There are few well-know styles of logical systems (LS): Hilbert-style, Sequent-style, Natural deducton style. And such lesser-know styles as Gottlob-Frege two-demensional notation, systems with graphical syntax etc. (In wikipedia)
And I have some questions:
For example, is the Resolution method (language of clauses and resolution rule) is another style of LS? Or is it (resolution method) something other than style of LS?
Is the Lambda-calsulus is another style of LS? Or one can consider it as kind of semantics? How Lambda-calculus relate to logical systems?
And finally, how one can modify logical systems (classical LS)? For example, One can otherwise interpret the logical connectives (the other semantics of logical connectives) and as a result get a constructive logic; or one can introduce anoter logical operation, and as a result get a modal logic; or one can modify type of quantifiers and as a result get a high-order logics; etc.