Principia Mathematica II

Subject: Proof Methods Version Overview
Date:    2003-11-24
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Prototype Warning
=================
This program suite is only a working prototype for the main project
*Hilbert II*. It concentrates on the basic logic foundation of 
mathematics. The software design of the main implementation will be 
highly different. The following information is only appropriate for 
this prototype. Look at 
 http://www.qedeq.org/
 http://sourceforge.net/projects/pmii/
to get the latest source code and information.


Rule Version Overview
=====================
The proof methods are listed in dependency from their version number.
The basic proof methods are those of Version 1.00.00. All other
versions of proof methods could be derived from the basic rules
together with the axioms of predicate calculus.


 Rule                       Description

Version 1.00.00
 ADDAXIOM                   add previous axiom to proof lines
 ADDSENTENCE                add previous proposition to proof lines
 GENERALIZATION             generalize a formula
 MODUSPONENS                use modus ponens
 PARTICULARIZATION          particularize a formula
 RENAMEBOUNDVARIABLE        rename a bound subject variable
 RENAMEFREEVARIABLE         rename a free subject variable
 REPLACEPREDICATE           replace predicate variable
 REPLACEPROP                replace proposition variable by formula
 USEABBREVIATION            use previous abbreviation
 REVERSEABBREVIATION        unuse previous abbreviation         

Version 1.01.00
 SUBSTLINE                  substitute various variables of a proof line

Version 1.01.01
 APPLYAXIOM                 add axiom, substitute, use modus ponens
 APPLYSENTENCE              add proposition, subsitute, use modus ponens

Version 1.01.02
 HYPOTHETICALSYLLOGISM      use hypothetical syllogism

Version 1.01.03
 RIGHTADDITION              right addition of disjunction to implication

Version 1.01.04
 LEFTADDITION               left addition of disjunction to implication
 REVERSEIMPLICATION         build correct reversion of an implication

Version 1.01.05
 LEFTADDITIONCONJUNCTION    left addition of conjunction to implication
 RIGHTADDITIONCONJUNCTION   right addition of conjunction to implication
 LEFTADDITIONIMPLICATION    left addition of implication to implication
 RIGHTADDITIONIMPLICATION   right addition of implication to implication

Version 1.01.06
 LEFTADDITIONEQUIVALENCE    left addition of equivalence to implication
 RIGHTADDITIONEQUIVALENCE   right addition of equivalence to implication

Version 1.02.00
 IMPLICATIONEQUIVALENT      if two formulas impies each other any
                             occurence of one formula could be replaced
                             by the other one
Version 1.02.01
 CONJUNCTION                conjunction of two proved formulas
