@misc{AOFA_L00.MIZ,
  AUTHOR = {Bancerek, Grzegorz},
  TITLE = {Algebraic Approach to Algorithmic Logic},
  SECTION1 = {Algorithmic Language Signature},
  SECTION2 = {Language},
  SECTION3 = {Algorithmic Theory},
  SECTION4 = {Propositional Calculus},
  SECTION5 = {Quantifier Calculus},
  SECTION6 = {Algorithmic Logic},
  ADDRESS1 = {Association of Mizar Users\\Bia\l ystok},
  DAY = {15},
  MONTH = {September},
  YEAR = {2014},
  SUMMARY = {We introduce algorithmic logic --  an algebraic approach according to
  \cite{Salwicki}.
 It is done in three stages: propositional calculus,
 quantifier calculus with equality, and finally proper algorithmic logic.
 For each stage appropriate signature and
 theory are defined. Propositional calculus and quantifier calculus with equality
 are explored according to \cite{Mendelson}. A language is introduced with
 language signature including free variables, substitution, and equality.
 Algorithmic logic requires a bialgebra structure which is an extension
 of language signature and program algebra. While-if algebra of generator set and
 algebraic signature is bialgebra with appropriate properties and is used as
 basic type of algebraic logic.}}

@Book{Mendelson,
  author = 	 {Elliott Mendelson},
  title = 	 {Introduction to Mathematical Logic},
  publisher = 	 {Chapman & Hall/CRC},
  year = 	 1997,
  url =          {http://books.google.pl/books?id=ZO1p4QGspoYC}}
