메뉴 건너뛰기




Volumn 127, Issue 1-3 SPEC. ISS., 2004, Pages 155-170

Intuitionistic logic and modality via topology

Author keywords

Closure algebra; Derivative algebra; Heyting algebras; Modal systems; Provability logic; Scattered space; Topological semantics

Indexed keywords


EID: 2342533916     PISSN: 01680072     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apal.2003.11.013     Document Type: Article
Times cited : (60)

References (43)
  • 1
    • 40949096877 scopus 로고
    • Algebraic analysis of the Gödel-Löb modal system
    • Ph.D. Thesis, Tbilisi State University, Tbilisi (in Russian)
    • M. Abashidze, Algebraic analysis of the Gödel-Löb modal system, Ph.D. Thesis, Tbilisi State University, Tbilisi, 1987 (in Russian).
    • (1987)
    • Abashidze, M.1
  • 2
    • 2342563928 scopus 로고
    • Cantor's scattered spaces and the provability logic
    • (Abstract, Part I), Baku
    • M. Abashidze, L. Esakia, Cantor's scattered spaces and the provability logic, Baku Internat. Topological Conf. (Abstract, Part I), Baku, 1987, p. 3.
    • (1987) Baku Internat. Topological Conf. , pp. 3
    • Abashidze, M.1    Esakia, L.2
  • 4
  • 5
    • 2342585588 scopus 로고
    • Infinitary combinatorics and modal logic
    • Blass A. Infinitary combinatorics and modal logic J. Symbolic Logic 55 1990 761-778
    • (1990) J. Symbolic Logic , vol.55 , pp. 761-778
    • Blass, A.1
  • 6
    • 0003843090 scopus 로고
    • Varieties of interior algebras
    • Ph.D. Thesis, University of Amsterdam
    • W.J. Blok, Varieties of interior algebras, Ph.D. Thesis, University of Amsterdam, 1976.
    • (1976)
    • Blok, W.J.1
  • 7
    • 0041340798 scopus 로고    scopus 로고
    • Scattered, Hausdorff-reducible, and hereditarily irresolvable spaces
    • Bezhanishvili G. Mines R. Morandi P. Scattered, Hausdorff-reducible, and hereditarily irresolvable spaces Topology Appl. 132 2003 291-306
    • (2003) Topology Appl. , vol.132 , pp. 291-306
    • Bezhanishvili, G.1    Mines, R.2    Morandi, P.3
  • 8
    • 2342653059 scopus 로고
    • Provability in arithmetic and a schema of Grzegorczyk
    • Boolos G. Provability in arithmetic and a schema of Grzegorczyk Fund. Math. 106 1980 41-45
    • (1980) Fund. Math. , vol.106 , pp. 41-45
    • Boolos, G.1
  • 12
    • 2342593437 scopus 로고
    • The modal logic of topological spaces
    • Preprint
    • L. Esakia, The modal logic of topological spaces, The Georgian Academy of Sciences, Preprint, 1976, 21pp.
    • (1976) The Georgian Academy of Sciences , pp. 21
    • Esakia, L.1
  • 13
    • 2342486837 scopus 로고
    • About modal "companions" of superinuitionistic logics, the VII Logic symposium
    • (Abstract), Kiev (in Russian)
    • L. Esakia, About modal "companions" of superinuitionistic logics, the VII Logic symposium (Abstract), Kiev, 1976, p. 160 (in Russian).
    • (1976) , pp. 160
    • Esakia, L.1
  • 14
    • 2342531890 scopus 로고
    • On varieties of Grzegorczyk algebras
    • Nauka, Moscow (in Russian) (Selective Soviet Mathematics 3 (1983/84) 343-366)
    • L. Esakia, On varieties of Grzegorczyk algebras, in: Studies in non-Classical Logic and Set Theory, Nauka, Moscow, 1979, pp. 257-287 (in Russian) (Selective Soviet Mathematics 3 (1983/84) 343-366).
