Limiting programs for induction in artificial intelligence

Abstract

This thesis examines a novel induction-based frameworkfor logic programming. Limiting programs are logic programs distinguishedby two features, in general they contain an infinite data streamover which induction will be performed, and in general it is not possiblefor a system to know when a solution for any program is correct. Thesefacts are characteristic of some problems involving induction in artificialintelligence, and several problems in knowledge representation andlogic programming have exactly these properties. This thesis presentsa specification language for problems with an inductive nature, limitingprograms, and a resolution based system, limiting resolution, for solvingthese problems. This framework has properties which guaranteethat the system will converge upon a particular answer in the limit.Solutions to problems which have such an inductive property bynature can be implemented using the language, and solved with thesolver. For instance, many classification problems are inductive bynature. Some generalized planning problems also have the inductiveproperty. For a class of generalized planning problems, we show thatidentifying a collection of domains where a plan reaches a goal is equivalentto producing a plan. This thesis gives examples of both.Limiting resolution works by a generate-and-test strategy, creatinga potential solution and iteratively looking for a contradiction with thegrowing stream of data provided. Limiting resolution can be implementedby modifying conventional PROLOG technology. The generateand-test strategy has some inherent inefficiencies. Two improvementshave arisen from this work; the first is a tabling strategy which recordspreviously failed attempts to produce a solution and thereby avoids redundanttest steps. The second is based on the heuristic observationthat for some problems the size of the test step is proportional to thecloseness of the generated potential-solution to the real solution, in asuitable metric. The observation can be used to improve the performanceof limiting resolution.Thus this thesis describes, from theoretical foundations to implementation,a coherent methodology for incorporating induction intoexisting general A.I. programming techniques, along with examples ofhow to perform such tasks