Axiomatizations and Computability of Weighted Monadic Second-Order Logic

Weighted monadic second-order logic is a weighted extension of monadic second-order logic that captures exactly the behaviour of weighted automata. Its semantics is parameterized with respect to a semiring on which the values that weighted formulas output are evaluated. Gastin and Monmege (2018) gav...

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Veröffentlicht in:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science S. 1 - 13
Hauptverfasser: Achilleos, Antonis, Pedersen, Mathias Ruggaard
Format: Tagungsbericht
Sprache:Englisch
Veröffentlicht: IEEE 29.06.2021
Schlagworte:
Automata
axiomatization
Complexity theory
Computer science
Model checking
monadic second-order logic
satisfiability
Semantics
Syntactics
weighted automata
weighted logic
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Zusammenfassung:Weighted monadic second-order logic is a weighted extension of monadic second-order logic that captures exactly the behaviour of weighted automata. Its semantics is parameterized with respect to a semiring on which the values that weighted formulas output are evaluated. Gastin and Monmege (2018) gave abstract semantics for a version of weighted monadic second-order logic to give a more general and modular proof of the equivalence of the logic with weighted automata. We focus on the abstract semantics of the logic and we give a complete axiomatization both for the full logic and for a fragment without general sum, thus giving a more fine-grained understanding of the logic. We discuss how common decision problems for logical languages can be adapted to the weighted setting, and show that many of these are decidable, though they inherit bad complexity from the underlying first- and second-order logics. However, we show that a weighted adaptation of satisfiability is undecidable for the logic when one uses the abstract interpretation.
DOI:10.1109/LICS52264.2021.9470615