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A decision procedure for propositional projection temporal logic with infinite models

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Abstract

This paper investigates the satisfiability of Propositional Projection Temporal Logic (PPTL) with infinite models. A decision procedure for PPTL formulas is given. To this end, Normal Form (NF) and Labeled Normal Form Graph (LNFG) for PPTL formulas are defined, and algorithms for transforming a formula to its normal form and constructing the LNFG for the given formula are presented. Further, the finiteness of LNFGs is proved in details. Moreover, the decision procedure is extended to check the satisfiability of the formulas of Propositional Interval Temporal Logic. In addition, examples are also given to illustrate how the decision procedure works.

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Authors and Affiliations

  1. Institute of Computing Theory and Technology, Xidian University, Xi’an, 710071, People’s Republic of China

    Zhenhua Duan, Cong Tian & Li Zhang

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  1. Zhenhua Duan
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  2. Cong Tian
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  3. Li Zhang
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Corresponding author

Correspondence to Zhenhua Duan.

Additional information

This research is supported by the NSFC Grant No. 60373103 and 60433010, and Defence Pre-Research Project of China, No. 51315050105.

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Duan, Z., Tian, C. & Zhang, L. A decision procedure for propositional projection temporal logic with infinite models. Acta Informatica 45, 43–78 (2008). https://doi.org/10.1007/s00236-007-0062-z

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