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Algebraic semantics (mathematical logic)
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Algebraic semantics (mathematical logic)
In
mathematical logic
,
algebraic semantics
is a
formal semantics
based on algebras studied as part of
algebraic logic
. 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
.
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