    • (1979) Studies in Non-Classical Logic and Set Theory , pp. 257-287
    • Esakia, L.1
  • 15
    • 2342571784 scopus 로고
    • On the theory of modal and superintuitionistic logics
    • V.A. Smirnov (Ed.), Nauka, Moscow (in Russian)
    • L. Esakia, On the theory of modal and superintuitionistic logics, in: V.A. Smirnov (Ed.), Logical Inference, Nauka, Moscow, 1979, pp. 147-171 (in Russian).
    • (1979) Logical Inference , pp. 147-171
    • Esakia, L.1
  • 16
    • 2342453425 scopus 로고
    • Diagonal constructions, Löb's formula and Cantor's scattered space
    • Z. Mikeladze (Ed.), Academic Press, Tbilisi (in Russian)
    • L. Esakia, Diagonal constructions, Löb's formula and Cantor's scattered space, in: Z. Mikeladze (Ed.), Logical and Semantical Studies, Academic Press, Tbilisi, 1981, pp. 128-143 (in Russian).
    • (1981) Logical and Semantical Studies , pp. 128-143
    • Esakia, L.1
  • 18
    • 0346436464 scopus 로고    scopus 로고
    • Quantification in intuitionistic logic with provability smack
    • Esakia L. Quantification in intuitionistic logic with provability smack Bull. Sec. Logic 27 1998 26-28
    • (1998) Bull. Sec. Logic , vol.27 , pp. 26-28
    • Esakia, L.1
  • 19
    • 2342474700 scopus 로고    scopus 로고
    • Synopsis of Fronton theory
    • Academic Press, Moscow (in Russian)
    • L. Esakia, Synopsis of Fronton theory, in: Logical Studies, vol. 7, Academic Press, Moscow, 2000, pp. 137-147 (in Russian).
    • (2000) Logical Studies , vol.7 , pp. 137-147
    • Esakia, L.1
  • 20
    • 0347522179 scopus 로고    scopus 로고
    • Weak-transitivity-restitution
    • Academic Press, Moscow (in Russian)
    • L. Esakia, Weak-transitivity-restitution, in: Logical Studies, vol. 8, Academic Press, Moscow, 2001, pp. 244-255 (in Russian).
    • (2001) Logical Studies , vol.8 , pp. 244-255
    • Esakia, L.1
  • 22
    • 0346261132 scopus 로고    scopus 로고
    • Modal Definability in Topology
    • Dick de Jongh (Ed.), ILLC Scientific Publications, MoL-2001-11, Amsterdam
    • D. Gabelaia, Modal Definability in Topology, in: Dick de Jongh (Ed.), ILLC Scientific Publications, MoL-2001-11, Amsterdam, pp. 1-47.
    • Gabelaia, D.1
  • 24
    • 84979110381 scopus 로고
    • Arithmetical necessity, provability and intuitionistic logic
    • Goldblatt R. Arithmetical necessity, provability and intuitionistic logic Theoria 44 1978 38-46
    • (1978) Theoria , vol.44 , pp. 38-46
    • Goldblatt, R.1
  • 25
    • 2342463124 scopus 로고
    • Some relations systems and the associated topological spaces
    • Grzegorczyk A. Some relations systems and the associated topological spaces Fund. Math. 60 1967 223-231
    • (1967) Fund. Math. , vol.60 , pp. 223-231
    • Grzegorczyk, A.1
  • 27
  • 29
    • 2342533981 scopus 로고
    • The proof-intuitionistic propositional calculus
    • Kuznetsov A.V. The proof-intuitionistic propositional calculus Dokl. Acad. Nauk SSSR 285 1 1985 27-30
    • (1985) Dokl. Acad. Nauk SSSR , vol.285 , Issue.1 , pp. 27-30
    • Kuznetsov, A.V.1
  • 31
    • 0002365425 scopus 로고
    • Contribution a la topologie des ensembles denombrables
