Substantial and formal deductions in logics with vector semantics

The problem of logic deduction for one class of logics with a vector semantics is discussed. In the given logics the trustiness is represented by a vector with components 〈Truth; Lie〉, which do not depend on each other. The problem of organization of “substantial” and “formal” deductions is considered. In the first case the meaning of truth (semantics) of judgements is taken into account, whereas in the second case only the structure of judgements (syntax) is considered.