No full-text available
To read the full-text of this research,
you can request a copy directly from the author.
Transformation of Guarded Horn Clauses for Model Building
Abstract
. The guarded fragment of first order logic has been defined in [ABN96]. It is interesting due to the fact that it is decidable and several modal logics can be translated into it. Guarded clauses, defined by de Nivelle in [Niv98], are a generalization of guarded formulas in clausal form. In [Niv98], it is shown that the class of guarded clause sets is decidable by saturation under ordered resolution. By now, no method exists that allows to build models for satisfiable sets of guarded clauses automatically. Such a method should be useful to build models for formulas of modal logics that can be translated into the guarded fragment, thus providing the same advantages to those logics as model building for first order logic has (see [Pel97] and references in it). In this work, we deal with the problem of model building for satisfiable sets of guarded Horn clauses. We define the following notion: a guarded Horn clause is primitive iff it is positive and ground (in this case, it contains on...
The guarded fragment of first order logic, defined in [1], has attracted much attention recently due to the fact that it is decidable and several interesting modal logics can be
translated into it. Guarded clauses, defined by de Nivelle in [7], are a generalization of guarded formulas in clausal form. In [7], it is shown that the class of guarded clause sets is decidable by saturation under ordered resolution.
In this work, we deal with guarded clauses that are Horn clauses. We introduce the notion of primitive guarded Horn clause: A guarded Horn clause is primitive iff it is either ground and its body is empty, or it contains exactly
one body literal which is flat and linear, and its head literal contains a non-ground functional term. Then, we show that
every satisfiable and finite set of guarded Horn clauses S can be transformed into a finite set of primitive guarded Horn clauses S′ such that the least Herbrand models of S and S′ coincide on predicate symbols that occur in S.
This transformation is done in the following way: first, de Nivelle’s saturation procedure is applied on the given set S, and certain clauses are extracted form the resulting set. Then, a resolution based technique that introduces new predicate
symbols is used in order to obtain the set S′. Our motivation for the presented method is automated model building.
ResearchGate has not been able to resolve any references for this publication.