Monadic second order logic as the model companion of temporal logic

• Published in: Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science pp. 417 - 426
• Main Authors: Ghilardi, Silvio, van Gool, Sam
• Format: Conference Proceeding
• Language: English
• Published: New York, NY, USA ACM 05.07.2016
• Series: ACM Conferences
• Subjects: Theory of computation > Logic; Theory of computation > Models of computation > Computability; model companions; monadic second order logic; tree automata; modal and temporal logic
• ISBN: 9781450343916; 1450343910
• DOI: 10.1145/2933575.2933609

The main focus of this paper is on bisimulation-invariant MSO, and more particularly on giving a novel model-theoretic approach to it. In model theory, a model companion of a theory is a first-order description of the class of models in which all potentially solvable systems of equations and non-equations have solutions. We show that bisimulation-invariant MSO on trees gives the model companion for a new temporal logic, "fair CTL", an enrichment of CTL with local fairness constraints. To achieve this, we give a completeness proof for the logic fair CTL which combines tableaux and Stone duality, and a fair CTL encoding of the automata for the modal μ-calculus. Moreover, we also show that MSO on binary trees is the model companion of binary deterministic fair CTL.