index.md (1184B)
1 +++ 2 title = 'Lecture 11' 3 +++ 4 # Lecture 11 5 In propositional dynamic logic (PDL), aim to prove: φ → [while σ do α] ψ 6 - i.e. starting with φ true, for any terminating execution of the program, we have ψ true. 7 8 Definitions: 9 - state of program execution: state/world 10 - program: regular program which slightly generalizes a while program 11 - statement {pre}program{post}: formula pre → [program] post 12 13 For every program α we have modality \<α\>: 14 - \<α\>: it's possible to execute α from current state, and successfully halt in state satisfying φ (like existential quantification) 15 - [α]φ: for all executions of α, if α successfully halts, then it halts in a state satisfying φ (like universal quantification) 16 17 Program definitions: 18 - a: program from set A of atomic programs (letters, like in prop. logic) 19 - α; β: sequential composition 20 - α ∪ β: non-deterministic choice 21 - α\*: iteration, 0 or more times. 22 - φ?: test, depends on the grammar for formulas 23 - if φ then continue without changing state, if not then block without halting 24 25 Examples of formulas: 26 27  28 29 We obtain semantics of PDL as instance of multi-modal logic.