Strong Completeness for Iteration-Free Coalgebraic Dynamic Logics
نویسندگان
چکیده
We present a (co)algebraic treatment of iteration-free dynamic modal logics such as Propositional Dynamic Logic (PDL) and Game Logic (GL), both without star. The main observation is that the program/game constructs of PDL/GL arise from monad structure, and the axioms of these logics correspond to certain compatibilty requirements between the modalities and this monad structure. Our main contribution is a general soundness and strong completeness result for PDL-like logics for T -coalgebras where T is a monad and the ”program” constructs are given by sequential composition, test, and pointwise extensions of operations of T .
منابع مشابه
Weak Completeness of Coalgebraic Dynamic Logics
We present a coalgebraic generalisation of Fischer and Ladner’s Propositional Dynamic Logic (PDL) and Parikh’s Game Logic (GL). In earlier work, we proved a generic strong completeness result for coalgebraic dynamic logics without iteration. The coalgebraic semantics of such programs is given by a monad T , and modalities are interpreted via a predicate lifting λ whose transpose is a monad morp...
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