axiomatizations of temporal logic

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Axiomatizations of Temporal Logic 10723029 Xu Zhaoqing

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Axiomatizations of Temporal Logic . 10723029 Xu Zhaoqing. I. Content. Introduction Basic temporal logic Branching time logic Conclusions. II. Introduction. Temporal Logic Broadly : all approaches to the representation of temporal information within a logical framework; - PowerPoint PPT Presentation

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Axiomatizations of Temporal Logic 10723029Xu ZhaoqingI. ContentIntroductionBasic temporal logicBranching time logicConclusionsII. IntroductionTemporal LogicBroadly: all approaches to the representation of temporal information within a logical framework;Narrowly: the modal-style of temporal logic;III. Basic Temporal Logic1. Syntax and semantics2. The Minimal logic Kt3. The IRR rule4. The logic of linear time 1. Syntax and SemanticsLanguage:,,G,HF =df GP =df HA temporal frame (or flow of time) F=(T,)where T is non-emptyis a binary relation which is irreflexive and transitive; A valuation V: P(T) ; A model M=(F,V);

Satisfaction:M, t ||- p ifftV(p), where p,M, t ||- iffnot M, t,M, t ||- iffM, t and M, t ,M, t ||- G ifffor all sT, if t