Soundness is the guarantee that well-typed Terms don’t go wrong: the algebra ensures that syntax respects the logic.
The Heyting algebra of Judgements constrains the syntax of Terms. Soundness is the first of three properties this constraint forces: if a Term has been typed — if a Judgement assigns it a property within a context — then Reduction cannot produce an error. Evaluation respects the types.
Soundness decomposes into two parts in the semantics stratum: type preservation (if a Term has a type before Reduction, it still has that type after) and progress (a well-typed Term is either a Value or can take another Reduction step). Together these guarantee that well-typed evaluation never gets stuck.
Soundness is the bridge between the logical layer (Judgements, Order, Implication) and the computational layer (Terms, Reduction, Values). It ensures they cohere: the logic does not make promises the computation cannot keep.