  Biclustering is a powerful approach to search for patterns in data, as it can
be driven by a function that measures the quality of diverse types of patterns
of interest. However, due to its computational complexity, the exploration of
the search space is usually guided by an algorithmic strategy, sometimes
introducing random factors that simplify the computational cost (e.g. greedy
search or evolutionary computation).
  Shifting patterns are specially interesting as they account constant
fluctuations in data, i.e. they capture situations in which all the values in
the pattern move up or down for one dimension maintaining the range amplitude
for all the dimensions. This behaviour is very common in nature, e.g. in the
analysis of gene expression data, where a subset of genes might go up or down
for a subset of patients or experimental conditions, identifying functionally
coherent categories.
  Boolean reasoning was recently revealed as an appropriate methodology to
address the search for constant biclusters. In this work, this direction is
extended to search for more general biclusters that include shifting patterns.
The mathematical foundations are described in order to associate Boolean
concepts with shifting patterns, and the methodology is presented to show that
the induction of shifting patterns by means of Boolean reasoning is due to the
ability of finding all inclusion--maximal {\delta}-shifting patterns.
  Experiments with a real dataset show the potential of our approach at finding
biclusters with {\delta}-shifting patterns, which have been evaluated with the
mean squared residue (MSR), providing an excellent performance at finding
results very close to zero.
