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2
Propositional Interval Temporal Logic Theorems
2.1
Basic ITL Theorems
AndChopA
AndChopB
NextChop
BiChopImpChop
BoxChopImpChop
LeftChopImpChop
RightChopImpChop
RightChopEqvChop
ChopOrEqv
OrChopImpRule
OrChopEqvRule
NextImpNext
NextImpDist
ChopImpDiamond
NowImpDiamond
NextDiamondImpDiamond
BoxImpNowAndWeakNext
BoxImpBoxRule
BoxImpDist
DiamondEmpty
BiImpDiImpDi
DiImpDi
BiImpBiRule
LeftChopEqvChop
DiEqvDi
BiEqvBi
LeftChopChopImpChopRule
AndChopCommute
StateAndChopImpChopRule
StateImpChopEqvChop
ChopEqvStateAndChop
DiIntro
BiElim
BiContraPosImpDist
BiImpDist
OrChopEqv
IfChopEqvRule
ChopOrImpRule
ChopOrEqvRule
EmptyOrChopEqv
EmptyOrNextChopEqv
EmptyOrChopImpRule
EmptyOrChopEqvRule
EmptyOrNextChopImpRule
EmptyOrNextChopEqvRule
ChopEmptyOrImpRule
BoxStateChopBoxEqvBox
NotBoxStateImpBoxYieldsNotBox
BoxStateAndChopEqvChop
StateEqvBi
DiNotEqvNotBi
DiEqvNotBiNot
BoxAndChopImport
ChopAndBoxImport
AndChopAndCommute
ChopImpChop
ChopEqvChop
MultChopImpChop
BoxChopImpChopBox
NotChopEqvYieldsNot
DiamondImpTrueChop
BiAndChopImport
2.2
Further properties of Diamond-i and Box-i
ImpDi
NotDiFalse
DiState
StateChop
StateChopExportA
StateAndChopImport
StateAndChop
StateAndEmptyChop
StateAndNextChop
NextStateAndChop
StateYieldsEqv
StateAndDi
DiNext
DiNextState
StateImpBiGen
ChopAndNotChopImp
ChopAndYieldsImp
ChopAndYieldsMP
OrYieldsImp
LeftYieldsImpYields
LeftYieldsEqvYields
StateImpYields
StateAndYieldsImpYields
AndYieldsA
AndYieldsB
RightYieldsImpYields
RightYieldsEqvYields
BoxImpYields
BoxEqvTrueYields
YieldsGen
YieldsAndYieldsEqvYieldsAnd
YieldsAndYieldsImpAndYieldsAnd
YieldsYieldsEqvChopYields
EmptyYields
NextYields
SkipChopEqvNext
SkipYieldsEqvWeakNext
NextImpSkipYields
MoreEqvSkipChopTrue
MoreChopImpMore
ChopMoreImpMore
MoreChopEqvNextDiamond
NotEqvYieldsMore
LeftChopImpMoreRule
RightChopImpMoreRule
NotDiEqvBiNot
ChopImpDi
TrueEqvTrueChopTrue
DiEqvDiDi
BiEqvBiBi
DiOrEqv
DiAndA
DiAndB
DiAndImpAnd
DiSkipEqvMore
DiMoreEqvMore
DiIfEqvRule
DiEmpty
2.3
Properties of Diamond-a and Box-a
DaEqvDtDi
DaEqvDiDt
DtDiEqvDiDt
BaEqvBiBt
BaEqvBtBi
BtBiEqvBiBt
DaNotEqvNotBa
DaEqvNotBaNot
BaElim
DaIntro
BaImpBt
BaImpBi
BaGen
BaImpDist
DaEqvDaDa
BaEqvBaBa
BaLeftChopImpChop
BaRightChopImpChop
BaAndChopImport
ChopAndBaImport
BaChopImpChopBa
BoxStateEqvBaBoxState
DiNotBaImpNotBa
NotBaChopImpNotBa
2.4
Properties of Fin
AndFinEqvChopStateAndEmpty
FinChopEqvOr
FinChopEqvDiamond
FinYields
AndFinChopEqvStateAndChop
DiAndFinEqvChopState
BiImpFinEqvYieldsState
ChopFinImpFin
FinImpYieldsFin
ChopAndFin
ChopAndNotFin
FinChopChain
ChopRule
ChopRep
ChopRepAndFin
MoreChopLoop
MoreChopContra
ChopLoop
ChopContra
2.5
Properties of
chop-plus
ImpChopPlus
ChopChopPlusImpChopPlus
ChopPlusEqvOrChopChopPlus
ChopPlusIntro
ChopPlusElim
ChopPlusElimWithoutMore
ChopPlusImpChopPlus
ChopPlusEqvChopPlus
2.6
Properties of
chop-star
CSEqv
EmptyImpCS
ChopPlusImpCS
ImpCS
CSChopEqvOrChopPlusChop
CSEqvOrChopCS
ChopCSImpCS
CSAndMoreImpChopPlus
CSAndMoreEqvAndMoreChop
CSAndMoreImpChopCS
CSAndMoreImpCSChop
CSMoreNotImpChopCSAndMore
CSChopCSImpCS
CSChopImpCS
CSCSImpCS
CSImpCS
CSEqvCS
AndCSA
AndCSB
CSIntro
CSElim
CSElimWithoutMore
CSChopEqvChopOrRule
CSChopIntroRule
CSImpBox
BoxCSEqvBox
BoxStateAndCSEqvCS
BaCSImpCS
BaCSEqvCS
BaAndCSImport
2.7
Properties of While
WhileEqvIf
WhileChopEqvIf
WhileChopEqvIfRule
WhileImpFin
WhileEqvEmptyOrChopWhile
WhileIntro
WhileElim
BaWhileImpWhile
WhileImpWhile
2.8
Properties of Halt
HaltChopEqv
AndHaltChopImp
NotAndHaltChopImpNext
NotAndHaltChopImpSkipYields
HaltChopImpNotHaltChopNot
HaltChopImpHaltYields
HaltChopAnd
HaltAndChopAndHaltChopImpHaltAndChopAnd
HaltImpBoxYields
2.9
Properties of groups of
chops
ChopGroupMerge
ChopGroupGroupMerge
ChopGroupImpCS
MultChopImpCS
NestedChopImpChop
MultNestedChopImpChop
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2023-09-12
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