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Raphael CAUDERLIER
dktactics
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27989ea2
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27989ea2
authored
Jan 26, 2018
by
Raphael CAUDERLIER
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[doc] fix small mistakes in the documentation of the resolution module
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@@ -773,11 +773,13 @@ combinator) and then uses the classical lemma
variables which are to be interpreted as universally quantified. A
*quantified clause* is an explicitly universally quantified clause.
The simplest way to define a clause is by parsing the corresponding
The types for atoms, litterals, clauses, and quantified clauses are
declared with their constructors in [[./fol/clauses.dk][fol/clauses.dk]]. However, the
simplest way to define a clause is by parsing the corresponding
proposition using the partial function
=resolution.qclause_of_prop=:
- =resolution.qclause_of_prop : fol.prop ->
resolution
.qclause=
- =resolution.qclause_of_prop : fol.prop ->
clauses
.qclause=
- =resolution.qclause_of_prop_correct : p : fol.prop -> fol.proof p -> resolution.qcproof (resolution.qclause_of_prop p)=
A resolution proof is a derivation of the empty clause
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@@ -786,11 +788,11 @@ combinator) and then uses the classical lemma
#+BEGIN_example
l₁ ∨ … ∨ lₙ σ = mgu(lᵢ, lⱼ)
—
-—————————————————————————————–
Factorisation
—
————————————————————————————————
Factorisation
(l₁ ∨ … ∨ lⱼ₋₁ ∨ lⱼ₊₁ ∨ … ∨ lₙ)σ
l₁ ∨ … ∨ lₙ l'₁ ∨ … ∨ l'ₘ σ = mgu(lᵢ, ¬l'ⱼ)
——————————————————
–—————————————————–————————–—––
——————————————————— Resolution
——————————————————
——————————————————————————————————
——————————————————— Resolution
(l₁ ∨ … ∨ lᵢ₋₁ ∨ lᵢ₊₁ ∨ … ∨ lₙ ∨ l'₁ ∨ … ∨ l'ⱼ₋₁ ∨ l'ⱼ₊₁ ∨ … ∨ l'ₘ)σ
#+END_example
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