    • Mazurkiewicz S. Sierpin̂ski W. Contribution a la topologie des ensembles denombrables Fund. Math. 1 1920 17-27
    • (1920) Fund. Math. , vol.1 , pp. 17-27
    • Mazurkiewicz, S.1    Sierpin̂ski, W.2
  • 32
    • 2342595341 scopus 로고
    • On the syntactical construction of systems of modal logic
    • McKinsey J.C.C. On the syntactical construction of systems of modal logic J. Symbolic Logic 10 1945 83-94
    • (1945) J. Symbolic Logic , vol.10 , pp. 83-94
    • McKinsey, J.C.C.1
  • 33
    • 0000863367 scopus 로고
    • The algebra of topology
    • McKinsey J. Tarski A. The algebra of topology Ann. Math. 45 1944 141-191
    • (1944) Ann. Math. , vol.45 , pp. 141-191
    • McKinsey, J.1    Tarski, A.2
  • 34
    • 0001728117 scopus 로고
    • On closed elements in closure algebras
    • McKinsey J. Tarski A. On closed elements in closure algebras Ann. of Math. 47 1946 122-162
    • (1946) Ann. of Math. , vol.47 , pp. 122-162
    • McKinsey, J.1    Tarski, A.2
  • 35
    • 0002479447 scopus 로고
    • Some theorems about the sentential calculi of Lewis and Heyting
    • McKinsey J.C.C. Tarski A. Some theorems about the sentential calculi of Lewis and Heyting J. Symbolic Logic 13 1948 1-15
    • (1948) J. Symbolic Logic , vol.13 , pp. 1-15
    • McKinsey, J.C.C.1    Tarski, A.2
  • 36
    • 2342470869 scopus 로고
    • A correspondence between extensions of the proof-intuitionistic logic and extensions of the provability logic
    • Muravitsky A.Yu. A correspondence between extensions of the proof-intuitionistic logic and extensions of the provability logic Dokl. Acad. Nauk SSSR 281 4 1985 27-30
    • (1985) Dokl. Acad. Nauk SSSR , vol.281 , Issue.4 , pp. 27-30
    • Muravitsky, A.Yu.1
  • 37
    • 0000637948 scopus 로고
    • The modal logic of inequality
    • de Rijke Maarten A The modal logic of inequality J. Symbolic Logic 57 1992 566-587
    • (1992) J. Symbolic Logic , vol.57 , pp. 566-587
    • de Rijke Maarten, A.1
  • 38
    • 0039715462 scopus 로고
    • Decidability of S4.1
    • Segerberg K. Decidability of S4.1 Theoria 34 1968 7-20
    • (1968) Theoria , vol.34 , pp. 7-20
    • Segerberg, K.1
  • 39
    • 0040197121 scopus 로고
    • An essay in classical modal logic
    • The Philosophical Society, Uppsala
    • K. Segerberg, An essay in classical modal logic, Philosophical Studies, vol. 13, The Philosophical Society, Uppsala, 1971.
    • (1971) Philosophical Studies , vol.13
    • Segerberg, K.1
  • 41
    • 84979115493 scopus 로고
    • A note on the logic of elswhere
    • Segerberg K. A note on the logic of elswhere Theoria 46 1980 183-187
    • (1980) Theoria , vol.46 , pp. 183-187
    • Segerberg, K.1
  • 42
    • 51249190137 scopus 로고
    • Provability interpretation of modal logic
    • Solovay R. Provability interpretation of modal logic Israel J. Math. 25 1976 287-304
    • (1976) Israel J. Math. , vol.25 , pp. 287-304
    • Solovay, R.1
  • 43
    • 0011045228 scopus 로고
    • Der Aussagenkalkul und die Topologie
    • Tarski A. Der Aussagenkalkul und die Topologie Fund. Math. 31 1938 103-134
    • (1938) Fund. Math. , vol.31 , pp. 103-134
    • Tarski, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.