Logic and Bisimulation for Guarded Teams

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" summary

Introduces guarded teams and proves characterization theorems: properties definable in team semantics that are invariant under guarded bisimulation correspond to guarded fragments of first order logic and to translations into existential second order logic. Distinguishes weak vs strong bisimulation and shows inclusion and exclusion atoms are invariant under the strong notion but not the weak one. Shows inclusion logic translates to a greatest fixed point fragment and on finite structures captures PTIME. Explores horizontal vs vertical guardedness and open questions for guarded fixpoint fragments.

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" chapters (11)

1. 0:00Introduction to research
2. 1:29Guarded logics overview
3. 5:22Guarded bisimulation
4. 7:02Team semantics basics
5. 12:11Logical expressivity
6. 15:19Characterization results
7. 16:52Guarded teams and properties
8. 20:58Characterization theorems
9. 24:28Fixed point logic
10. 26:17Future research outlook
11. 28:43Q&A session