Tableaux for constructive concurrent dynamic logic
This is the first paper on constructive concurrent dynamic logic (CCDL). For the first time, either for concurrent or sequential dynamic logic, we give a satisfactory treatment of what statements are forced to be true by partial information about the underlying computer. Dynamic logic was developed...
Saved in:
| Published in: | Annals of pure and applied logic Vol. 135; no. 1; pp. 1 - 72 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier B.V
01.09.2005
|
| ISSN: | 0168-0072 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | This is the first paper on constructive concurrent dynamic logic (CCDL). For the first time, either for concurrent or sequential dynamic logic, we give a satisfactory treatment of what statements are forced to be true by partial information about the underlying computer. Dynamic logic was developed by Pratt [V. Pratt, Semantical considerations on Floyd–Hoare logic, in: 17th Annual IEEE Symp. on Found. Comp. Sci., New York, 1976, pp. 109–121, V. Pratt, Applications of modal logic to programming, Studia Logica 39 (1980) 257–274] for nondeterministic sequential programs, and by Peleg [D. Peleg, Concurrent dynamic logic, Journal of the Association for Computing Machinery 34 (2) (1987), D. Peleg, Communication in concurrent dynamic logic, Journal of Computer and System Sciences 35 (1987)] for concurrent programs, for the purpose of proving properties of programs such as correctness. Here we define what it means for a dynamic logic formula to be forced to be true knowing only partial information about the results of assignments and tests. This informal CCDL semantics is formalized by intuitionistic Kripke frames modeling this partial information, and each such frame is interpreted as an idealized concurrent machine (a concurrent transition system). In CCDL, proofs and deductions are
ω
-height,
ω
-branching, well-founded labeled subtrees of
ω
ω
. These are a generalization of the signed tableaux of Nerode [A. Nerode, Some lectures in modal logic, Technical Report, M.S.I. Cornell University, 1989, CIME Logic and Computer Science Montecatini Volume, Springer-Verlag Lecture Notes, 1990, A. Nerode, Some lectures in intuitionistic logic, Technical Report, M.S.I. Cornell University, 1988, Marktoberdorf Logic and Computation NATO Summer School Volume, NATO Science Series, 1990 (in press)] stemming from the prefix tableaux of Fitting [M.C. Fitting, Proof Methods for Modal and Intuitionistic Logic, Reidel, 1983]. We demonstrate the correctness of our tableau proofs, define consistency properties, prove that consistency properties yield models, construct systematic tableaux, prove that systematic tableaux yield a consistency property, and conclude that CCDL is complete. This infinitary semantics and proof procedure will be the primary guide for defining, in a sequel,
the correct finitary CCDL (FCCDL) based on induction principles. FCCDL is suitable for implementation in constructive logic software systems such as Constable’s NUPRL or Huet-Coquand’s CONSTRUCTIONS. Our goal is to develop a constructive logic programming tool for specification and modular verification of programs in any imperative concurrent language, and for the extraction of concurrent programs from constructive proofs. Subsequent papers will introduce analogous logics for declarative and functional concurrent languages. |
|---|---|
