We describe here a Hilbert system with nine axioms and just the rule modus ponens, which we call the one-rule axiomatisation and which describes classical equational logic.
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Equational logic was developed over the years ( beginning in the early 1980s ) by researchers in the formal development of programs, who felt a need for an effective style of manipulation, of calculation.
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Equational logic was common before " Principia Mathematica " ( e . g ., Peirce, 1, 2, 3 Johnson 1892 ), and has present-day advocates ( Gries and Schneider 1993 ).
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"' EQP "', an abbreviation for "'equational prover "', is an automated theorem proving program for equational logic, developed by the Mathematics and Computer Science Division of the Argonne National Laboratory.
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