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( Begriffsschrift)
Begriffsschrift is the title of a short book on logic by Gottlob Frege, published in 1879, and is also the name of the formal system set out in that book. The calculus contains the first appearance of quantified variables, and is essentially classical bivalent second-order logic with identity, albeit presented using a highly idiosyncratic two-dimensional notation connectives and quantifiers are written using lines connecting formulas, rather than the symbols ¬, ?, and ? in use today. For example, that judgement B materially implies judgement A, i.e.  is written as  . In the first chapter, Frege defines basic ideas and notation, like proposition ("judgement"), the universal quantifier ("the generality"), the conditional, negation and the "sign for identity of content"  ; in the second chapter he declares nine formalized propositions as axioms. In chapter 1, §5, Frege defines the conditional as follows
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