| AbstractList | This is the first paper on constructive concurrent dynamic logic (CCDL). For the first time, either for concurrent or sequential dynamic logic, we give a satisfactory treatment of what statements are forced to be true by partial information about the underlying computer. Dynamic logic was developed by Pratt [V. Pratt, Semantical considerations on Floyd–Hoare logic, in: 17th Annual IEEE Symp. on Found. Comp. Sci., New York, 1976, pp. 109–121, V. Pratt, Applications of modal logic to programming, Studia Logica 39 (1980) 257–274] for nondeterministic sequential programs, and by Peleg [D. Peleg, Concurrent dynamic logic, Journal of the Association for Computing Machinery 34 (2) (1987), D. Peleg, Communication in concurrent dynamic logic, Journal of Computer and System Sciences 35 (1987)] for concurrent programs, for the purpose of proving properties of programs such as correctness. Here we define what it means for a dynamic logic formula to be forced to be true knowing only partial information about the results of assignments and tests. This informal CCDL semantics is formalized by intuitionistic Kripke frames modeling this partial information, and each such frame is interpreted as an idealized concurrent machine (a concurrent transition system). In CCDL, proofs and deductions are
ω
-height,
ω
-branching, well-founded labeled subtrees of
ω
ω
. These are a generalization of the signed tableaux of Nerode [A. Nerode, Some lectures in modal logic, Technical Report, M.S.I. Cornell University, 1989, CIME Logic and Computer Science Montecatini Volume, Springer-Verlag Lecture Notes, 1990, A. Nerode, Some lectures in intuitionistic logic, Technical Report, M.S.I. Cornell University, 1988, Marktoberdorf Logic and Computation NATO Summer School Volume, NATO Science Series, 1990 (in press)] stemming from the prefix tableaux of Fitting [M.C. Fitting, Proof Methods for Modal and Intuitionistic Logic, Reidel, 1983]. We demonstrate the correctness of our tableau proofs, define consistency properties, prove that consistency properties yield models, construct systematic tableaux, prove that systematic tableaux yield a consistency property, and conclude that CCDL is complete. This infinitary semantics and proof procedure will be the primary guide for defining, in a sequel,
the correct finitary CCDL (FCCDL) based on induction principles. FCCDL is suitable for implementation in constructive logic software systems such as Constable’s NUPRL or Huet-Coquand’s CONSTRUCTIONS. Our goal is to develop a constructive logic programming tool for specification and modular verification of programs in any imperative concurrent language, and for the extraction of concurrent programs from constructive proofs. Subsequent papers will introduce analogous logics for declarative and functional concurrent languages. |
| Author | Nerode, Anil Wijesekera, Duminda |
| Author_xml | – sequence: 1 givenname: Duminda surname: Wijesekera fullname: Wijesekera, Duminda email: duminda@ise.gmu.edu organization: Department of Information and Software Engineering, George Mason University, 160 Sci., Technology Bldg. II, Fairfax, VA 22101, United States – sequence: 2 givenname: Anil surname: Nerode fullname: Nerode, Anil email: anil@math.cornell.edu organization: Department of Mathematics, Cornell University, Ithaca, NY 14853, United States |
