Mathematical logic

Monadic second-order logic

In mathematical logic, monadic second-order logic (MSO) is the fragment of second-order logic where the second-order quantification is limited to quantification over sets. It is particularly important in the logic of graphs, because of Courcelle's theorem, which provides algorithms for evaluating monadic second-order formulas over graphs of bounded treewidth. It is also of fundamental importance in automata theory, where the Büchi-Elgot-Trakhtenbrot theorem gives a logical characterization of the regular languages. Second-order logic allows quantification over predicates. However, MSO is the fragment in which second-order quantification is limited to monadic predicates (predicates having a single argument). This is often described as quantification over "sets" because monadic predicates are equivalent in expressive power to sets (the set of elements for which the predicate is true). (Wikipedia).

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Related pages

Fragment (logic) | Connectivity (graph theory) | Monadic predicate calculus | Nonelementary problem | Tree automaton | Predicate (mathematical logic) | Büchi-Elgot-Trakhtenbrot theorem | Courcelle's theorem | Regular language | Formal verification | Automata theory | Decidability (logic) | S2S (mathematics) | Fagin's theorem | Logic of graphs | Second-order logic | Descriptive complexity theory | Enumeration algorithm | NP (complexity) | Tree (data structure) | Treewidth | Mathematical logic | Shape analysis (program analysis) | First-order logic | Binary tree