Proceedings of the Workshop on the lambda-Prolog Programming Language

The expressiveness of logic programs can be greatly increased over first-order Horn clauses through a stronger emphasis on logical connectives and by admitting various forms of higher-order quantification. The logic of hereditary Harrop formulas and the notion of uniform proof have been developed to provide a foundation for more expressive logic programming languages. The λ-Prolog language is actively being developed on top of these foundational considerations. The rich logical foundations of λ-Prolog provides it with declarative approaches to modular programming, hypothetical reasoning, higher-order programming, polymorphic typing, and meta-programming. These aspects of λ-Prolog have made it valuable as a higher-level language for the specification and implementation of programs in numerous areas, including natural language, automated reasoning, program transformation, and databases

Indefinite Reasoning with Definite Rules

In this paper we present a novel explanation of the source of indefinite information in common sense reasoning: Indefinite information arises from reports about the world expressed in terms of concepts that have been defined using only definite rules. Adopting this point of view, we show that first-order logic is insufficiently expressive to handle important examples of common sense reasoning. As a remedy, we propose the use of circumscribed definite rules, and we then investigate the proof theory of this more expressive framework. We consider two approaches: First, prototypical proofs, a special type of proof by induction, which yields a sound proof theory. Second, we describe cases in which there exists a decision procedure for answering queries, a particularly significant result because it shows that it is possible to have decidable query processing in circumscribed theories that are not equivalent to any first order theory.