transition relations -4, and their expression in a modal logic. From Kuratowski's Topology, §18, given a topology T on X, a relation 4 is said to be upper-(respectively, lower-) semi-continuous iff ra(U) (aa(U)) is open whenever U is open in T, where 0a(A) --(-7-r)(A). Let TALo, (basic) Topological Action Logic, be the modal logic obtained from AL by extending the language with a new 0 modality and adding the axioms and necessitation rule for the box modality of S4. From McKinsey and Tarski's work ifn the 40's, S4 admits a topological semantics with 51 interpreted by the topological interior operator. We take a topological structure to be a transition system ® = (X, T, {f-4 }aEAct, A), additionally equipped with a topology T on X and a valuation algebra A: a Boolean algebra of subsets of X containing T and closed under each ra. The range of atomic assignments ý for E is restricted to A. Then 4 is upper-(lower-) semi-continuous w.r.t. T iff the schema [a]0p -+ O[a]W ((a)[] -+ 0(a)W) is valid in E. Let TAL be the logic obtained from TALo by adding the two continuity axiom schemes for each a E Act. In proving completeness of TAL, one can proceed with the usual canonical model construction: the state space X is the set of all ultrafilters of the Lindenbaum algebra of TAL, and is equipped with a topology TR defined by a pre-order R on X. Pre-orders on a set X are in one-one correspondance with the class of Alexandroff topologies on X. Continuity with respect to an Alexandroff topology is intimately connected with the notion of a bisimulation equivalence on a transition system, and reveals a richer class of "nice" quotient transition systems. Applications to the theory of hybrid control systems (see [3]) are discussed. Modal logics of continuous functions are investigated in [2], and independently considered in
  133. M. BONSANGUE AND M. KWIATKOWSKA, Re-interpreting the Modal fi-calculus, in A. Ponse et al. (eds.), Modal Logic and Process Algebra, CSLI Publications, Stanford, 1995; pp. 65-83.
  134. J. M. DAVOREN, Modal Logics for Continuous Dynamics, PhD dissertation, Depart- ment of Mathematics, Cornell University, January 1998.
  135. T. A. HENZINGER, The Theory of Hybrid Automata, in Logic in Computer Science LICS'96, IEEE Computer Society Press, 1996; pp. 278-292.
  136. P. KREMER AND G. MINTS, Dynamic Topological Logic, abstract in Bulletin of Symbolic Logic, vol. 3 (1997), pp. 371-372. -97- LC '98 Book of Abstracts Title: Characterizing persistent formulas preserved under bisimulations References
  137. C.A.ANDERSON -Some emendations to G6del's ontological proof, Faith and Philosophy 7 (1990).
  138. C.A.ANDERSON, M.E.GETTINGS -G6del's ontological argument revisited, in Ghdel '96 (P.Hijek ed.), Lecture Notes in Logic 6, Springer V., New York 1996, 167-172.
  139. E.DE GIORGI, M.FoRTI, G.LENZI -Verso i sistemi assiomatici del 2000 in Matematica, Logica e Informatica, Quad. S.N.S. Pisa 26, Pisa 1996.
  140. M. FORTI, G. LENZI -A general axiomatic framework for the foundations of Mathematics, Logic and Computer Science, Rend.Mat.Accad.Naz.Sci.d.XL (1997).
  141. K.G6DEL -Collected Works, Vol III, Unpublished Essays and Lectures (S.Feferman et al. eds.), Oxford University Press, Oxford 1995.
  142. P.HmJEK -Magari and others on G6del's ontological proof, in Proceedings of the International conference on Logic and Algebra in memory of Roberto Magari (P.Aglianb and A.Ursini eds.)(1996), 125-135.
  143. R.MAGARI -Logica e Teofilia, Notizie di Logica 7-4 (1988), 11-20.
  144. F.ORILIA -A note on G6del's ontological argument, European Review of Philosophy 1 (1994), 125-131.
  145. J.H.SOBEL -G6del's Ontological Argument, in On Being and Saying. Es- says for Richard Cartwright (J.J.Thomson ed.), MIT Press, Cambridge MA, (1987), 241-261.
  146. Y. Suzuki, F. Wolter and M. Zakharyaschev, Speaking about transitive frames in propositional languages, Research Report in JAIST, 1997.
