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Propositional truth maintenance systems: Classification and complexity analysis

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Abstract

Truth maintenance (TM) has been an active area of artificial intelligence (AI) research in recent years. In particular, truth maintenance systems (TMSs) in many variant types have become popular mechanisms for implementing nonmonotonic inference systems. Knowledge about the computational foundations of a TMS is indispensable for their use. We present a classification of computational complexity of tasks performed by basic existing TMS types. Our results include the proof ∑ p2 -completeness of the clause maintenance system's computation task. This is the first problem in AI proved to be ∑ p2 -complete. It is likely to provide a basis for proving ∑ p2 -completeness of other problems in logic and AI. As part of the proof, we prove the ∑ p2 -completeness of the generalized node deletion problem, one of the first natural graph problems to be complete for any one of the classes ∑ p i , forp>1. We also prove the polynomial equivalence of Boolean Constraint Propagation-based (logic-based) approaches (LTMSs) and justification-based approaches (JTMSs) to TM, and exhibit efficient algorithms for transforming an LTMS into a JTMS and vice versa.

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  1. SRI International, 333 Ravenswood Ave., 94025, Menlo Park, CA, USA

    Vladislav Rutenburg

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  1. Vladislav Rutenburg
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Rutenburg, V. Propositional truth maintenance systems: Classification and complexity analysis. Ann Math Artif Intell 10, 207–231 (1994). https://doi.org/10.1007/BF01530952

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