Tableaux theorem prover for first order logic
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This is a simple interactive theorem prover for first order logic
using the tableaux method. The "tableau" is a tree depicting a proof
where each node is a sentence; linear branches represent conjunctions
while forks represent disjunctions. At each step one introduces
new nodes by "breaking down" a formula into its logical
consequences. To prove a formula F it is sufficient to show that
~F is unsatisfiable, i.e. that all branches of the tableau lead
to contradictions.
The prover is implemented in Haskell as a CGI that shows the
current proof tree and highlights one focus node
(initially the whole formula). The interface is consists of:
* navigate the proof tree (point and click)
* expand the current node
* apply resolution to the branch with the current node
Closed branches end in a "false" sentence, i.e. have been shown to
be inconsistent/unsatisfiable. To prove the original theorem one must close
all branches.
Pedro Vasconcelos <pbv@dcc.fc.up.pt>, 2009.
Tree "zipper" implementation by Krasimir Angelov & Iavor S. Diatchki, 2008.
References: First Order Logic, R. Smullyan, Dover.
On the web: http://en.wikipedia.org/wiki/Method_of_analytic_tableaux
