Skip to main content Accessibility help
×
Home

Axiomatic semantics of projection temporal logic programs

  • XIAOXIAO YANG (a1), ZHENHUA DUAN (a2) and QIAN MA (a3)

Abstract

In this paper, we investigate the axiomatic semantics of the projection temporal logic programming language MSVL. To this end, we employ Propositional Projection Temporal Logic (PPTL) as an assertion language to specify the desired properties. We give a set of state axioms and state inference rules. In order to deduce a program over an interval, we also formalise a set of rules in terms of a Hoare logic-like triple. These rules enable us to deduce a program into its normal form and from the current state to the next one. They also enable us to verify properties over intervals. In this way, an axiom system for proving the correctness of MSVL programs is established. The axiom system is proved to be sound and relatively complete with respect to an operational model of MSVL, and give an example showing how the axiom system works. Finally, we employ a recently developed prototype verifier based on PVS as an example of semi-automatic verification using MSVL.

Copyright

References

Hide All
Abadi, M. and Manna, Z. (1989) Temporal Logic Programming. Journal of Symbolic Computation 8 277295.
Biere, A., Cimati, A., Clark, E. M., Strichman, O. and Zhu, Y. S. (2003) Bounded Model Checking. Advances in Computers 58.
Brzoska, C. (1993) Temporal Logic Programming with Bounded Universal Modality Goal. Proceedings of the Tenth International Conference on Logic Programming, MIT Press 239256.
Brzoska, C. (1998) Programming in Metric Temporal Logic. Theoretical Computer Science 202 (1–2)55125.
Clarke, E. M., Grumberg, O. and Peled, D. (1999) Model Checking, MIT Press.
Cook, S. A. (1978) Soundness and Completeness of An Axiom System for Program Verification. SIAM Journal on Computing 7 7090.
Duan, Z. (1996) An Extended Interval Temporal Logic and A Framing Technique for Temporal Logic Programming, Ph. D. Thesis, University of Newcastle upon Tyne. (Technical Report No. 556.)
Duan, Z. and Koutny, M. (2004) A Framed Temporal Logic Programming Language. Journal of Computer Science and Technology 19 341351.
Duan, Z., Koutny, M. and Holt, C. (1994) Projection in temporal logic programming. Proceedings of Logic Programming and Automatic Reasoning. Springer-Verlag Lecture Notes in Artificial Intelligence 822 333344.
Duan, Z., Tian, C. and Zhang, L. (2008a) A Decision Procedure for Propositional Projection Temporal Logic with Infinite Models. Acta Informatica 45 (1)4378.
Duan, Z., Yang, X. and Koutny, M. (2008b) Framed Temporal Logic Programming. Science of Computer Programming 70 (1)3161.
Fujita, M., Kono, S., Tanaka, H. and Moto-oka, T. (1986) Tokio: Logic programming language based on temporal logic and its compilation to PROLOG. In: Third International Conference on Logic Programming. Springer-Verlag Lecture Notes in Computer Science 225 695709.
Gabbay, D. M. (1987) Modal and Temporal Logic Programming. Temporal Logics and Their Applications, Academic Press 197237.
Hale, R. (1987) Temporal Logic Programming. Temporal Logics and Their Applications, Academic Press 91119.
Hansen, M. R. and Zhao, C. (1997) Duration Calculus: Logical Foundations. Formal Aspects of Computing 9 283330.
Hoare, C. A. R. (1969) An axiomatic basis for computer programming. Communications of ACM 12 (10)576583.
Hrycej, T. (1988) Temporal Prolog. In: Kodratoff, Y. (ed.) Proceedings of the European Conference on Artificial Intelligence (ECAI-88), Pitman Publishing 296301.
Hrycej, T. (1993) A Temporal Extension of Prolog. The Journal of Logic Programming 15 113145.
Jones, C. B. (1981) Development Mehods for Computer Programs including a Notion of Interference, Ph. D. thesis, Oxford University.
Lamport, L. (1994) The temporal logic of actions. ACM Transactions on Programming Languages and Systems 16 (3)872923.
Ma, Q., Duan, Z. and Yang, X. (2010) Case Study of MSVL Axiom System. Technical Report available at http://lcs.ios.ac.cn/~xzx/case.pdf.
Manna, Z. and Pnueli, A. (1992) Temporal Logic of Reactive and Concurrent Systems, Springer-Verlag.
Misra, J. and Chandy, K. M. (1981) Proofs of Networks of Processes. IEEE Transactions on Software Engineering 7 417426.
Moszkowski, B. C. (1986) Executing temporal logic programs, Cambridge University Press.
Orgun, M. A. and Wadge, W. W. (1988) Chronolog: A Temporal Logic Programming Language and Its Formal Semantics, Department of Computer Science, University of Victoria, B.C., Canada.
Orgun, M. A. and Wadge, W. W. (1992) A Theory and Practice of Temporal Logic Programming. Intensional Logics for Programming, Oxford University Press 2350.
Owicki, S. (1975) Axiomatic Proof Techniques for Parallel Programs, Ph. D. thesis, Department of Computer Science, Cornell University.
Owicki, S. and Gries, D. (1976) An Axiomatic Proof Technique for Parallel Programs I. Acta Informatica 6 319340.
Owre, S., Shankar, N., Rushby, J. M. and Stringer-Calvert, D. W. J. (1999) PVS Language Reference, Computer Science Laboratory, SRI International, Menlo Park, CA.
Pnueli, A. (1977) The temporal semantics of concurrent programs, Tel-Aviv University.
de Roever, W. P. (1985) The Quest for Compositionality. Proceedings of IFIP Working Conference on the Role of Abstract Models in Computer Science, North-Holland.
Rondogiannis, R., Gergatsoulis, M. and Panayiotopoulos, T. (1997) Cactus: A Branching Time Logic Programming Language. Proceedings of the 1st International Joint Conference Qualitative and Quantitative Practical Reasoning. Springer-Verlag Lecture Notes in Artificial Intelligence 1244 511524.
Rondogiannis, R., Gergatsoulis, M. and Panayiotopoulos, T. (1998) Branching Time Logic Programming: The Language Cactus and Its Application. Computer Languages 24 (3)155178.
Shankar, N., Owre, S., Rushby, J. M. and Stringer-Calvert, D. W. J. (1999) PVS Prover Guide, Computer Science Laboratory, SRI International, Menlo Park, CA.
Tang, C. S. (1983) Toward a unified logic basis for programming languages. Proceedings of IFIP Congress 83, Elsevier Science Publishers 425429.
Tian, C. and Duan, Z. (2008) Propositional Projection Temporal Logic, Bchi Automata and omega-Regular Expressions. In: Proceedings TAMC2008. Springer-Verlag Lecture Notes in Computer Science 4978 4758.
Wadge, W. W. (1988) Tense Logic Programming. A Respectable Alternative. In: Proceedings of the 1988 International Symposium on Lucid and Intensional Programming, Sidney, B.C., Canada 26–32.
Wolper, P. L. (1983) Temporal logic can be more expressive. Information and Control 56 7299.
Xu, Q., de Roever, W. P. and He, J. (1997) The Rely-Gurarantee Method for Verifying Shared Variable Concurrent Programs. Formal Aspects of Computing 9 (2)149174.
Yang, X. and Duan, Z. (2008) Operational Semantics of Framed Tempura. Journal of Logic and Algebraic Programming 78 (1)2251.

Axiomatic semantics of projection temporal logic programs

  • XIAOXIAO YANG (a1), ZHENHUA DUAN (a2) and QIAN MA (a3)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.