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Volumn 24, Issue 3, 2000, Pages 319-364

Single step tableaux for modal logics: Computational properties, complexity and methodology

Author keywords

Complexity; Confluence; Decision procedures; Direct and translation methods; Modal logics; Prefixed tableaux

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; DECISION THEORY; FORMAL LOGIC; SET THEORY;

EID: 0034174114     PISSN: 01687433     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1006155811656     Document Type: Article
Times cited : (68)

References (47)
  • 2
  • 3
    • 0026385742 scopus 로고
    • TABLEAUX, a general theorem prover for modal logics
    • Catach, L.: TABLEAUX, a general theorem prover for modal logics, J. Automated Reasoning 7(1991), 489-510.
    • (1991) J. Automated Reasoning , vol.7 , pp. 489-510
    • Catach, L.1
  • 5
    • 0040977644 scopus 로고    scopus 로고
    • A polynomial translation of S4 into T and contraction-free tableaux for S4
    • Cerrito, S. and Cialdea Mayer, M.: A polynomial translation of S4 into T and contraction-free tableaux for S4, J. Interest Group in Pure Appl. Logic 5(2) (1997), 287-300.
    • (1997) J. Interest Group in Pure Appl. Logic , vol.5 , Issue.2 , pp. 287-300
    • Cerrito, S.1    Cialdea Mayer, M.2
  • 8
    • 0342672928 scopus 로고
    • Uniform and non uniform strategies for tableaux calculi for modal logics
    • Demri, S.: Uniform and non uniform strategies for tableaux calculi for modal logics, J. Appl. Non-Classical Logics 5(1) (1995), 77-96.
    • (1995) J. Appl. Non-Classical Logics , vol.5 , Issue.1 , pp. 77-96
    • Demri, S.1
  • 11
    • 0018454915 scopus 로고
    • Propositional dynamic logic of regular programs
    • Fischer, N. and Ladner, R.: Propositional dynamic logic of regular programs, J. Comput. System Sci. 18 (1979), 194-211.
    • (1979) J. Comput. System Sci. , vol.18 , pp. 194-211
    • Fischer, N.1    Ladner, R.2
  • 12
    • 0342672862 scopus 로고
    • Tree proofs in modal logic
    • Fitch, F.: Tree proofs in modal logic, J. Symbolic Logic 31 (1966).
    • (1966) J. Symbolic Logic , vol.31
    • Fitch, F.1
  • 14
    • 0001063429 scopus 로고
    • First-order modal tableaux
    • Fitting, M.: First-order modal tableaux, J. Automated Reasoning 4 (1988), 191-213.
    • (1988) J. Automated Reasoning , vol.4 , pp. 191-213
    • Fitting, M.1
  • 15
    • 0001604343 scopus 로고
    • Basic modal logic
    • D. Gabbay, C. Hogger, and J. Robinson (eds), Oxford Univ. Press
    • Fitting, M.: Basic modal logic, in D. Gabbay, C. Hogger, and J. Robinson (eds), Handbook of Logic in Artificial Intelligence and Logic Programming, Volume 1, Oxford Univ. Press, 1993, pp. 365-448.
    • (1993) Handbook of Logic in Artificial Intelligence and Logic Programming , vol.1 , pp. 365-448
    • Fitting, M.1
  • 16
    • 0003728505 scopus 로고
    • Labelled deductive systems
    • Max Plank Institute für Informatik (MPII), Saarbrüken, Germany, To appear as a book by Oxford Univ. Press
    • Gabbay, D.: Labelled deductive systems, Technical Report MPI-I-94-223, Max Plank Institute für Informatik (MPII), Saarbrüken, Germany, 1994. To appear as a book by Oxford Univ. Press.
    • (1994) Technical Report MPI-I-94-223
    • Gabbay, D.1
  • 18
    • 0343107119 scopus 로고
    • Theory matrices (for modal logics) using alphabetical monotonicity
