Contextual correspondences

Contextual correspondences improve on noncontextual correspondences in two main aspects. First, it allows the specification of alternative correspondences for the same attribute, under different conditions. Second, its refined definition of a correspondence allows it to connect attributes via correspondences in cases where a common correspondence is too weak to be considered valid. 

The way contextual correspondences are defined, they are deterministic, not allowing a probabilistic interpretation of a correspondence. Therefore, contextual correspondences are meant to resolve an issue of uncertainty by finding a more refined, yet deterministic, correspondence. It is worth noting, however, that an introduction of stochastic analysis already exists in the form of statistical significance, which can be extended to handle probabilistic mappings as well. 

With regard to the standardized multiaxial assessment, of the score of schemas that have been published (and reviewed by Mezzich, 1979), the ones that are currently most frequently seen are those included in the CIE-10 (World Health Organization, 1997) and the DSM-IV (APA, 1994). Although these systems vary in the number of axes they have, their contents do largely match up axis I (Clinical diagnoses) of the CIE-10 covers the contents of the first three axes of the DSM-IV axis II of the CIE-10 assesses the area of disabilities divided into four aspects (personal care, occupational, with the family, and social in general), and corresponds to axis V of the DSM-IV finally, axis III (Contextual factors) of the CIE-10 essentially matches axis IV of the DSM-IV. 

Esteve28 analyses the correspondence between biomedical research and the pharmaceutical industry, contextual changes that affect this relationship, the present situation of pharmaceutical research in Spain, and measures that the government could take to promote it. 

Attribute correspondences may hold under certain instance conditions. With contextual attribute correspondences, selection conditions are associated with attribute correspondences. Therefore, a contextual attribute correspondence is a triplet of the form (Ai,Aj,c), where A, and Aj are attributes and c is a condition whose structure is defined in Sect. 3.1. 

Example 2. With contextual attribute correspondences, we could state that R.Card-Info.cardNum is the same as S.HotelCardlnfo.clientNum if R. Card Info, type is assigned with the value RoomsRUs. For all other type values, R.Card-Info.cardNum is the same as S.Cardlnfo.cardNum. These contextual attribute correspondences are given as follows. 

Contextual attribute correspondences are specified in terms of a condition on the value assignments of attributes. A k-context of an attribute correspondence is a condition that involves k database attributes. For k = 0, a contextual attribute correspondence becomes a common attribute correspondence. For k = 1, the condition is simple, of the form a = v, where a is an attribute and v is a constant in a s domain. For example, R.Cardlnfo.type= RoomsRUs . Disjunctive, conjunctive, and general / -contexts generalize simple conditions in the usual way. For example, simple disjunctive k-context for k = 1 is a condition of the form a e (iq, v2, , v. ... 

Contextual attribute correspondences can be modeled with similarity matrices. An entry in the similarity matrix Mjj is extended to be a tuple v,c), where v e [0,1] is a similarity value and c is a context as defined above. This modeling allows a smooth extension of contextual attribute correspondences to matcher ensembles [Domshlak et al. 2007 He and Chang 2005], in which matchers are combined to improve the quality of the outcome of the matching process. For example, Do et al. [2002] and Domshlak et al. [2007] proposed several ways to combine similarity matrices, generated by different matchers, into a single matrix. Such combination, which was based solely on aggregating similarity scores, can be extended... 

The similarity matrix inherently captures attribute correspondence information while r can handle schema level constraints. For example, using only the similarity matrix, one can assume that the contextual attribute correspondence... 

A few challenges arise when designing an algorithm for finding contextual attribute correspondences. First, one may risk overfitting the correspondences to the training data. For example, it is possible that one could find a contextual attribute correspondence stating... 

It has been proposed in Bohannon et al. [2006] that A-contexts with k > 1 will yield more trustworthy contextual attribute correspondences. The algorithm first determines an initial list of 1-context conditions. Then, it creates and evaluates disjunctive conditions that are generated from the original 1-context conditions. The generation of conditions is carried out using view selection. Views are chosen... 

A major performance concern is the determination of candidate attributes for contextual attribute correspondences. The approach above is based on context identification using categorical attributes. Clearly, with more categorical attributes, an exhaustive search of all categorical values becomes more expensive. However, even with a small set of categorical values, the attribute candidates for correspondences depends on the number of attributes in the target database. 

This chapter introduces three recent advances to the state-of-the-art, extending the abilities of attribute correspondences. Contextual attribute correspondences associate selection conditions with attribute correspondences. Semantic matching extends attribute correspondences to be specified in terms of ontological relationship. Finally, probabilistic attribute correspondences extend attribute correspondences by generating multiple possible models, modeling uncertainty about which one is correct by using probability theory. 

The first observation is that top-AT schema matchings play a pivotal role in identifying attribute correspondences. We have shown that top-AT matchings can serve in identifying both good candidates for contextual attribute correspondences and probabilistic attribute correspondences. In this research direction, there are still many open questions, first of which is the ability to identify top-AT matchings in polynomial time. 

Contextual and by-tuple probabilistic attribute correspondences seem to be complementary. A by-tuple probabilistic attribute correspondence represents a situation in which there is uncertainty as to whether a given tuple should be interpreted using one correspondence or the other. Contextual attribute correspondences models exactly such knowledge. Therefore, By-tuple probabilistic attribute correspondence is needed whenever no information regarding the contextual attribute correspondence is available. Whenever contextual attribute correspondence is gathered automatically, using statistical methods as described in Sect. 3.2, another layer of uncertainty is added to the modeling. Therefore, contextual attribute correspondences should also be extended to provide probabilistic alternative versions. 

If identification of contextualized kinds is all that we possibly get, we have to deny property monism (non-contextualized high-level kinds are not physical) or, as is sometimes argued, we have to accept that predicates and terms allegedly picking out high-level kinds do not pick out kinds at all (this is Kim s strategy (e.g. Kim 2002)) - again an idea that can be nicely modeled within the present framework. On this latter view, we do not get identification because the property structures do not determine any entity at all. No property corresponds to the property structure -hence, we do not get identification. All we get is the property structure itself. Not so for the contextualized descriptions. When presented under a contextualized description, a kind x reduced to x when presented under a description that is more transparent to the properties in virtue of which it behaves the way it does, or is what it is. Directionality and diversity, as cashed out above, are, thus, constitutive for the contextualized kind approach. 

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