Recycling Computed Answers in Rewrite Systems for Abduction

In rule-based systems, goal-oriented computations correspond naturally to the possible ways that an observation may be explained. In some applications, we need to compute explanations for a series of observations with the same domain. The question whether previously computed answers can be recycled arises. A yes answer could result in substantial savings of repeated computations. For systems based on classic logic, the answer is YES. For nonmonotonic systems however, one tends to believe that the answer should be NO, since recycling is a form of adding information. In this paper, we show that computed answers can always be recycled, in a nontrivial way, for the class of rewrite procedures that we proposed earlier for logic programs with negation. We present some experimental results on an encoding of the logistics domain.Comment: 20 pages. Full version of our IJCAI-03 pape

Communicating answer set programs

Answer set programming i s a form of declarative programming that has proven very successful in succinctly formulating and solving complex problems. Although mechanisms for representing and reasoning with the combined answer set programs of multiple agents have already been proposed, the actual gain in expressivity when adding communication has not been thoroughly studied. We show that allowing simple programs to talk to each other results in the same expressivity as adding negation-as-failure. Furthermore, we show that the ability to focus on one program in a network of simple programs results in the same expressivity as adding disjunction in the head of the rules

Classical Mathematics for a Constructive World

Interactive theorem provers based on dependent type theory have the flexibility to support both constructive and classical reasoning. Constructive reasoning is supported natively by dependent type theory and classical reasoning is typically supported by adding additional non-constructive axioms. However, there is another perspective that views constructive logic as an extension of classical logic. This paper will illustrate how classical reasoning can be supported in a practical manner inside dependent type theory without additional axioms. We will see several examples of how classical results can be applied to constructive mathematics. Finally, we will see how to extend this perspective from logic to mathematics by representing classical function spaces using a weak value monad.Comment: v2: Final copy for publicatio

Canonical Abstract Syntax Trees

This paper presents Gom, a language for describing abstract syntax trees and generating a Java implementation for those trees. Gom includes features allowing the user to specify and modify the interface of the data structure. These features provide in particular the capability to maintain the internal representation of data in canonical form with respect to a rewrite system. This explicitly guarantees that the client program only manipulates normal forms for this rewrite system, a feature which is only implicitly used in many implementations