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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)

Abstract

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.

Keywords

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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