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Hilbert II - JAVA-Packages - Principia Mathematica II | ||||||||||
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Interface Summary | |
Rule | Every logical rule must implement this interface. |
RuleConstants | This interface provides constants of this package. |
Class Summary | |
AddAxiom | Implementation of adding an Axiom:
---------
A0 |
AddSentence | Implemention of adding an Sentence:
---------
A0 |
ApplyAxiom | Implementation of applying an Axiom:
A1 => A2
A3
---------
A4
if A1 => A2 matches A3 => A4 |
ApplySentence | Implementation of applying a Sentence:
A1 => A2
A3
---------
A4
if A1 => A2 matches A3 => A4 |
ConjunctionRule | Implemention of conjunction rule:
A1
A2
---------
A1 & A2 |
ElementaryEquivalence | Implemention of using an elementary equivalence:
a => b
b => a
A(a)
---------
A(b) |
Generalization | Implemention of making a conclusion universal. |
HypotheticalSyllogism | Implemention of (pure) Hypothetical Syllogism:
A1 => A2
A2 => A3
---------
A1 => A3 |
LeftAddition | Implemention of "addition" on the left side. |
LeftAdditionConjunction | Implemention of "addition" of an conjunction on the left side. |
LeftAdditionEquivalence | Implemention of "addition" of an equivalence on the left side. |
LeftAdditionImplication | Implemention of "addition" of an implication on the left side. |
LinkReference | A reference label. |
ModusPonens | Implemention of Modus Ponens:
A0
A0 => A1
---------
A1 |
Particularization | Implemention of making a conclusion special. |
RenameBoundSubjectVariable | Replace a free subject variable by another subject variable:
A[x]
-----------
A[y] |
RenameFreeSubjectVariable | Replace a free subject variable by another subject variable:
A[x]
x is free in A[x]
y is not bound in A[x]
----------------------
A[y] |
ReplacePredicateVariable | Replace predicate variable by a formula:
A[R(x,y,z)]
formula F(x,y,z)
------------------
A[F(x,y,z)] |
ReplacePropositionVariable | Replace predicate variables by formulas:
A[p]
formula F
-----------
A[F] |
ReverseAbbreviation | Implemention of reversing an abbreviation:
A1
---------
A0 |
ReverseImplication | Implemention of reversing an implication. |
RightAddition | Implemention of "addition" on the right side. |
RightAdditionConjunction | Implemention of "addition" of an conjunction on the left side. |
RightAdditionEquivalence | Implemention of "addition" of an equivalence on the right side. |
RightAdditionImplication | Implemention of "addition" of an implication on the left side. |
RuleCreator | This class provides static methods for reading and
writing an Argument . |
SubstLine | Implementation of substituting variables:
A1
---------
A2
if A1 matches A2 (e.g. |
UseAbbreviation | Implemention of using an abbreviation for a formula:
A1
---------
A2 |
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Hilbert II - JAVA-Packages - Principia Mathematica II | ||||||||||
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