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Algebraic semantics (mathematical logic)
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<p>In <a href="/facts/Mathematical_logic/SaI7Y3wN">mathematical logic</a>, algebraic semantics is a <a href="/facts/Formal_semantics_(logic)/VdAKHszK">formal semantics</a> based on algebras studied as part of <a href="/facts/Algebraic_logic/bnkuqNb0">algebraic logic</a>. For example, the <a href="/facts/Modal_logic/I7uXvYYT">modal logic</a> S4 is characterized by the class of <a href="/facts/Interior_algebra/TYhpHoYN">topological boolean algebras</a>—that is, boolean algebras with an <a href="/facts/Interior_operator/Ysc3N0co">interior operator</a>. Other modal logics are characterized by various other algebras with operators. The class of <a href="/facts/Boolean_algebra_(structure)/cHbo65jm">boolean algebras</a> characterizes <a href="/facts/Classical_propositional_logic/MNt5v31V">classical propositional logic</a>, and the class of <a href="/facts/Heyting_algebra/Rrny2LRq">Heyting algebras</a> propositional <a href="/facts/Intuitionistic_logic/zI7ulCnM">intuitionistic logic</a>. <a href="/facts/MV-algebra/FzNChXEv">MV-algebras</a> are the algebraic semantics of <a href="/facts/%25C5%2581ukasiewicz_logic/PTfTcuNw">Łukasiewicz logic</a>. </p>