I am new in model checking field. I want to know why it's preferred to use linear-time temporal logic properties in interpolation and bounded model checking. Why can't we directly use propositional logic?
Why use temporal logic for interpolation-based model checking?
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You can also restrict yourself to propositional logic, but then you cannot express interesting properties of your model.
Propositional logic is less expressive than temporal logic. In propositional logic you can only describe one situation/state/world, and model checking is very easy: Given the current state (i.e. the set of true propositions) you only need to evaluate a propositional formula.
In contrast, temporal logics like LTL can talk about the future and the past, with operators like Gϕ saying "ϕ will always be true in the future". A model for temporal logic then is not just the current state, but also a description (transition relation) of what was the case before and how it will develop.