  147. A. Visser, A propositional logic with explicit fixed points, Studia Logica, 40, 1981, pp.155-178. 'Department of Information systems and Quantitative Sciences, Nanzan University, 18 Yamazato- cho, Showa-ku, Nagoya 466-8673, Japan; e-mail: sasaki0iq.nanzan-u.ac.jp. (Institut fiir informatik, Universitut Leipzig, Augustus-Platz 10-11, 04109 Leipzig, Germany; e-mail: sasakicinformatik.uni- leipzig.de.) -105- LC '98 Book of Abstracts References
  148. Tishkovsky D. E. On algebraic semantics for superintuitionistic predicate logic. Minisemester "Logic, Algebra and Computer Science" (Helena Rasiowa in memoriam), War- saw, December 1996. -106- LC '98 Book of Abstracts References
  149. de Paiva, Valeria and Pereira, Luiz C., A New ProofSystem for Intuitionistic Logic, in Abstracts of the Logic Colloquium '93, 1993.
  150. Hyland, Martin and de Paiva, Valeria, Full intuitionistic linear logic, in Annals of Pure and Applied Logic, 64, pp.273-291, 1993.
  151. L6pez-Escobar, E.G.K., A Natural Deduction System for someIntermediate Logics, in The Journal of Non-Classical Logic, vol.1, no.1, pp.21-41, 1982. -107- LC '99 Book of Abstracts References
  152. T.Hosoi. On intermediate logics I, J.Fac.Sci.Univ.Tokyo, 1967,14,293-312.
  153. L.Maksimova. Craig's theorem in superintuitionistic logics and amalgamable varieties. Algebra and Logic, 16, N 6 (1977), 643-681.
  154. L.Maklsimova. On variable separation in modal and superintuitionistic logics. Studia Logica, 55 (1995). 99-112.
  155. -109- LC '98 Book of Abstracts References
  156. Marco Benini. The collection method in second-order intuitionistic logic, sub- mitted to Annals of Pure and Applied Logic, 1997.
  157. Mauro Ferrari. Strongly Constructive Formal Systems. PhD thesis, Dept. of Computer Science -University of Milano, 1997.
  158. FM971 Mauro Ferrari and Pierangelo Miglioli. Strongly constructive formal systems. submitted to Annals of Pure and Applied Logic, 1997.
  159. Pierangelo Miglioli and Mario Ornaghi. A purely logical computing model: the open proofs as programs. Technical Report MIG-7, Istituto di Cibernetica -University of Milano, 1979.
  160. Pierangelo Miglioli and Mario Ornaghi. A logically justified model of compu- tation. Fundamenta Informaticae, IV(1,2):151-172, 277-341, 1981.
  161. -L10- LC '98 Book of Abstracts References
  162. Maksimova L.L., Interpolation in superintuitionistic predicate logic 'with equality. Al- gebra and Logic, 36, 5(1997), 319-329.
  163. Schreiner P.A.. Failure of interpolation property and Beths property in some predicate superintuitio'nistic logic, Algebra and Logic, 35, 1(1996), 59-65.
  164. Schreiner P.A.. Intermediate predicate logic 'without Beth's property, Algebra and Log- ic, 37, 1(1998). 107-117.
  165. -Ill- LC '98 Book of Abstracts References:
  166. M.E. Coniglio, The Logic of Sheaves over Right-sided and Idempotent Quantales, Doctoral Thesis (in Portuguese), Sdo Paulo University (1997).
  167. M.P. Fourman, D.S. Scott, Sheaves and Logic, L.N.M. 753 (1979), 302-401.
  168. P. Johnstone, Notes on Categorical Logic, Tutorials of Wollic '97, Fortaleza (1997).
  169. M. Makkai, G.E. Reyes, First-Order Categorical Logic, L.N.M 611 (1977). -112- LC '99 Book of Abstracts References
  170. R. Dyckhoff. Contraction-free sequent calculi for intuitionistic logic, Thfi Journial of Symbolic Logic, vol. 57, pp. 795-807, 1992.
  171. R. Dyckhoff, S. Negri. Admissibility of structura.l rules in coiit ract ion- free systems for intuitionistic logic, manuscript, 1997.
  172. J. Hudelmaier. Bounds for cut elimination in intuitionistic propositional logic, Archive for Watheematical Logic, vol. 31, pp. 331-354, 1992.
  173. S. Negri. Sequent calculus proof theory of intuitionistic apartness and order relations, 1997, to appear in Archive for Mathematical Logic.
  174. S. Negri, J. von Plato. Cut elimination in the presence of axioms. manuscript, 1998. -113- LC '98 Book of Abstracts References
