A modal perspective on monadic second-order alternation hierarchies
نویسنده
چکیده
We establish that the quantifier alternation hierarchy of formulae of Second-Order Propositional Modal Logic (SOPML) induces an infinite corresponding semantic hierarchy over the class of finite directed graphs. This is a response to an open problem posed in [4] and [8]. We also provide modal characterizations of the expressive power of Monadic Second-Order Logic (MSO) and address a number of points that should promote the potential advantages of viewing MSO and its fragments from the modal perspective.
منابع مشابه
Second-order propositional modal logic and monadic alternation hierarchies
We establish that the quantifier alternation hierarchy of formulae of secondorder propositional modal logic (SOPML) induces an infinite corresponding semantic hierarchy over the class of finite directed graphs. This solves an open problem problem of van Benthem (1985) and ten Cate (2006). We also identify modal characterizations of the expressive powers of second-order logic (SO) and monadic se...
متن کاملAlternating Set Quantifiers in Modal Logic
We establish the strictness of several set quantiVer alternation hierarchies that are based on modal logic, evaluated on various classes of Vnite graphs. This extends to the modal setting a celebrated result of Matz, Schweikardt and Thomas (2002), which states that the analogous hierarchy of monadic second-order logic is strict. Thereby, the present paper settles a question raised by van Benthe...
متن کاملA Characterization Theorem for the Alternation-Free Fragment of the Modal µ-Calculus
We provide a characterization theorem, in the style of van Benthem and Janin-Walukiewicz, for the alternation-free fragment of the modal μ-calculus. For this purpose we introduce a variant of standard monadic second-order logic (MSO), which we call well-founded monadic second-order logic (WFMSO). When interpreted in a tree model, the second-order quantifiers of WFMSO range over subsets of conve...
متن کاملSubshifts, MSO Logic, and Collapsing Hierarchies
We use monadic second-order logic to define two-dimensional subshifts, or sets of colorings of the infinite plane. We present a natural family of quantifier alternation hierarchies, and show that they all collapse to the third level. In particular, this solves an open problem of [Jeandel & Theyssier 2013]. The results are in stark contrast with picture languages, where such hierarchies are usua...
متن کاملComplexity of Monadic inf-datalog. Application to temporal logic
In [] we defined Inf-Datalog and characterized the fragments of Monadic inf-Datalog that have the same expressive power as Modal Logic (resp. CTL, alternation-free Modal μ-calculus and Modal μ-calculus). We study here the time and space complexity of evaluation of Monadic inf-Datalog programs on finite models. We deduce a new unified proof that model checking has 1. linear data and program comp...
متن کامل