A modal perspective on monadic second-order alternation hierarchies

abstract. 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.

• Type: Conference
• Year: 2008
• Where: AIML
• Authors: Antti Kuusisto
• Keywords: AIML 2008, Logical Reasoning, Monadic Second-order Logic, Propositional Modal Logic, Quantifier Alternation Hierarchy