    • Gent, I.: Theory matrices (for modal logics) using alphabetical monotonicity, Studia Logica 52 (1993), 233-257.
    • (1993) Studia Logica , vol.52 , pp. 233-257
    • Gent, I.1
  • 19
    • 84957645011 scopus 로고    scopus 로고
    • Building decision procedures for modal logics from propositional decision procedures - The case study of modal K
    • M. McRobbie and J. Slaney (eds.), LNAI 1104, Springer-Verlag
    • Giunchiglia, F. and Sebastiani, R.: Building decision procedures for modal logics from propositional decision procedures - the case study of modal K, in M. McRobbie and J. Slaney (eds.), Proc. of the 13th Internat. Conf. on Automated Deduction (CADE-96), LNAI 1104, Springer-Verlag, 1996, pp. 583-597.
    • (1996) Proc. of the 13th Internat. Conf. on Automated Deduction (CADE-96) , pp. 583-597
    • Giunchiglia, F.1    Sebastiani, R.2
  • 20
    • 0001919918 scopus 로고
    • Tableaux method for modal and temporal logics
    • Technical Report TR-ARP-15-5, by Kluwer Australian Nat. University, To appear as chapter on the Handbook of Tableau Methods by Kluwer
    • Gore, R.: Tableaux method for modal and temporal logics, Technical Report TR-ARP-15-5, Australian Nat. University, 1995. To appear as chapter on the Handbook of Tableau Methods by Kluwer.
    • (1995) Handbook of Tableau Methods
    • Gore, R.1
  • 21
    • 0000686226 scopus 로고
    • Modelling knowledge and action in distributed systems
    • Halpern, J. and Fagin, R.: Modelling knowledge and action in distributed systems, Distrib. Comput. 3(4) (1989), 159-177.
    • (1989) Distrib. Comput. , vol.3 , Issue.4 , pp. 159-177
    • Halpern, J.1    Fagin, R.2
  • 22
    • 0026853865 scopus 로고
    • A guide to completeness and complexity for modal logics of knowledge and belief
    • Halpern, J. and Moses, Y.: A guide to completeness and complexity for modal logics of knowledge and belief, Artif. Intell. 54 (1992), 319-379.
    • (1992) Artif. Intell. , vol.54 , pp. 319-379
    • Halpern, J.1    Moses, Y.2
  • 24
    • 84976811006 scopus 로고
    • Confluent reductions: Abstract properties and applications to term rewriting systems
    • Huet, G.: Confluent reductions: Abstract properties and applications to term rewriting systems, J. ACM 27(4) (1980), 797-821.
    • (1980) J. ACM , vol.27 , Issue.4 , pp. 797-821
    • Huet, G.1
  • 27
    • 0001951331 scopus 로고
    • A catalog of complexity classes
    • J. van Leeuwen (ed.), Elsevier Science Publishers (North-Holland), Amsterdam
    • Johnson, D.: A catalog of complexity classes, in J. van Leeuwen (ed.), Handbook of Theoretical Computer Science, Elsevier Science Publishers (North-Holland), Amsterdam, 1990, pp. 67-162.
    • (1990) Handbook of Theoretical Computer Science , pp. 67-162
    • Johnson, D.1
  • 29
    • 37949002557 scopus 로고
    • Semantical analysis of modal logic I: Normal propositional calculi
    • Kripke, S.: Semantical analysis of modal logic I: normal propositional calculi, Z. Math. Logik Grundlag. Math. 9 (1963), 67-96.
    • (1963) Z. Math. Logik Grundlag. Math. , vol.9 , pp. 67-96
    • Kripke, S.1
  • 30
    • 0000595575 scopus 로고
    • The computational complexity of provability in systems of modal propositional logic
    • Ladner, R.: The computational complexity of provability in systems of modal propositional logic, SIAM J. Comput. 6(3) (1977), 467-480.
