Haneclou, P. (1987). A Formal Approach to Reason-Maintenance based on Abstract Domains. Technical Report LiTH-IDA-R-87-07, Department of Computer and Information Science, Linköping University, Sweden. (bibtex),
Abstract: Recently the need for a more formal treatment of reason-maintenance has become obvious. Current systems are often ad hoc and most of them only apply to toy-world problems. This paper presents an approach that gives a strict formalization of reason-maintenance. Our approach is similar to the approach taken in denotational semantics (Scott domains).A strict formalization gives one a firm ground to stand on when designing a reason-maintenance system, while also giving the means to determine properties about the system without actually having to build it first.Our abstract domain is a lattice of information states called valuations. valuations are mappings from formulae to truth-values. In order to treat incomplete and inconsistent information we assume an extended set of truth-values. Besides true and false we have the truth-values undefined, meaning lack of information and contradiction, meaning inconsistent information. Sets of inference rules are represented as relations over the set of valuations. The work of a reason-maintenance system is then characterized in terms of operations on the set of valuations.
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