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Algebraic Logic

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4 domain-specific abstractions whose origin domain is Algebraic Logic.

  • Action algebra — An algebraic-logic structure combining Kleene algebra's composition and iteration with residuated semilattice implication operations.
  • Boolean algebra — An algebraic structure with conjunction, disjunction and complementation satisfying laws that model two-valued logic and set operations.
  • Lindenbaum–Tarski algebra — The quotient algebra of formulas or sentences of a logical theory by provable equivalence, with logical connectives inducing well-defined algebraic operations on equivalence classes.
  • Modal algebra — A Boolean algebra equipped with a unary normal meet-preserving modal operator, providing algebraic semantics for normal propositional modal logics.