    • (1977) SIAM J. Comput. , vol.6 , Issue.3 , pp. 467-480
    • Ladner, R.1
  • 31
    • 0027659347 scopus 로고
    • Modal nonmonotonic logics: Ranges, characterization, computation
    • Marek, W., Schwarz, S. and Truszczynski, M.: Modal nonmonotonic logics: Ranges, characterization, computation, J. ACM 40(4) (1993), 963-990.
    • (1993) J. ACM , vol.40 , Issue.4 , pp. 963-990
    • Marek, W.1    Schwarz, S.2    Truszczynski, M.3
  • 32
    • 85026906242 scopus 로고
    • Strongly analytic tableaux for normal modal logics
    • A. Bundy (ed.), LNAI 814, Springer-Verlag
    • Massacci, F.: Strongly analytic tableaux for normal modal logics, in A. Bundy (ed.), Proc. of the 12th Internat. Conf. on Automated Deduction (CADE-94), LNAI 814, Springer-Verlag, 1994, pp. 723-737.
    • (1994) Proc. of the 12th Internat. Conf. on Automated Deduction (CADE-94) , pp. 723-737
    • Massacci, F.1
  • 35
    • 0001110606 scopus 로고
    • Gentzen-type systems and resolution rules
    • LNCS 417, Springer-Verlag
    • Mints, G.: Gentzen-type systems and resolution rules, in Internat. Conf. on Computer Logic (COLOG), LNCS 417, Springer-Verlag, 1988, pp. 198-231.
    • (1988) Internat. Conf. on Computer Logic (COLOG) , pp. 198-231
    • Mints, G.1
  • 38
    • 0001424061 scopus 로고
    • Semantic-based translation methods for modal logics
    • Ohlbach, H.: Semantic-based translation methods for modal logics, J. Logic Comput. 1(5) (1991), 691-746.
    • (1991) J. Logic Comput. , vol.1 , Issue.5 , pp. 691-746
    • Ohlbach, H.1
  • 39
    • 85032069392 scopus 로고
    • Translation methods for non-classical logics - An overview
    • Ohlbach, H.: Translation methods for non-classical logics - an overview, J. Interest Group in Pure Appl. Logic 1(1) (1993), 69-89.
    • (1993) J. Interest Group in Pure Appl. Logic , vol.1 , Issue.1 , pp. 69-89
    • Ohlbach, H.1
  • 40
    • 84972546589 scopus 로고
    • Gentzen method in modal calculi
    • Ohnishi, M. and Matsumoto, K.: Gentzen method in modal calculi, Osaka Math. J. 9 (1957), 113-130.
    • (1957) Osaka Math. J. , vol.9 , pp. 113-130
    • Ohnishi, M.1    Matsumoto, K.2
  • 41
    • 84972550251 scopus 로고
    • Gentzen method in modal calculi, II
    • Ohnishi, M. and Matsumoto, K.: Gentzen method in modal calculi, II, Osaka Math. J. 11 (1959), 115-120.
    • (1959) Osaka Math. J. , vol.11 , pp. 115-120
    • Ohnishi, M.1    Matsumoto, K.2
  • 44
    • 0342672853 scopus 로고    scopus 로고
    • Resolution is a decision procedure for many propositional modal logics
    • M. Kracht, M. de Rijke, H. Wansing, and M. Zakharyaschev (eds.), Lecture Notes 87, CSLI Publications, Stanford
    • Schmidt, R.: Resolution is a decision procedure for many propositional modal logics, in M. Kracht, M. de Rijke, H. Wansing, and M. Zakharyaschev (eds.), Advances in Modal Logic, Vol. 1, Lecture Notes 87, CSLI Publications, Stanford, pp. 189-208.
    • Advances in Modal Logic , vol.1 , pp. 189-208
    • Schmidt, R.1
  • 46
    • 0003631438 scopus 로고
    • Springer-Verlag, 1968. Republished by Dover, New York
    • Smullyan, R.: First Order Logic, Springer-Verlag, 1968. Republished by Dover, New York, in 1995.
    • (1995) First order Logic
    • Smullyan, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.