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of possible schema constraints. However, since they are inferred from data, they
highlight possible schema properties, but do not represent actual schema properties.
An instance constraint may become a schema property when it is validated by
an application domain expert.
Since our aim is to infer unknown constraints from data, we will focus on instances
constraints. We will denote instance constraints with the term constraint in
the remainder of this chapter. For example, a constraint may be inferred by analyzing
the values of the Age attribute. If it always has positive values, we can infer
the (instance) domain constraint Age>0. Instead, by analyzing a mark database,
we may detect a tuple constraint between the values of the attributes Mark and
Honours. If the Honours attribute is true, Mark should take the highest value. Instead,
if Mark does not take the highest value, Honours is false. If all the values of
two attributes are linked by tuple constraints, then there is a functional dependency
between the attributes. A functional dependency states that if in a relation
two rows agree on the value of a set of attributes X, then they also agree on the
value of a set of attributes Y. The dependency is written as X → Y. For example, in
a relation such as Buyers (Name, Address, City, Nation, Age, Product), there is a
functional dependency City → Nation, because for each row the value of the attribute
City identifies the value of the attribute Nation (i.e., a city always belongs
to the same nation).
Unfortunately, real datasets are affected by errors. Errors can be divided into
two categories: syntactic and semantic. Among syntactic errors there are incompleteness
(due to the lack of attribute values), inaccuracy (due to the presence of
errors and outliers), lexical errors, domain format errors and irregularities. Among
semantic errors there are discrepancies, due to a conflict between some attribute
values (i.e. age and date of birth), ambiguities, due to the presence of synonyms,
homonyms or abbreviations, redundancies, due to the presence of duplicate information,
inconsistencies, due to an integrity constraint violation (i.e. the attribute
age must be a value grater than 0) or a functional constraint violation (i.e. if the attribute
married is false, the attribute wife must be null), invalidities, due to the
presence of tuples that do not display anomalies of the classes defined above but
still do not represent valid entities [12].
Public genomic and proteomic databases may be affected by the aforementioned
errors, mainly because they grew some years ago, under the pressing
need of storing the large amount of genetic information available at the time,
without having neither a standard method to collect it, nor a standard format to
represent it. Due to these problems it is difficult to clearly describe the actual relationships
among data. Recently, a significant effort has been devoted to the integration
of distributed heterogeneous databases, where researchers continuously
store their new experimental results. However, the existence of erroneous or poor
data may harmfully affect any further elaboration or application.
Errors can occur in different phases of data production: experiment (unnoticed
experimental setup failure or systematic errors), analysis (misinterpretation of
information), transformation (from one representation into another), propagation