| BookMark | eNp9z71qwzAQwHENKTRJ-wKd_AJ2T3LsRNClhH5BoEs6C_l0KgqOFCQlNG9fm3TqkOk4jt_Bf8YmPnhi7IFDxYG3j7tKH3RfCYBFxUUFwCdsOhxWJcBS3LJZSjsAaBbLesrEVnc96eNPYUMsMPiU4xGzO9G44DFG8rkwZ6_3Dos-fDu8YzdW94nu_-acfb2-bNfv5ebz7WP9vCmxBshlY2Qnai0bS9LaGlu0iFwCNdh2WHMjOQmztNiC7YxtFlYY0FKSQdOtCOo5W13-YgwpRbIKXdbZBZ-jdr3ioMZetVNjrxp7FRdq6B2o-EcP0e11PF9HTxdEQ9TJUVQJHXkk4yJhVia4a_wXVTN1IA |
| CitedBy_id | crossref_primary_10_1016_j_jal_2009_06_001 crossref_primary_10_1093_logcom_exac013 crossref_primary_10_1007_s10992_019_09539_3 crossref_primary_10_1093_logcom_exv042 crossref_primary_10_1016_j_tcs_2013_04_029 crossref_primary_10_1145_2785967 crossref_primary_10_1145_2964907 crossref_primary_10_1016_j_apal_2011_12_002 crossref_primary_10_1016_j_ic_2011_10_003 |
| Cites_doi | 10.1007/BF00370324 10.1016/0304-3975(81)90019-0 10.1145/23005.23008 10.2977/prims/1195183579 10.1145/322234.322243 10.1007/BFb0093923 10.1016/0022-0000(87)90035-3 10.1145/363235.363259 10.1007/BF02429840 10.1016/0168-0072(90)90059-B 10.1090/psapm/019/0235771 |
| ContentType | Journal Article |
| Copyright | 2005 Elsevier B.V. |
| Copyright_xml | – notice: 2005 Elsevier B.V. |
| DBID | 6I. AAFTH AAYXX CITATION |
| DOI | 10.1016/j.apal.2004.12.001 |
| DatabaseName | ScienceDirect Open Access Titles Elsevier:ScienceDirect:Open Access CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics Philosophy |
| EndPage | 72 |
| ExternalDocumentID | 10_1016_j_apal_2004_12_001 S0168007204001794 |
| GroupedDBID | --K --M -ET -~X .~1 0R~ 1B1 1RT 1~. 1~5 23M 4.4 457 4G. 5GY 5VS 6I. 6TJ 7-5 71M 8P~ 9JN AACTN AAEDT AAEDW AAFTH AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABAOU ABFNM ABMAC ABTAH ABVKL ABXDB ABYKQ ACAZW ACDAQ ACGFS ACRLP ADBBV ADEZE ADMUD AEBSH AEKER AENEX AETEA AEXQZ AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CS3 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 FDB FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HZ~ H~9 IHE IXB J1W KOM M26 M41 MHUIS MO0 MVM N9A NCXOZ O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 R2- RIG ROL RPZ SCC SDF SDG SDP SES SEW SPC SPCBC SSW SSZ T5K TN5 WH7 WUQ XJT YYP ZY4 ~G- 9DU AATTM AAXKI AAYWO AAYXX ABJNI ABWVN ACLOT ACRPL ACVFH ADCNI ADMHG ADNMO ADVLN ADXHL AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD |
| ID | FETCH-LOGICAL-c300t-5d9b23a95fe9ff3c6cfcc190e5c6bc31d91e2d7fc60fbdf54f2d0a99edcdb8e03 |
| ISICitedReferencesCount | 17 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000231109900001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0168-0072 |
| IngestDate | Sat Nov 29 01:52:29 EST 2025 Tue Nov 18 21:19:30 EST 2025 Fri Feb 23 02:27:25 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Language | English |
| License | http://www.elsevier.com/open-access/userlicense/1.0 https://www.elsevier.com/tdm/userlicense/1.0 https://www.elsevier.com/open-access/userlicense/1.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c300t-5d9b23a95fe9ff3c6cfcc190e5c6bc31d91e2d7fc60fbdf54f2d0a99edcdb8e03 |
| OpenAccessLink | https://dx.doi.org/10.1016/j.apal.2004.12.001 |
| PageCount | 72 |
| ParticipantIDs | crossref_citationtrail_10_1016_j_apal_2004_12_001 crossref_primary_10_1016_j_apal_2004_12_001 elsevier_sciencedirect_doi_10_1016_j_apal_2004_12_001 |
| PublicationCentury | 2000 |
| PublicationDate | 2005-09-01 |
| PublicationDateYYYYMMDD | 2005-09-01 |
| PublicationDate_xml | – month: 09 year: 2005 text: 2005-09-01 day: 01 |
| PublicationDecade | 2000 |
| PublicationTitle | Annals of pure and applied logic |
