| | 3 Propositional
Interval Temporal Logic (PITL)
Propositional Interval Temporal Logic (PITL) is a
- discrete,
- linear temporal logic
- for both finite and infinite time which includes
- a basic construct for sequential composition and
- an analog of Kleene star and Omega star
where
is an interval (sequence) of 2 states.
is called ‘ chop ’ and denotes sequential composition of two
intervals.
is called ‘ chopstar’ and denotes (in)finite iteration of an interval.
The main semantic notion is interval which is a sequence of states.
Let
denotes the set of states.
denote the set of non-empty finite sequences of states.
denote the set of infinite sequences of states.
denote an interval, .
- Let
be the “meaning” (semantic) function from to .
where denotes length of and is defined as
number of states minus 1
![[[ f1 ;f2 ]] σ = ttiff
(exists k, s.t. [[ f1]] σ0...σk = ttand [[ f2 ]] σk...σ|σ| = tt)
or (σ isinfiniteand[[ f1]]σ = tt)](itl-atp-www22x.png)
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