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- W4284888488 abstract "Abstract We extend the languages of both basic and graded modal logic with the infinity diamond, a modality that expresses the existence of infinitely many successors having a certain property. In both cases we define a natural notion of bisimilarity for the resulting formalisms, that we dub $mathtt {ML}^{infty }$ and $mathtt {GML}^{infty }$ , respectively. We then characterise these logics as the bisimulation-invariant fragments of the naturally corresponding predicate logic, viz., the extension of first-order logic with the infinity quantifier. Furthermore, for both $mathtt {ML}^{infty }$ and $mathtt {GML}^{infty }$ we provide a sound and complete axiomatisation for the set of formulas that are valid in every Kripke frame, we prove a small model property with respect to a widened class of weighted models, and we establish decidability of the satisfiability problem." @default.
- W4284888488 created "2022-07-09" @default.
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- W4284888488 date "2022-07-07" @default.
- W4284888488 modified "2023-09-26" @default.
- W4284888488 title "COUNTING TO INFINITY: GRADED MODAL LOGIC WITH AN INFINITY DIAMOND" @default.
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- W4284888488 doi "https://doi.org/10.1017/s1755020322000247" @default.
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