| PublicationYear | 2005 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Dosen (b4) 1985; 1 D. Kozen, J. Tiuryn, Logics of Programs, Technical Report 89-962, Dept. of Computer Science, Cornell University 1989 Kozen, Parikh (b17) 1981; 14 Peleg (b24) 1987; 35 Leivant (b19) 1981; vol. 107 Floyd (b6) 1967; 19 Troelstra, Van Dalen (b30) 1988 Pratt (b26) 1976 Hähnle, Heisel, Reif, Stephan (b10) 1986; vol. 230 Hoare (b16) 1969; 12 W. Reif, Vollständigkeit einer modifizierten Goldblatt-Logik und Approximation der Omegaregel durch Induktion, Diplomarbeit, Facultät für Informatik, Universität Karlsruhe, 1986 Bozic, Dosen (b1) 1984; 43 Heisel, Reif, Stephan (b13) 1987; vol. 329 Wijesekera (b31) 1990; 50 Burstall (b2) 1974; 74 R.I. Goldblatt, Parallel Action: Concurrent dynamic logic with independent modalities. Technical Report 91-73, Victoria University of Wellington, 1991 A. Nerode, Some lectures in modal logic, Technical Report, M.S.I. Cornell University, 1989 CIME Logic and Computer Science Montecatini Volume, Springer-Verlag Lecture Notes, 1990 Chandra, Kozen, Stockmeyer (b3) 1981; 28 Fitting (b5) 1983 H. Nishimura, Semantical analysis of constructive PDL, Publications of the Research Institute of Mathematical Sciences 18 (2) (1982) Gabbay, Guenthner (b7) 1983 Goldblatt (b8) 1987; vol. 7 M. Heisel, W. Reif, W. Stephan, A functional language to construct proofs, Interner Bericht 1/86, Facultät für Informatik, Universität Karlsruhe, 1986 ) Plotkin, Stirling (b25) 1986 Peleg (b23) 1987; 34 W. Reif, A completeness result in non-standard dynamic logic, Interner Bericht 5/85, Facultät für Informatik, Universität Karlsruhe, 1986 Harel (b15) 1976; vol. 68 A. Nerode, Some lectures in intuitionistic logic, Technical Report, M.S.I. Cornell University, 1988, Marktoberdorf Logic and Computation NATO Summer School Volume, NATO Science Series, 1990 (in press) D. Harel, Dynamic Logic (in Pratt (b27) 1980; 39 Heisel, Reif, Stephan (b12) 1987; vol. 152 Burstall (10.1016/j.apal.2004.12.001_b2) 1974; 74 Wijesekera (10.1016/j.apal.2004.12.001_b31) 1990; 50 Hähnle (10.1016/j.apal.2004.12.001_b10) 1986; vol. 230 Hoare (10.1016/j.apal.2004.12.001_b16) 1969; 12 Floyd (10.1016/j.apal.2004.12.001_b6) 1967; 19 10.1016/j.apal.2004.12.001_b18 Heisel (10.1016/j.apal.2004.12.001_b13) 1987; vol. 329 Plotkin (10.1016/j.apal.2004.12.001_b25) 1986 Troelstra (10.1016/j.apal.2004.12.001_b30) 1988 Peleg (10.1016/j.apal.2004.12.001_b23) 1987; 34 10.1016/j.apal.2004.12.001_b9 10.1016/j.apal.2004.12.001_b14 10.1016/j.apal.2004.12.001_b20 10.1016/j.apal.2004.12.001_b21 10.1016/j.apal.2004.12.001_b22 Harel (10.1016/j.apal.2004.12.001_b15) 1976; vol. 68 Pratt (10.1016/j.apal.2004.12.001_b26) 1976 Kozen (10.1016/j.apal.2004.12.001_b17) 1981; 14 Gabbay (10.1016/j.apal.2004.12.001_b7) 1983-1985 Pratt (10.1016/j.apal.2004.12.001_b27) 1980; 39 Chandra (10.1016/j.apal.2004.12.001_b3) 1981; 28 Fitting (10.1016/j.apal.2004.12.001_b5) 1983 10.1016/j.apal.2004.12.001_b28 Dosen (10.1016/j.apal.2004.12.001_b4) 1985; 1 Peleg (10.1016/j.apal.2004.12.001_b24) 1987; 35 10.1016/j.apal.2004.12.001_b29 Leivant (10.1016/j.apal.2004.12.001_b19) 1981; vol. 107 10.1016/j.apal.2004.12.001_b11 Bozic (10.1016/j.apal.2004.12.001_b1) 1984; 43 Heisel (10.1016/j.apal.2004.12.001_b12) 1987; vol. 152 Goldblatt (10.1016/j.apal.2004.12.001_b8) 1987; vol. 7 |
