Construction Rules

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    Basic Principle

    If all branches of a truth tree from A are closed then A is unsatisfiable

    If a branch remains open at the end of a constructionprocess we can use the information in that branch to construct a model for A.

    (The domain of the model will be all the constants in that branch.)

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    Total Universal Instantiation (TUI)

    If ("x)A occurs in a branch and it has been instantiated, and if every formula ($x)B in that branch has been instantiated, and if ("x)A has been instantiated for every constant in the branch, then ("x)A has been totally universally instantiated in that branch.

    Completion Rule

    Continue the tree construction process until

    (i)    All branches close

    (ii)    there is one open branch in which

            (a)    every formula ("x)A in it is TUI for every open branch from it, and

            (b)    no other formulae are available for construction rules