Abstract
The logic MSOL+\(\mathbb{B}\) is defined, by extending monadic second-order logic on the infinite binary tree with a new bounding quantifier \(\mathbb{B}\). In this logic, a formula \(\mathbb{B}\)X. φ(X) states that there is a finite bound on the size of sets satisfying φ(X). Satisfiability is proved decidable for two fragments of MSOL+\(\mathbb{B}\): formulas of the form \(\neg\mathbb{B}\)X.φ(X), with φ a \(\mathbb{B}\)-free formula; and formulas built from \(\mathbb{B}\)-free formulas by nesting \(\mathbb{B}\), ∃, ∨ and ∧.
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Bojańczyk, M. (2004). A Bounding Quantifier. In: Marcinkowski, J., Tarlecki, A. (eds) Computer Science Logic. CSL 2004. Lecture Notes in Computer Science, vol 3210. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30124-0_7
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DOI: https://doi.org/10.1007/978-3-540-30124-0_7
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