Abstract
In classical logic, the predicate P in “if P∧(P⇒Q) then Q” retains its truth value even after Q has been derived. In other words, in classical logic the truth of a formula is static. However, real-life implications are causal and temporal. To handle these, it must be possible to specify that “an event happened when P was true, moments after that Q became true, and now “P is not true and Q is true”. This may also be stated using “states”. We associate predicates with states such that a predicate is true in some state S and false in some other states.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Baier C, Katoen JP (2007) Principles of model checking. MIT Press, Cambridge
Ben-Ari M, Pnueli A, Manna Z (1983) The temporal logic of branching time. Acta Inform 20:207–226
Büchi JR (1960) On a decision method in restricted second order arithmetic. Z Math Log Grundl Math 6:66–92
Carnap R (1947) Meaning and necessity. Chicago University Press, Chicago. Enlarged Edition 1956
Clarke EM, Emerson EA, Sistala AP (1986) Automatic verification of finite state concurrent systems using temporal logic specifications. ACM Trans Program Lang Syst 8(2):244–263
Clarke EM, Grumberg O, Peled DA (1999) Model checking. MIT Press, Cambridge
Courcoubetis C, Vardi M, Wolper P, Yannakakis M (1992) Memory efficient algorithms for the verification of temporal logic properties. Form Methods Syst Des 1:275–288
Dijkstra E (1965) Solutions of a problem in concurrent programming control. Commun ACM 8(9):569
Emerson EA, Clarke EM (1980) Characterizing correctness properties of parallel programs using fixpoints. In: Automata, languages, and programming. Lecture notes in computer science, vol 85, pp 169–181
Gabbay D, Pnueli A, Stavi J (1980) The temporal analysis of fairness. In: Proceedings of the seventh ACM symposium on principles of programming languages, January 1980, pp 163–173
Gabbay D, Hodkinson I, Reynolds M (1994) Temporal logic: mathematical foundations and computational aspects. Oxford logic guides, vol 1. Clarendon, Oxford
Holzmann G (2003) The SPIN model checker: primer and reference manual. Addison-Wesley, Reading
Kripke SA (1963) Semantic considerations on modal logic. Acta Philos Fenn 16:83–94
Gröger F (1986) Temporal logic of programs. EATCS monographs on theoretical computer science. Springer, Berlin
Lamport L (1983) What good is temporal logic. In: Proceedings of IFIP’83 congress, information processing. North-Holland, Amsterdam, pp 657–668
Lamport L (1994) The temporal logic of actions. ACM Trans Program Lang Syst 16(3):872–923
Manna Z, Pnueli A (1992) The temporal logic of reactive and concurrent systems—specifications. Springer, New York
Melham TF (1989) Formalizing abstraction mechanisms for hardware verification in higher order logic. PhD thesis, University of Cambridge, August 1989
Moszkowski B (1986) Executing temporal logic programs. Cambridge University Press, Cambridge
Owiciki S, Lamport L (1982) Proving liveness properties of concurrent programs. ACM Trans Program Lang Syst 4(3):455–495
Peterson GL (1981) Myths about the mutual exclusion problem. Inf Process Lett 12(3):115–116
Pnueli A (1977) The temporal logic of programs. In: Proceedings of the eighteenth symposium on the foundations of computer science, Providence, USA
Pnueli A (1981) The temporal semantics of concurrent programs. Theor Comput Sci 13:45–60
Pnueli A (1986) Applications of temporal logic to the specification and verification of reactive systems: a survey of current trends. Lecture notes in computer science, vol 224
Prior A (1957) Time and modality. Oxford University Press, London
Rescher N, Urquhart A (1971) Temporal logic. Springer, Berlin
Sistala AP, Vardi M, Wolper P (1983) Reasoning about infinite computation paths. In: Proceedings of the 24th IEEE FOCS, pp 185–194
Sistala AP, Clarke EM (1985) The complexity of linear propositional temporal logic. J ACM 32(3):733–749
Stirling C (1992) Modal and temporal logics. In: Handbook of logic in computer science. Oxford University Press, London
Wan K (2006) Lucx: Lucid Enriched with context. PhD thesis, Concordia University, Montreal, Canada
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer-Verlag London Limited
About this chapter
Cite this chapter
Alagar, V.S., Periyasamy, K. (2011). Temporal Logic. In: Specification of Software Systems. Texts in Computer Science. Springer, London. https://doi.org/10.1007/978-0-85729-277-3_11
Download citation
DOI: https://doi.org/10.1007/978-0-85729-277-3_11
Publisher Name: Springer, London
Print ISBN: 978-0-85729-276-6
Online ISBN: 978-0-85729-277-3
eBook Packages: Computer ScienceComputer Science (R0)