By Jeffrey D. Ullman
Classical database know-how is orientated towards a well-understood category of purposes. lately the sphere has tried to resolve the issues linked to new different types of functions: computer-aided layout, software program engineering, and others that mix the necessity to care for quite a lot of information successfully and the necessity to aid queries in languages which are extra expressive than these present in classical database structures. This e-book makes an attempt to combine the learn of either the hot and the classical kinds of database structures.
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We equip the rules with application conditions (M-conditions over the left- and right-hand graphs), and deﬁne rule application via the standard double-pushout construction . Deﬁnition 4 (Rule; direct derivation). A plain rule r = L ← K → R comprises two inclusions K → L, K → R. We call L, R the left- (resp. right-) hand graph and K the interface. An application condition ac = acL , acR for r consists of two M-conditions over L and R respectively. A rule r = r , ac is a plain rule r and an application condition ac for r .
C1 h1 C2 h2 C3 Fig. 1. A graph property For our convenience, we will express these properties using a nested notation  and avoiding the use of universal quantifiers. Moreover, the conditions that we define below are slightly more general than what may seem to be needed. Instead of defining properties about graphs, nested conditions define properties of graph monomorphisms. Definition 1 (condition, nesting level). Given a finite graph C, a condition over C is defined inductively as follows: – true is a condition over C.
28 L. Lambers and F. Orejas Fig. 5. Tableau for condition c in Example 1 So, the tableau for d with context Node is depicted in Fig. 6. Again, it includes a single branch whose hook is the only positive literal in d. In this case, the leaf of the branch would be ∃(Node → Loop, d ), where d is equivalent to the conjunction of shifting along Node → Loop with the rest of the literals in d. But in this case, because of shifting the negative literal ¬∃(Node → Loop,true) the conjunction d would include the f alse literal: As a consequence, when opening a tableau for d at the next level of nesting, the only branch would include the f alse literal, which would close the single branch.
Principles of Database and Knowledge-Base Systems by Jeffrey D. Ullman