Abstract
A central problem of logic in computer science is finding logics for which the satisfiability problem is decidable. A famous non-example is first-order logic, for which satisfiability is undecidable. One method to avoid such undecidability is to find syntactic restrictions on first-order logic (or even stronger logics, like second-order logic), which guarantee that satisfiable formulas have tree-like models, and then to use tree automata to check for the existence of tree-like models. Examples of logics covered by this method include modal logics and guarded logics. In this column, Luc Segoufin surveys the current state of first-order logics with tree-like models, with an emphasis on the newest member of the family, called guarded negation logic.
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