  175. V.C.V. De Paiva. A Dialectica Model of the Lambek Calculus. University of Cambridge.1991. Manuscript.
  176. J.-Y. Girard. Linear Logic. Theoretical Computer Science, Vol 50, 1987, 1-102.
  177. J. Lambek. The Mathematics of Sentence Structure. American Math. Monthly 65,1958,154- 169.
  178. D. N. Yetter. Quantales and (Noncommutative) Linear Logic. Journal of Symbolic Logic 55, 1990, 41-64.
  179. -l14- LC '98 Book of Abstracts References
  180. BUCHHOLZ, W., FEFERMAN, S., POHLERS, W., AND SIEG, W. Iterated Inductive Definitions and Subsystems of Analysis: Recent Proof-Theoretical studies, LNM 897. Springer, 1981.
  181. CANTINI, A. A theory of formal truth arithmetically equivalent to ID 1 . Journal of Symbolic Logic, 55(1):244-259, 1990.
  182. CANTINI, A. Logical Frameworks for Truth and Abstraction. North-Holland, 1996.
  183. KAHLE, R. Applikative Theorien und Frege-Strukturen. Dissertation, Institut ffir Infor- matik und angewandte Mathematik, Universitit Bern, 1997.
  184. KAHLE, R. Frege structures for partial applicative theories. 199x. Submitted. References [F-K] S. Fajardo and H.J. Keisler, Neometric Spaces, Advances in Mathematics 118 (1996), pp. 13 4 -1 7 5 .
  185. C.W. Henson, Nonstandard hulls of Banach spaces, Israel J. Math. 25 (1976), pp.108-144.
  186. J. Iovino, A quick introduction to Banach space model theory, preprint.
  187. H.J. Keisler, Quantifier elimination for neocompact sets, to appear.
  188. W.A.J. Luxemburg, A general theory of monads, in "Applications of Model Theory to Algebra, Analysis and Probability" (W.A.J. Luxemburg ed.), Holt, Rinehart and Winston, New York, 1969. -117- LC '98 Book of Abstracts References
  189. S.A.ADELEKE,'Semilinear tower of Steiner systems', Journal of Combina- torial Theory, Series A 72 (1995) 243-255
  190. S.A.ADELEKE AND H.D.MACPHERSON,'Classification of infinite primitive Jordan permutation groups', Proc. London Math. Soc. (3) 72 (1996) 63-123
  191. G.L.CHERLIN, L.HARRINGTON AND A.H.LAcHLAN,'jo-categorical, No- stable structures', Annals of Pure and Applied Logic 28 (1985) 103-135
  192. P.M. NEUMANN,'Some primitive permutation groups', Proc. London Math. Soc. (3) 50 (1985) 265-281 -118- LC '98 Book of Abstracts Reference [N] Newleski, Omitting Tpes and the Real Line, The Journal of Symbolic Logic, Vol.52, No.4 Dec. 1987, pp. 1020-1026. -120- LC '98 Book of Abstracts References
  193. C. Berge Graphes et hypergraphes , Paris, 1970.
  194. A. V. Molchanov, On definability of hypergraphs by semigroups of homomorphisms, Summaries of Talks, 2-d Siberian Congress on Applied and Industrial Mathematics, Novosibirsk, 1996, p. 193.
  195. A. V. Molchanov, On definability of hypergraphs by their semi- groups of homomorphisms , Semigroup Forum, to appear. -121- LC '98 Book of Abstracts References
  196. B.Plotkin, S.Vovsi "Varieties of representations of groups". Riga, 1983, 338pp.
  197. B.Plotkin, E.Koublanova "Varieties and pseudovarieties of group representa- tions" Proc. of Int. Conf. Groups-97 in Bath, to appear. -122- LC '98 Book of Abstracts References
  198. A.I.Mal'cev, On general theory of algebraic systems, Matem. sbornik, 1954, V.35. P. 3-20.
  199. S. Eilenberg and M. P. Schiitzenberger, On pseudovarieties, Advances in Math., 1976, V. 19, N
  200. V.A.Molchanov, Nonstandard varieties of pseudotopological algebraic systems, Sibirskii matem- aticheskii zhurnal, 1991, V.32, No.
  201. V.A.Molchanov, Nonstandard characterization of pseudovarieties, Algebra Universalis, 1995, V. 33. P. 533-547. -123- LC '98 Book of Abstracts References
  202. Tarski, A., Der Wahrheitsbegriff in den formalisierten Sprachen, Studia Logica 1, 1935, pp. 261-405.
  203. Gupta, A., Belnap, N., The Revision Theory of Truth, MIT Press, Cambridge, Massachusetts, 1993. -124- LC '98 Book of Abstracts Non standard finite fields in $I\Delta_0 +\Omega._l$ Paola D'Aquino (joint work with A. Macintyre) Seconda Universita' di Napoli "daquinoi@,axrma.uniromaI.it