| References_xml | – volume: vol. 329 year: 1987 ident: b13 article-title: Program verification using dynamic logic publication-title: Workshop on Computer Science Logic – start-page: 109 year: 1976 end-page: 121 ident: b26 article-title: Semantical considerations on Floyd–Hoare logic publication-title: 17th Annual IEEE Symp. on Found. Comp. Sci., New York – volume: 50 start-page: 271 year: 1990 end-page: 301 ident: b31 article-title: Constructive modal logic I publication-title: Annals of Pure and Applied Logic – reference: H. Nishimura, Semantical analysis of constructive PDL, Publications of the Research Institute of Mathematical Sciences 18 (2) (1982) – volume: 14 start-page: 113 year: 1981 end-page: 118 ident: b17 article-title: An elementary proof of the completeness of PDL publication-title: Theoretical Computer Science – reference: R.I. Goldblatt, Parallel Action: Concurrent dynamic logic with independent modalities. Technical Report 91-73, Victoria University of Wellington, 1991 – volume: 34 year: 1987 ident: b23 article-title: Concurrent dynamic logic publication-title: Journal of the Association for Computing Machinery – volume: 35 year: 1987 ident: b24 article-title: Communication in concurrent dynamic logic publication-title: Journal of Computer and System Sciences – volume: 39 start-page: 257 year: 1980 end-page: 274 ident: b27 article-title: Applications of modal logic to programming publication-title: Studia Logica – reference: W. Reif, A completeness result in non-standard dynamic logic, Interner Bericht 5/85, Facultät für Informatik, Universität Karlsruhe, 1986 – volume: vol. 7 year: 1987 ident: b8 article-title: Logic of Time and Computation publication-title: CSLI Lecture Notes – volume: 74 start-page: 308 year: 1974 end-page: 312 ident: b2 article-title: Program proving as hand simulation with a little induction publication-title: Information Processing – volume: 28 year: 1981 ident: b3 article-title: Alternation publication-title: Journal of the Association for Computing Machinery – year: 1983 ident: b7 article-title: Handbook of Philosophical Logic I, II, III – volume: 12 start-page: 576 year: 1969 end-page: 583 ident: b16 article-title: An axiomatic basis for computer programming publication-title: Communications of the ACM – volume: 19 start-page: 19 year: 1967 end-page: 32 ident: b6 article-title: Assigning meaning to programs publication-title: Proceedings of Symposia in Applied Mathematics – reference: D. Kozen, J. Tiuryn, Logics of Programs, Technical Report 89-962, Dept. of Computer Science, Cornell University 1989 – reference: D. Harel, Dynamic Logic (in – volume: vol. 152 year: 1987 ident: b12 article-title: Program verification by symbolic execution and induction publication-title: Proc. 11th German Workshop on Artificial Intelligence – volume: vol. 107 year: 1981 ident: b19 article-title: Proof Theoretic Methodology for Propositional Dynamic Logic publication-title: Lecture Notes in Computer Science – reference: A. Nerode, Some lectures in modal logic, Technical Report, M.S.I. Cornell University, 1989 CIME Logic and Computer Science Montecatini Volume, Springer-Verlag Lecture Notes, 1990 – volume: 43 start-page: 217 year: 1984 end-page: 245 ident: b1 article-title: Models for normal intuitionistic logics publication-title: Studia Logica – volume: 1 year: 1985 ident: b4 article-title: Models for strongly normal intuitionistic modal logics publication-title: Studia Logica – reference: ) – volume: vol. 230 start-page: 306 year: 1986 end-page: 315 ident: b10 article-title: An interactive verification system based on dynamic logic publication-title: