By Serge Abiteboul, Victor Vianu (auth.), Val Tannen, Limsoon Wong, Leonid Libkin, Wenfei Fan, Wang-Chiew Tan, Michael Fourman (eds.)

This Festschrift quantity, released in honour of Peter Buneman, comprises contributions written through a few of his colleagues, former scholars, and associates. In occasion of his unusual occupation a colloquium used to be held in Edinburgh, Scotland, 27-29 October, 2013. The articles awarded herein belong to a couple of the numerous parts of Peter's study interests.

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**Example text**

Rk ) be an instance for the schema Σ = {A1 , . . , Ak }. Deﬁne R := ki=1 Ri . Then a universal relation for the instance exists if and only if R|Ai = Ri , i = 1, . . , k, and in this case R is the largest relation in R( i Ai ) satisfying the gluing condition. Proof. We note that, if a relation S satisﬁes S|Ai = Ri , i = 1, . . , k, then S ⊆ k i=1 Ri by the adjoint property of the natural join. Moreover, since projection is monotone, in this case Ri ⊆ S|Ai ⊆ ( ki=1 Ri )|Ai ⊆ Ri . There are further categorical aspects of relational databases which it might prove interesting to pursue.

RDF, or XML, or JSON). , [8]). In addition to giving examples of extraction rules, we also include a discussion of the need for automatic or semi-automatic extraction of structured records that is based on data examples. Such technology, while non-trivial, would be particularly useful when the developer is in the exploration phase and does not know enough about the data and its peculiarities. Based on a few examples that are representative of the type of entities that the developer is interested to extract, the system must ﬁrst be able to derive all the other entries that are “similar” to the given examples.

We also note the rˆole played by provenance semirings in database theory [14,9,11]. We ﬁx a semiring R. Given a set X, the support of a function v : X → R is the set of x ∈ X such that v(x) = 0. We write supp(v) for the support of v. We shall write VR (X) for the set of functions v : X → R of ﬁnite support. We shall write DR (X) for the subset of VR (X) of those functions d : X → R such that d(x) = 1. x∈X Note that the ﬁnite support condition ensures that this sum is well-deﬁned. We shall refer to elements of VR (X) as R-valuations on X, and of DR (X) as R-distributions.