Normal Form Expressions of Propositional Projection Temporal Logic

  • Zhenhua Duan
  • Cong Tian
  • Nan Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8591)


This paper presents normal form expressions of Propositional Projection Temporal Logic (PPTL). For doing so, a PPTL formula is represented as the disjunction of formulas in form of \(e_\varepsilon^k=\bigwedge_{0\leq i\leq k\in N_0} \bigcirc^iS_i\wedge \bigcirc^k\varepsilon\) or \(e_\omega^{(k,l)}=\bigwedge_{0\leq i\leq k\in N_0} \bigcirc^iS_i\wedge\bigwedge_{k\leq j\in N_\omega}\bigcirc^j(\bigcirc S_{k+1}\wedge\bigcirc^2 S_{k+2}\wedge \cdots\wedge\bigcirc^l S_{k+l}),1\leq l\in N_0\). Here \(e_\varepsilon^k\) denotes a finite model with length being k while \(e_\omega^{(k,l)}\) indicates an infinite model. We show that any PPTL formula can be expressed as a normal form expression. As a consequence, satisfiability of PPTL formulas can easily be achieved.


Propositional projection temporal logic normal form expression normal form specification satisfiability 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Zhenhua Duan
    • 1
  • Cong Tian
    • 1
  • Nan Zhang
    • 1
  1. 1.Institute of Computing Theory and Technology, and ISN LaboratoryXidian UniversityXi’anChina

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