Proc. 8th Inter. Conf. on Automated Deduction – year: 1986 ident: b25 article-title: A framework for intuitionistic modal logic publication-title: Theoretical Aspects of Reasoning About Knowledge – reference: M. Heisel, W. Reif, W. Stephan, A functional language to construct proofs, Interner Bericht 1/86, Facultät für Informatik, Universität Karlsruhe, 1986 – volume: vol. 68 year: 1976 ident: b15 article-title: First Order Dynamic logic publication-title: Lecture Notes in Computer Science – reference: W. Reif, Vollständigkeit einer modifizierten Goldblatt-Logik und Approximation der Omegaregel durch Induktion, Diplomarbeit, Facultät für Informatik, Universität Karlsruhe, 1986 – year: 1983 ident: b5 article-title: Proof Methods for Modal and Intuitionistic Logic – reference: A. Nerode, Some lectures in intuitionistic logic, Technical Report, M.S.I. Cornell University, 1988, Marktoberdorf Logic and Computation NATO Summer School Volume, NATO Science Series, 1990 (in press) – year: 1988 ident: b30 article-title: Constructivism in Mathematics: An Introduction I, II – ident: 10.1016/j.apal.2004.12.001_b18 – year: 1986 ident: 10.1016/j.apal.2004.12.001_b25 article-title: A framework for intuitionistic modal logic – volume: 39 start-page: 257 year: 1980 ident: 10.1016/j.apal.2004.12.001_b27 article-title: Applications of modal logic to programming publication-title: Studia Logica doi: 10.1007/BF00370324 – volume: 14 start-page: 113 year: 1981 ident: 10.1016/j.apal.2004.12.001_b17 article-title: An elementary proof of the completeness of PDL publication-title: Theoretical Computer Science doi: 10.1016/0304-3975(81)90019-0 – ident: 10.1016/j.apal.2004.12.001_b20 – volume: 34 issue: 2 year: 1987 ident: 10.1016/j.apal.2004.12.001_b23 article-title: Concurrent dynamic logic publication-title: Journal of the Association for Computing Machinery doi: 10.1145/23005.23008 – year: 1988 ident: 10.1016/j.apal.2004.12.001_b30 – ident: 10.1016/j.apal.2004.12.001_b22 doi: 10.2977/prims/1195183579 – year: 1983-1985 ident: 10.1016/j.apal.2004.12.001_b7 – ident: 10.1016/j.apal.2004.12.001_b14 – volume: 74 start-page: 308 year: 1974 ident: 10.1016/j.apal.2004.12.001_b2 article-title: Program proving as hand simulation with a little induction publication-title: Information Processing – volume: 28 year: 1981 ident: 10.1016/j.apal.2004.12.001_b3 article-title: Alternation publication-title: Journal of the Association for Computing Machinery doi: 10.1145/322234.322243 – volume: vol. 7 year: 1987 ident: 10.1016/j.apal.2004.12.001_b8 article-title: Logic of Time and Computation – ident: 10.1016/j.apal.2004.12.001_b21 doi: 10.1007/BFb0093923 – volume: 35 year: 1987 ident: 10.1016/j.apal.2004.12.001_b24 article-title: Communication in concurrent dynamic logic publication-title: Journal of Computer and System Sciences doi: 10.1016/0022-0000(87)90035-3 – volume: 12 start-page: 576 year: 1969 ident: 10.1016/j.apal.2004.12.001_b16 article-title: An axiomatic basis for computer programming publication-title: Communications of the ACM doi: 10.1145/363235.363259 – volume: vol. 68 year: 1976 ident: 10.1016/j.apal.2004.12.001_b15 article-title: First Order Dynamic logic – ident: 10.1016/j.apal.2004.12.001_b28 – volume: vol. 152 year: 1987 ident: 10.1016/j.apal.2004.12.001_b12 article-title: Program verification by symbolic execution and induction – ident: 10.1016/j.apal.2004.12.001_b11 – volume: 1 year: 1985 ident: 10.1016/j.apal.2004.12.001_b4 