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Inconsistency Robustness in Logic ProgramsInconsistency robustness is â€œinformation system performance in the face of continually pervasive inconsistencies.â€ Inconsistency robustness is both an observed phenomenon and a desired feature: This paper explores the role of Inconsistency Robustness in the history and theory of Logic Programs. Inconsistency Robustness has been a continually recurring issue in Logic Programs from the beginning including Church's system developed in the early 1930s based on partial functions (defined in the lambda calculus) that he thought would allow development of a general logic without the kind of paradoxes that had plagued earlier efforts by Frege, Russell, etc. Unfortunately, Church's system was quickly shown to be inconsistent because: [Kowalski 1988] advocated a bold thesis: â€œLooking back on our early discoveries, I value most the discovery that computation could be subsumed by deduction.â€ However, mathematical logic cannot always infer computational steps because computational systems make use of arbitration for determining which message is processed next by a recipient that is sent multiple messages concurrently. Since reception orders are in general indeterminate, they cannot be inferred from prior information by mathematical logic alone. Therefore mathematical logic alone cannot in general implement computation. Logic Programs (like Functional Programs) are useful idioms even though they are not universal. For example Logic Programs can provide useful principles and methods for systems which are quasicommutative and quasimonotonic even though the systems themselves cannot be implemented using Logic Programs. According to [Feferman 2008]:"So far as I know, it has not been determined whether such [inconsistency robust] logics account for 'sustained ordinary reasoning', not only in everyday discourse but also in mathematics and the sciences." Direct Logic is put forward as an improvement over classical logic with respect to Fefermanâ€™s desideratum above using Independent developments by different research groups in the fall of 1972 gave rise to a controversy over Logic Programs that persists to this day in the form of following alternatives: Consequently, Direct Logic is proposed as a foundation for Logic Programs. Going beyond the limitations of programclause syntax, a core subset of Logic Program constructs is presented in this article (using explicit assertions and goals to invoke patterndirected procedures) that are applicable to both mathematical theories and theories of practice. The above examples are intended to be case studies in Inconsistency Robustness in which information is formalized, contradictions are derived using Inconsistency Robust reasoning, and arguments are formalized for and against contradictory propositions. A challenge for the future is to automate the reasoning involved in these case studies. Above abstract is from the full article By Hewitt at 20131127 21:17  LtU Forum  previous forum topic  next forum topic  other blogs  9088 reads

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