In this talk we present a translation of formulas and models of classical and non-classical logics into factor algebras. The correspondence:

• Propositional variables - operator of decompositions

• Logical operations - substitutions

• Formulas - algebraic terms

• Models - factor algebras,

provides a uniform calculus of provability for all the logics which admit the translation. Many examples will be discussed: classical logic, intuitionistic logic, linear logic, many-valued logics.