PHILOS 143 Chapter Notes - Chapter 3: Bisimulation, Binary Relation, Determinacy
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De nition 3. 2. 2 tree unraveling: worlds in a tree unraveling are all nite paths in m starting at s. De nition sketch: bisumulation contraction is a minimal representation of the modally relevant structure of m . Lemma, invariance: for any bisimulation e between m and n and any two worlds x, y such that xey: m, x |= i n, y |= for all . Assertion: every is invarient across all bisimulation links. Assertion says that the above holds for all . By truth-de nition, then not m, x |= . So by assertion/inductive hypothesis, then not n, y |= . Let xey and suppose m, x |= . By truth-de nition, there is a world z such that xr(m )z and m, z |= . By inductive hypothesis for on zeu gives us n, u |= . Give m, s such that the property holds at s.
