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Extending Horn clause theories by reflection principles.pdf

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Extending Horn clause theories by reflection principles

UPMAIL Technical Report No. 9520 January, 1995 Extending Horn Clause Theoriesby Re ection PrinciplesStefania Costantini, Pierangelo DellAcquaand Gaetano A. LanzaroneUppsala UniversityComputing Science DepartmentBox 311, S-751 05 Uppsala, SwedenPhone: +481818 25 00Fax: +461851 19 25AbstractIn this paper, we introduce logical re ection as a principled way toempower the representation and reasoning capabilities of logic pro-gramming systems. In particular, re ection principles take the role ofaxiom schemata of a particular form that, once added to a given logicprogram (the basic theory, or the initial axioms), enlarge the set ofconsequences sanctioned by those initial axioms. The main advantageof this approach is that it is much easier to write a basic theory andthen to augment it with condensed axiom schemata, than it is to writea corresponding large (or even in nite) set of axioms in the rst place.Moreover, the well-established semantic properties of Horn clauses,carry over to Horn clauses with re ection. In fact, the semantics ofRe ective SLD Resolution and the semantics of the Re ective LeastHerbrand Model are obtained by making slight variations to, respec-tively, the procedural and the declarative semantics classically de nedfor Horn clauses. We present a complete formalization of this conceptof re ection, that should constitute a simple way of understanding re- ective programs; and a description of how re ection allows one totreat uniformly di erent application areas. To support this claim, thefollowing three case studies will be discussed: metalevel reasoning; rea-soning with multiple communicating theories (agents); and analogicalreasoning. For each of these areas, the choice of a suitable re ectionprinciple is shown, which tries to capture the speci city of the problemdomain.Dipartimento di Scienze dellInformazione, Universita degli Studi di Milano 1 IntroductionLogic programming languages have proved to be powerful means for knowl-edge representatio

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