Hybrid logic
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Hybrid logic is a form of formal logic which extends modal logic with constructs allowing semantical features of its relational semantics to be expressed. The resulting language is as expressive as first-order logic; it is called hybrid since its ideas are a hybrid of ideas from modal logic and first-order logic.
Unlike ordinary modal logic, hybrid logic makes it possible to refer to states (possible worlds) in formulas. This is achieved by a class of formulas called nominals, which are true in exactly one state, and by the use of the @ operator, which is defined as follows:
- @ip is true iff p is true in the unique state named by the nominal i (i.e., the state where i is true).
Hybrid logics have many features in common with temporal logic (which use nominal-like constructs to denote specific points in time), and they are a rich source of ideas for researchers in modern modal logic. They also find applications in the areas of feature logic, model theory, proof theory and logical analysis of natural language.
