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Published in:
2010 | OriginalPaper | Chapter
A Transformation from PPTL to S1S
Authors : Cong Tian, Zhenhua Duan
Published in: Combinatorial Optimization and Applications
Publisher: Springer Berlin Heidelberg
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A transformation from Propositional Projection Temporal Logic (PPTL) as well as Propositional Interval Temporal Logic (PITL) with infinite models to monadic second order logic with one successor (S1S) is presented in this paper. To this end, intervals where PPTL and PITL formulas are interpreted over are represented as
$\mathfrak{T}$
-structures. Further, the semantics of PPTL and PITL formulas are redefined over
$\mathfrak{T}$
-structures. Moreover, according to
$\mathfrak{T}$
-structure semantics, a PPTL or PITL formula is translated to a formula in S1S. As a result, many mature theoretical and technical results, such as decidability etc. for S1S can be easily inherited by PPTL and PITL.