By Paul J. Cohen

This exploration of a infamous mathematical challenge is the paintings of the guy who stumbled on the answer. Written by an award-winning professor at Stanford collage, it employs intuitive factors in addition to precise mathematical proofs in a self-contained treatment. This special textual content and reference is acceptable for college kids and execs. 1966 version. Copyright renewed 1994.

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Additional info for Set Theory and the Continuum Hypothesis (Dover Books on Mathematics)

Example text

Another point for further research is the use of non-deterministic constructs that are more appropriate for deductive databases, like these proposed in [GPZ01]. Apart from its theoretical interest, the transformation algorithm can be viewed as the basis of new evaluation strategies for a class of moded Datalog programs. It would therefore be interesting to carry out a careful performance comparison with related optimization techniques, which would reveal the strong and weak points of each approach.

Let P be a Choice DatalognS program, D a database and I an interpretation of PD . Then, CPD (I) is deﬁned as follows: CPD (I) = {I ∪ {#p(L, e)} | p, L, e ∈ SI } A Transformation Technique for Datalog Programs 39 Some observations can be made about the CPD operator. The ﬁrst one is that CPD preserves the previous computed atoms (it does not reject anything). The next thing is that CPD when applied to an interpretation I, chooses exactly one among all the possible p, L, e triples in SI , and returns the atom #p(L, e).

Rondogiannis, and M. Gergatsoulis The language we will be using in the rest of this paper as the target language of the transformation, is DatalognS extended with choice predicates. Notice that for every predicate symbol p (either IDB or EDB) a predicate #p is associated. Deﬁnition 3. A Choice DatalognS program is a DatalognS program which may contain choice atoms in the bodies of its clauses. An exposition of the formal semantics of Choice DatalognS is given in the Appendix of the paper. 5 The Transformation Algorithm In this section we provide a formal deﬁnition of the transformation algorithm.