Incremental models of updating data bases
This paper introduces a generalization of weak model-theoretic forcing of [Rob71] and [Kei73]. This generalized forcing preserves classic properties of weak model-theoretic forcing, e.g. Generic Set Theorem (Thm. 3.23), Generic Model Theorem (Thm. 3.24, Thm. 4.8), and Henrard's Theorem (Thm. 5.8). It is applied in this paper to investigate a deductive model for updating a deductive data base with incomplete information, whose possible variations are restricted to certain finite sets of atomic or negated atomic first-order sentences. Moreover, the paper introduces the notion of pragmatic truth pertinent to those models, and characterizes it in terms of generalized forcing (Thm. 5.11).
In conclusion, the paper offers (Thm. 8.4) two semantic and two syntactic characterizations of the ∀-fragment of minimal entailment.
Key wordsclosed world assumption deductive data bases machine reasoning minimal entailment model theory of non-monotonic logics model-theoretic forcing non-standard negation pragmatic truth theory of update
AMS classification03C25 03C40 03C52 68G99
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