Theorems on pre-fixed points of non-monotonic functions with applications in logic programming and formal grammars

Abstract

We derive two novel theorems regarding pre-fixed points of non-monotonic functions and demonstrate that they have immediate applications in logic programming and formal grammars. In particular, the results of the paper lead to a natural generalization of the model intersection theorem for definite logic programs, to the more general class of normal logic programs. Moreover, the obtained results also offer the first (to our knowledge) model intersection result for Boolean grammars. © 2014 Springer-Verlag.