A theorem prover for lukaszewicz open default theory

Abstract

We present here a correct and complete theorem prover for a certain class of formulas in Lukaszewicz' default logic. Whereas many papers are concerned by calculus of extensions for some default logic, we have developed a theorem prover, that means a computation method to check whether a given formula belongs to some extension of a default theory. This theorem prover works in Lukaszewicz' default logic, which ensures that an extension always exists. More precisely, we define a class of formulas called range-restricted Horn default logic. The restriction to Horn logic enables to use SLD-resolution to build proofs. Moreover range restriction, the constraint on variables occurring in the formulas, enables to deal with open defaults by using the unification mechanism. This point is quite original since open defaults are usually replaced by a set of instanciated defaults. Another point is the fact that computing a proof (in a backward chaining way), instead of building an extension (in a forward chaining way or by eliminating conflicts between defaults), allows us to hope a better efficiency in presence of open defaults.