Information axiom example

A design that meets the information axiom is called a robust design (see Technique 38) because it maximizes the probability that it will meet its specihcations (process variables, or PVs) on an ongoing basis. For example, a process variable like tensile strength or data-entry errors can function as intended along a spectrum from zero to absolute perfection but in reality it always functions somewhere in between the two extremes. 

C[ and Cj are the concepts of nodes i and j in the two schemas, as generated in the first step and C is the conjunction of all the relations that hold between concepts of labels mentioned in C, and Cj (this includes all nodes on the path to nodes i and j). This is done by using a SAT solver to test unsatisfiability. It is worth noting that the unsatisfiability problem is known to be CO-NP, yet modern SAT solvers have shown very good performance in solving such problems. To reason about relations between concepts of nodes, a set of premises (axioms) is built as a conjunction of the concepts of labels computed in the third step. For example, R. Card Info, type will be defined to be subsumed by S. Card Information while an equivalence semantic relationship is defined between R. Card Info, type and S.Cardlnformation.type. 

This introductory chapter describes the scope of the book and gives a brief summary of the history, advantages, limitations, and some common-sense axioms of HPLC. Major separation modes are discussed and illustrated with examples. Information resources on HPLC are also listed. 

But, on the other hand, one could aim at incomplete specifications and add some stronger form of axioms to the examples so as to overcome the weaknesses of specifications by examples only. We call properties [Hener and Deville 92, 93ab] such a strong form of axioms, and only require them to be written in (some subset of) logic. Indeed, until Part III, we do not restrict ourselves to any syntax or required computational content of properties. We only assume that properties are an incomplete source of information. Actually, in case properties were a complete source of information, most of the results hereafter would remain valid, but not always be relevant. 

In terms of related work, specifications by examples are surveyed in Section 3.1. Also, the notion of specifying property can be traced back to the notion of specifying axiom, and specifications by axioms are surveyed in Section 2.1. In this section, we only survey research on extending example-based specifications by another incomplete information source. 

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