 It was only in the 1920s that algebras and logical matrices (an algebra together with a set of designated elements) started to be taken as models of logical deduction systems, that is, as providing a formal semantics for formal languages of logic. Moreover, they were also used to define sets of formulas with similar properties to the ones the sets of theorems of the known logical deduction systems have, in particular the property of being closed under substitution instances; soon after  logical matrices were also  used to define logics as consequence relations.