A Probabilistic Variant of Projection Temporal Logic

TL;DR

This paper introduces Probabilistic discrete-time Projection Temporal Logic (PrPTL), extending PTL with probability, and develops a normal form and graph for probabilistic model checking.

Contribution

It presents the first formalization of PrPTL, including formulas, laws, and a normal form, enabling probabilistic model checking for temporal logic.

Findings

Defined Time Normal Form (TNF) for PrPTL

Proved all PrPTL formulas can be rewritten to TNF

Constructed a time normal form graph for model checking

Abstract

In this paper, we propose Probabilistic discrete-time Projection Temporal Logic (PrPTL), which extends Projection Temporal Logic (PTL) with probability. To this end, some useful formulas are derived and some logic laws are given. Further, we define Time Normal Form (TNF) for PrPTL as the standard form and prove that any PrPTL formulas can be rewritten to TNF. According to the TNF, we construct the time normal form graph which can be used for the probabilistic model checking on PrPTL.