  204. Let $M$ be a model of I\Delta_0 + \OmegaiS and $K$ be the residue field of SM$ for a non standard prime $p$ in $M$.
  205. If $M$ is a model of SPAS then $K$ is a pseudo-finite field (see [M]), i.e. it satisfies the following axioms of Ax
  206. every absolutely irreducible curve has a point in the field. In the case of Open Induction, Macintyre e Marker proved in [MM] that for any field $L$ of characteristic $0$ there is a model $M$ of Open Induction and a prime Sp\in M$ such that the residue field $K$ is elementary equivalent to $L$. In particular, $K$ can have infinitely many extensions of each degree. Using results of bounded arithmetic and some Galois theory we can prove the following results. (\bf Theorem 1.) Let $M$ be a model of $I\Delta_0 +\Omega_1$, Sp\in MS a non standard prime and $K$ the residue field. Suppose $K$ contains the primitive Sn$-roots of unity, for SnWin {\bfN)$. Then there exists a unique abelian extension of SK$ of dimension $n$. . Then all Sylow subgroups of SG$ are cyclic (i.e. $G$ is a $Z$-group in the sense of Passman [P]).
  207. \bf Corollary 2.) The Galois group of $F$ over $K$ is generated by two elements $x,y$ such that $xAn-y,^m=l$, $xA(^1)yx=yI$, $(r-l,m)=(n,m)=1$ and $rAn\equiv I(\nbox( mod m))$.
  208. A Macintyre, Residue fields of models of $P$, in Logic, Methodology and Philosophy of Science VI (ed. L.E. Cohen et al.), Amsterdam 1982.
  209. A. Macintyre and D. Marker, Primes and their residue rings in models of Open Induction, Annals of Pure and Applied Logic 43, (1989).
  210. D. Passman, Permutation Groups, Benjamin 1968. -125- LC '98 Book of Abstracts References
  211. J. Johannsen. A bounded arithmetic theory for constant depth threshold circuits. In P. HMjek, editor, GODEL '96, pages 224-234, 1996. Springer Lecture Notes in Logic 6.
  212. J. Krajfiek. Bounded Arithmetic, Propositional Logic and Complexity The- ory. Cambridge University Press, 1995. -126- LC '98 Book of Abstracts REFERENCES
  213. A. Bbs, On Pascal triangles modulo a prime power, Annals of Pure and Applied Logic 89 (1997), 17-35, (Logic Colloquium'94, Clermont-Ferrand).
  214. A. A. Karatsuba, Foundations of the analytical number theory (in Russian), "Nauka", Moscow, 1983.
  215. I. Korec, Definability of arithmetic operations in Pascal triangle modulo an integer divis- ible by two primes, Grazer Mathematische Berichte 318 (1993), 53-61.
  216. -, Theories of generalized Pascal triangles, Annals of Pure and Applied Logic 89 (1997), 45-52, (Logic Colloquium'94, Clermont-Ferrand).
  217. J. Robinson, Definability and decision problems in arithmetic, Journal of Symbolic Logic References
  218. A. Hoogewijs Partial Predicate Logic in ComputerScience Acta Informatica 24, pp381-393, Springer-Verlag, 1987.
  219. W.A. Carnielli -On sequents and tableaux for Many-Valued Logics The Journal of Non-Classical Logic -Vol 8, nr. 1, 1991 -135- LC '98 Book of Abstracts References
  220. R. Hihnle, B. Beckert, S. Gerbertding -3TAP: The Many-Valued The- orem Prover 3rd Edition, September 94,University of Karslruhe , Institue for Logic, Complexity and Deduction Systems. http://il2www.ira.uka.de/-threetap.
  221. F. Oppacher, E. Suen -HARP: A tableau-based theorem prover. Journal of Automated Reasoning, 4:69-100, 1988
  222. A. Hoogewijs Partial Predicate Logic in ComputerScience Acta Informatica 24, pp381-393, Springer-Verlag, 1987.
  223. L. Paulson -Isabelle -A Generic Theorem Prover Lecture Notes in Computer Science -Springer Verlage, 1994. -136- LC '98 Book of Abstracts References
  224. Jones, C. Middelburg C. A Typed Logic of Partial Functions Reconstructed Classically, Acta Informatica 31, pp399-430(1994)
  225. Jones, C. Jones, K. Lindsay, P. Moore, R. Mural: a Formal Development Support System, Springer-Verlag(1991) -137- LC '98 Book of Abstracts References [1] Andre Fuhrmann and Sven Ove Hansson. A survey of multiple contractions. Journal of Logic, Language and Information, 3:39-76, 1994.
