Abstract
In order to meet the demands for more expressive and flexible ways to interact with a database, it is often relevant to go beyond what can be formalized in an obvious way in first order logic or its traditional, higher-order or modal extensions. Metalogical programming is proposed as a framework in which new query-answering and update mechanisms can be characterized and implemented.
A model is shown, extending deductive databases by a classification of the clauses in the database, an integration of nonstandard inference rules, and a notion of proof constraints. In this model, we can embed flexibility by transformations of query and subgoals, e.g., using taxonomy rules in the opposite direction for widening an otherwise failed subgoal. In the same model, a variation of counterfactual reasoning can be characterized; it can be implemented efficiently and useful database applications can be shown. Dynamic aspect of databases such as view update and datamining can be seen as cases of abductive and inductive reasoning, which can be characterized in straight-forward ways in terms of metalogical statements involving a reversible metainterpreter.
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Andreasen, T., Christiansen, H. (1997). Nonstandard Database Interaction from Metalogic Programming. In: Andreasen, T., Christiansen, H., Larsen, H.L. (eds) Flexible Query Answering Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6075-3_4
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