1.1 Propositional Axioms and Inference Rules

The proof system uses a number of the propositional axioms suggested by Rosner and Pnueli but also includes our own axioms and inference rules for the operators and chop-plus.

⊢ All substitution instances of valid propositional PTL
chop-free temporal logic formulas for finite time
⊢ (f ; g) ; h ≡ f ; (g ; h) ChopAssoc
⊢ (f ∨ f1) ; g ⊃ (f ; g) ∨ (f1 ; g) OrChopImp
⊢ f ; (g ∨ g1) ⊃ (f ; g) ∨ (f ; g1) ChopOrImp
⊢ empty ; f ≡ f EmptyChop
⊢ f ; empty ≡ f ChopEmpty
⊢ (f ⊃ f1) ∧ (g ⊃ g1) ⊃ (f ; g) ⊃ (f1 ; g1) BiBoxChopImpChop
⊢ w ⊃ w StateImpBi
⊢ f ⊃¬¬f NextImpNotNextNot
⊢ (f ⊃ f) ∧ f ⊃ f BoxInduct
⊢ f+ ≡ f ∨ (f ∧more) ; f+ ChopPlusEqv
⊢ f ⊃ g, ⊢ f ⇒ ⊢ g MP
⊢ f ⇒ ⊢ f BoxGen
⊢ f ⇒ ⊢ f BiGen

Instead of ChopPlusEqv one can use

⊢ f∗≡empty ∨ (f ∧more) ; f∗ ChopStarEqv

2024-08-03
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