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 (if and only if) 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.
External links
- Hybrid Logics' Home Page (http://hylo.loria.fr/)