  226. Peter Girdenfors. Knowledge in Flux : Modeling the Dynamics of Epistemic States. The MIT Press, Cambridge Massachusetts, 1988. -140- LC '98 Book of Abstracts
  227. A. Avellone, M. Ferrari, P. Miglioli, Duplication-free tableau calculi together with cut- free and contraction-free sequent calculi for the interpolable propositional intermediate logics. Technical Report 210-97, Dipartimento di Scienze dell'Informazione, Universita degli Studi di Milano, 1997. (Submitted to JLC).
  228. G. Corsi, Completeness theorem for Dummett's LC quantified and some of its exten- sions, Studia Logica vol. 51, pp 3176-335, 1992.
  229. M. Dummett, A propositional calculus with denumerable matrix, Journal of Symbolic Logic, vol. 24, pp 96-107, 1959.
  230. R. Dyckhoff, Contraction-free sequent calculi for intuitionistic logic, Journal of Symbolic Logic, vol. 57, pp 795-807, 1992.
  231. J. Hudelmaier, Bounds for cut elimination in intuitionistic propositional logic, Archive for Mathematical Logic, vol. 31, pp 331-354, 1992.
  232. Sonobe, A Gentzen-type formulation of some intermediate propositional logics, Jour- nal of Tsuda College vol. 7, pp 7-13, 1975.
  233. A. S. Troelstra and H. Schwichtenberg, Basic Proof Theory, Cambridge University Press, 1996. -142- LC '98 Book of Abstracts References:
  234. Serembus, John H., AOFunctional Completeness Revisited^(, presented to the European meeting of the Association of Symbolic Logic. Vesprem, Hungary. August 9 to 15, 1992. [2] Serembus, John H., A6 A Study of Truth Table Notation of Propositional LogicA(O, presented to the Conference on Notational Engineering, George Washington University, Washington, D. C. May 23 to 24, 1996. -143- LC '98 Book of Abstracts A linear logic with maximal distributivity properties Jean Leneutre* Itcole Nationale Sup~rieure des T6lcommunications D6partement Informatique et R1seaux 46 rue Barrault, 75634 PARIS Cedex 13, FRANCE References.
  235. Philippe de Groote. Partially commutative linear logic: Sequent calculus and phase semantics. In V. M. Abrusci and C. Casadio, editors, Proofs and Linguistic Categories, Application of Logic to the Analysis and Implementation of Natural Language, pages 199-208, Roma, 1996. Cooperativa Libraria Universitaria Editrice Bologna.
  236. Paul Ruet. Non-Commutative Logic and Concurrent Constraint Programming. PhD thesis, Universit6 Denis Diderot, Paris 7, 1997.
  237. *demailleeinf enst. fr, Tel: + 33 1 45 81 78 68, http: //www. inf. enst.fr/-demaille/papers/ -146- LC '98 Book of Abstracts References
  238. H.J. Hoehnke, Fully invariant algebraic closure systems of congruences and quasivarieties of algebras, in L. Szabo and A. Szendrei (eds.), "Lectures in universal algebra, Szeged '83", Colloq. Math. Soc. J. Bolyai 43, North- Holland, Amsterdam, 1986; pp. 189-207.
  239. B.H. Neumann, "Universal algebra", Lecture Notes, Courant Institute of Math. Sci., New York University, 1962.
  240. R.W. Quackenbush, Completeness theorems for universal and implicational logics of algebras via congruences, Proc. of the AMS 103 (1988), 1015-1021.
  241. Baeten, J. and B. Boerboom (1979), Q can be anything it should not be, Indag. Mathematicae 41, 111 -120.
  242. Berarducci, A., I. Intrigila (1993), Some new results on easy lambda terms, Theoretical Computer Science 121, 71 -88.
  243. Jacopini, G. (1975), A condition for identifying two elements of whatever model of combinatory logic, in: B6hm, C. (Editor), Lambda Calculus and Computer Science, Springer Verlag, Berlin, 213 -219.
  244. Kuper, J. (1997), On the Jacopini technique, Information and Computation 138, 101 -123.
  245. Plotkin, G.D. (1977), LCF considered as a programming language, Theoretical Computer Science 5, 223 -255. -150- LC '98 Book of Abstracts Title: MIM Logik References [Lee 1972] Lee R. C. T. Fuzzy Logic and the Resolution Principle. Journal of the ACM, v. 19, No. 1, (January 1972), pp. 109-119.
