# Catalogue of Artificial Intelligence Techniques

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## Hybrid Logic

**Keywords:**
hybrid logic, nominal, satisfaction operator

### Categories: Logic Programming

Author(s): **Yingzhi Luo**

Hybrid logic is the logic that between thee concept of first-model logic and the propositional logic, it¡¯s the extension of the ordinary model logic, it express the ordinary model logic with more power. In order to build the hybrid logic, we need to use the nominal as the second type atomic formula to add into propositional modal logic. E.g ,p and q for ordinary propositional modal logic, i and j for nominal. The formula is: (iÙp)Ù (iÙq)® (pÙq) and is the possible modalities. Each nominal must be true at exactly one point in any model. Many logics have been enriched just by using this idea. E.g in the previous example, the formula is valid: if the antecedent is satisfied at a point s, the unique point I must be accessible from s,. and p and q must be true.

There is an operator called satisfaction operator (@) can be added to the formula as well.(satisfaction operator is important in AI field) It can formalise a statement being true at a possible world. E.g The satisfaction statement @:¦Õ expresses that the formula ¦Õ is true relative to one particular point, and the point is that the nominal refers to There is an operator called satisfaction operator (@) can be added to the formula as well.(satisfaction operator is important in AI field) It can formalise a statement being true at a possible world. E.g The satisfaction statement @:¦Õ expresses that the formula ¦Õ is true relative to one particular point, and the point is that the nominal refers to.

∀ and are the binding nominals in hybrid logic. In recent years, binding nominal ¡ý have been created and it can bind variables to the current point.

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