Logic & Boolean Algebra
The Wolfram Language represents Boolean expressions in symbolic form, so they can not only be evaluated, but also be symbolically manipulated and transformed. Incorporating state-of-the-art quantifier elimination, satisfiability, and equational logic theorem proving, the Wolfram Language provides a powerful framework for investigations based on Boolean algebra.
Logical Operators »
And(&&, ∧) ▪ Or(||, ∨) ▪ Not(!,¬) ▪ Nand(⊼) ▪ Nor(⊽) ▪ Xor(⊻) ▪ Implies() ▪ Equivalent(⧦) ▪ Equal(==) ▪ Unequal(!=) ▪ ...
True, False — symbolic truth values
Boole — convert symbolic truth values to 0 and 1
Boolean Computation »
BooleanFunction — general Boolean function
BooleanConvert ▪ BooleanMinimize ▪ SatisfiableQ ▪ ...
Mathematical Logic
FullSimplify — simplify logic expressions and prove theorems
ForAll (∀), Exists (∃) — quantifiers
Resolve ▪ Reduce ▪ FindInstance
Automated Theorem Proving »
FindEquationalProof — generate representations of proofs in equational logic
ProofObject ▪ AxiomaticTheory ▪ ...
Boolean Vector Operations
Nearest, FindClusters — operate on Boolean vectors