  246. Rents 19961 Rents I. Gentzen type sequent calculus for propositional fuzzy logics. In proc. EU- FIT'96, 4th European Congress on Intelligent Techniques and Soft Computing, Aachen, Ger- many, v. 1, pp. 9 6 -9 9 .
  247. Rents 1998] Rents I. Gentzen type sequent calculus for first-order fuzzy logics. submited to EU- FIT'98, 6th European Congress on Intelligent Techniques and Soft Computing, Aachen, Ger- many. [Zadeli 1965] Zadeh L. A. Fuzzy sets. Inform. Contr. 8 (1965), 338-353. References
  248. Baaz, M., and Veith, H.: Interpolation in Fuzzy Logic. To appear in Archive of Mathematical Logic.
  249. Gould, H.W.: Binomial Coefficients, the Bracket Function, and Compositions with Relatively Prime Summands. Fibonacci Quarterly 2, No. 4, 241-260, 1964.
  250. Hdjek, P.: Metamathematics of Fuzzy Logic. Book in preparation.
  251. Krystek, P.S., Zachorowski, S.: Lukasiewicz logics have not the interpolation property. Rep. Math. Logic 9, 39-40, 1977.
  252. Ling, H.C.: Representation of associative functions. Publ. Math. Debrecen 12, 182-212, 1965.
  253. Maksimova, L.: Craig's interpolation theorem and amalgamable varieties. Dok- lady Akademii Nauk SSSR, 237/6, 1281-1284, 1977. -163- LC '98 Book of Abstracts References
  254. J. A. Goguen, L-Fuzzy Sets, J. Math. Anal. Appl. 18(1), 145-174, 1967.
  255. M. Shimoda, Categorical aspects of Heyting-valued models for intuitionistic set theory, Com- ment. Math. Univ. Sancti Pauli, 30(1), 17-35, 1981.
  256. L. A. Zadeh, Fuzzy sets, Inf. Control, 8(3), 338-353, 1965.
  257. L. A. Zadeh, Similarity relations and fuzzy orderings, Inf. Sci., 3(2), 177-200, 1971. -165- LC '98 Book of Abstracts References
  258. C.C. Chang, Algebraic analysis of many-valued logics, Trans. Amer. Math. Soc. 88 (1958), 467-490.
  259. P. H1jek, Metamathematics of fuzzy logic. Inst. of Comp. Science, Academy of Scienec of Czech Rep. Technical report 682 (1996).
  260. C.S. Hoo, MV-algebras, ideals and semisimplicity, Math. Japonica 34 (1989), 563-583.
  261. E. Turunen, BL-algebras and Basic Fuzzy Logic (submitted). -166- LC '98 Book of Abstracts [L_____________________ References
  262. Hijek P.: Metamathematics of fuzzy logic. Kluwer, Dordrecht (to appear).
  263. McNaughton, R.: Theorem about infinite-valued sentential logic. J. Symb. Log., 16(1951), 1-13.
  264. Novik, V.: On the Syntactico-Semantical Completeness of First-Order Fuzzy Logic. Part I -Syntactical Aspects; Part HI- Main Results. Kybernetika 26(1990), 47-66; 134-154.
  265. Novik, V: Open Theories, Consistency and Related Results in Fuzzy Logic. Int. J. of Approximate Reasoning 1997 (to appear).
  266. Tonis, A. and I. Perfilieva: Functional System of Infinite-valued Propositional Calculus. In: Novik, V. and I. Perfilieva (eds.): Discovering World with Fuzzy Logic: Perspectives and Approaches to Formalization of Human-Consistent Logical Systems. Springer-Verlag, Heidelberg (to appear). -169- LC '98 Book of Abstracts References
  267. Dekker, J.C.E., e Myhill, J. Retraceable sets, Can. J. Math., 10 (1958) 357-373.
  268. Jockusch, C.G. Uniformly introreducible sets, J. Symbolic Logic, 33 (1968) 521-536. -174- LC '98 Book of Abstracts
  269. FIADEIRO, J. L. and SERNADAS, A. -Structuring Theories on Consequence. In Sannella, D. and Tarlecki, A. (eds.) Recent TRends in Data Type Specification, Springer-Verlag, Berlin, 1988 (pp. 44-72).
  270. -176- LC '98 Book of Abstracts References
  271. Kohlenbach, U., On the arithmetical content of restricted forms of com- prehension, choice and general uniform boundedness. To appear in: Ann. Pure Appl. Logic.
  272. Kohlenbach, U., On the no-counterexample interpretation. To appear in: JSL.
  273. Kohlenbach, U., Proof theory and computational analysis. Submitted. -177- LC '98 Book of Abstracts

