_Connective

Marker trait for the five logical connectives: And, Or, Not, Implies, and Xor.

Operands are untyped core._Expressions so equations and other domains compose without cross-domain imports. eval runs the shared Kleene/Zadeh min–max rule table (kleeneAnd, kleeneOr, kleeneNot, kleeneImplies, kleeneXor) over operands widened by asTruth, so core._Bool and core._Truth operands mix freely and the boolean behaviour is a special case of the graded table rather than a separate branch. The result is rebuilt through _Truth.of, which collapses a crisp degree back to _Bool. Any other concrete operand (a _Number, a matrix) leaves the node symbolic.

eval consults its Environment for two knobs, neither of which is a second node hierarchy: the truth-value encoding (symmetricLogic, which additionally admits the digits {-1, 0, 1} as truth values -- a change of digits, never a change of meaning) and the semantics (LogicSemantics, selecting the t-norm / t-conorm pair: min-max, product, or Lukasiewicz). All three semantics agree with classical logic on the crisp values, so the boolean and three-valued tiers are unaffected by the default.

Deliberately NOT marked core._ElementWise: that marker means derive/simplify/ expand/integrate distribute over children (linear containers only), and the connectives are not linear -- derive(a and b, x) must stay symbolic.