article-title: Models for strongly normal intuitionistic modal logics publication-title: Studia Logica – year: 1983 ident: 10.1016/j.apal.2004.12.001_b5 – start-page: 109 year: 1976 ident: 10.1016/j.apal.2004.12.001_b26 article-title: Semantical considerations on Floyd–Hoare logic – ident: 10.1016/j.apal.2004.12.001_b29 – volume: vol. 107 year: 1981 ident: 10.1016/j.apal.2004.12.001_b19 article-title: Proof Theoretic Methodology for Propositional Dynamic Logic – volume: 43 start-page: 217 year: 1984 ident: 10.1016/j.apal.2004.12.001_b1 article-title: Models for normal intuitionistic logics publication-title: Studia Logica doi: 10.1007/BF02429840 – volume: 50 start-page: 271 year: 1990 ident: 10.1016/j.apal.2004.12.001_b31 article-title: Constructive modal logic I publication-title: Annals of Pure and Applied Logic doi: 10.1016/0168-0072(90)90059-B – volume: vol. 329 year: 1987 ident: 10.1016/j.apal.2004.12.001_b13 article-title: Program verification using dynamic logic – ident: 10.1016/j.apal.2004.12.001_b9 – volume: 19 start-page: 19 year: 1967 ident: 10.1016/j.apal.2004.12.001_b6 article-title: Assigning meaning to programs publication-title: Proceedings of Symposia in Applied Mathematics doi: 10.1090/psapm/019/0235771 – volume: vol. 230 start-page: 306 year: 1986 ident: 10.1016/j.apal.2004.12.001_b10 article-title: An interactive verification system based on dynamic logic |
| SSID | ssj0005473 |
| Score | 1.7921824 |
| Snippet | This is the first paper on constructive concurrent dynamic logic (CCDL). For the first time, either for concurrent or sequential dynamic logic, we give a... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 1 |
| Title | Tableaux for constructive concurrent dynamic logic |
| URI | https://dx.doi.org/10.1016/j.apal.2004.12.001 |
| Volume | 135 |
| WOSCitedRecordID | wos000231109900001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 issn: 0168-0072 databaseCode: AIEXJ dateStart: 19950115 customDbUrl: isFulltext: true dateEnd: 20180131 titleUrlDefault: https://www.sciencedirect.com omitProxy: false ssIdentifier: ssj0005473 providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1bS9xAFD7o6oM-lKoV117Ig28SmVwmm3kUsWihi6CFfQuTuUBXjYury_bf98xtk60iKvQlhJDJhPmGky9nvvkOwAFGfI0sXMa0yIo4Z3UWI0uoY5LngkgtE06FLTYxGA7L0Yhd-CqOU1tOYNA05XzOJv8VaryGYJuts2-Ae_FQvIDnCDoeEXY8vg54sxmKP86tgFDcBYfYmZWlC2_HJF0h-kMb-boEtTVUnoSlBe6JanuvzdOM1VRdq3u3XvR42_23HyoMyy5T2ngJR0gs0IVyyme7nux4cQnIooyN3fhSBHWOI0tTxcXDpPNhdW2ehGyXPRgfITewS0G5Tc_6F1m2wr40vZvOTeQxkWQV1tIBZWUP1o7PT0c_WnFP7rQF4W39dimn7Pu3p-cpSYdmXH2ED_7_IDp2uG7Bimq2YfPnwlx3ug0bF6H8xJ8dSAPcEcIddeGOWrgjD3dkIfwEv76fXp2cxb4ORiwyQh5iKlmdZpwZXaDWmSiEFgKJnKKiqEWWSJaoVA60KIiupaa5TiXhjCkpZF0qku1Cr7lr1B5EJdG81LLWOlG5KkrOElGnXFOOT9Gc9CEJQ1EJbxJvapXcVEENOK7M8JnqpXmVpEYS2YfDRZuJs0h58W4aRrjyJM-RtwonxAvt9t_Z7jNstJP7C_QQBPUV1sXs4ff0_pufN38BewF4hQ |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Tableaux+for+constructive+concurrent+dynamic+logic&rft.jtitle=Annals+of+pure+and+applied+logic&rft.au=Wijesekera%2C+Duminda&rft.au=Nerode%2C+Anil&rft.date=2005-09-01&rft.pub=Elsevier+B.V&rft.issn=0168-0072&rft.volume=135&rft.issue=1&rft.spage=1&rft.epage=72&rft_id=info:doi/10.1016%2Fj.apal.2004.12.001&rft.externalDocID=S0168007204001794 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0168-0072&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0168-0072&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0168-0072&client=summon |