Regular Search Spaces as a Foundation of Logic Programming

First, we aim to provide a proof-theoretic reconstruction of logic programming, both for definite and for normal programs. This leads us to a better understanding of negation-as-failure (NF) [5] and of other proof-theoretically well-founded extensions of Prolog. Our ambition is to show that almost everything in the vulgate of logic programming can be carried out in a style close to natural deduction, and in particular in a restricted fragment of minimal logic. Secondly, we embark on a generalization and abstraction of the nice properties of SLD-resolution. The outcome is our formulation of the concept of regular search space. Here many logics can be expressed and provided they can be shown to be regular, they are then guaranteed to enjoy an analogue of the very features that make Prolog a feasible and successful implementation of logic. This can also serve as a basis of a fairly general new logic programming language, similarly to what is done in [11].

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