In logic, algebraic semantics is a formal semantics based on algebras. For example, the modal logic S4 is characterized by the class of topological boolean algebras—that is, boolean algebras with an interior operator. Other modal logics are characterized by various other algebras with operators. The class of boolean algebras characterizes classical propositional logic, and the class of Heyting algebras propositional intuitionistic logic.
See also
- Axiomatic semantics
- Operational semantics
- Denotational semantics
- Formal semantics of programming languages
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