On decidability of monadic logic of order over the naturals extended by monadic predicates
نویسندگان
چکیده
منابع مشابه
On decidability of monadic logic of order over the naturals extended by monadic predicates
A fundamental result of Büchi states that the set of monadic second-order formulas true in the structure (Nat,<) is decidable. A natural question is: what monadic predicates (sets) can be added to (Nat,<) while preserving decidability? Elgot and Rabin found many interesting predicates P for which the monadic theory of 〈Nat,<,P〉 is decidable. The Elgot and Rabin automata theoretical method has b...
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A major result concerning Temporal Logics (TL) is Kamp’s theorem [Kam68, GHR94], which states that the temporal logic over the pair of modalities X until Y and Xsince Y is expressively complete for the first order fragment of monadic logic of order over the natural numbers. We show that there is no finite set of modalities B such that the temporal logic over B and monadic logic of order have th...
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Pioneers of logic, among them J.R. Büchi, M.O. Rabin, S. Shelah, and Y. Gurevich, have shown that monadic second-order logic offers a rich landscape of interesting decidable theories. Prominent examples are the monadic theory of the successor structure S1 = (N,+1) of the natural numbers and the monadic theory of the binary tree, i.e., of the two-successor structure S2 = ({0, 1} ∗, ·0, ·1). We c...
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A monadic formula ψ(Y ) is a selector for a monadic formula φ(Y ) in a structure M if ψ defines inM a unique subset P of the domain and this P also satisfies φ inM. If C is a class of structures and φ is a selector for ψ in everyM ∈ C, we say that φ is a selector for φ over C. For a monadic formula φ(X, Y ) and ordinals α ≤ ω1 and δ < ω , we decide whether there exists a monadic formula ψ(X, Y ...
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In this paper we introduce so-called asymptotic logics, logics that are meant to reason about weights of elements in a model in a way inspired by topology. Our main subject of study is Asymptotic Monadic Second-Order Logic over infinite words. This is a logic talking about ωwords labelled by integers. It contains full monadic second-order logic and can express asymptotic properties of integers ...
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ژورنال
عنوان ژورنال: Information and Computation
سال: 2007
ISSN: 0890-5401
DOI: 10.1016/j.ic.2006.12.004