Related papers

Contraction-free sequent calculi for intuitionistic logic
Roy Dyckhoff

The Journal of Symbolic Logic, 1992

View PDFchevron_right
Admissibility of structural rules for contraction-free systems of intuitionistic logic
Sara Negri

The Journal of Symbolic Logic, 2000

We give a direct proof of admissibility of cut and contraction for the contraction-free sequent calculus G4ip for intuitionistic propositional logic and for a corresponding multi-succedent calculus: this proof extends easily in the presence of quantifiers, in contrast to other, indirect, proofs, i.e., those which use induction on sequent weight or appeal to admissibility of rules in other calculi.

View PDFchevron_right
Cut-Elimination and a Permutation-Free Sequent Calculus for Intuitionistic Logic
Roy Dyckhoff

Studia Logica, 1998

View PDFchevron_right
A Permutation-Free Sequent Calculus for Intuitionistic Logic
Roy Dyckhoff

St Andrews University Computer Science Research …

View PDFchevron_right
A cut-free sequent calculus for the bi-intuitionistic logic 2Int
Sara Ayhan

arXiv:2009.14787, 2020

The purpose of this paper is to introduce a bi-intuitionistic sequent calculus and to give proofs of admissibility for its structural rules. The calculus I will present, called SC2Int, is a sequent calculus for the bi-intuitionistic logic 2Int. Calculi for this logic represent a kind of bilateralist reasoning, since they do not only internalize processes of verification or provability but also the dual processes in terms of falsification or what is called dual provability. A normal form theorem for a natural deduction calculus of 2Int has already been stated, in this paper I want to prove a cut-elimination theorem for SC2Int, i.e. if successful, this would extend the results existing so far.

View PDFchevron_right
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved