We address the identification of propositional theories for which entailment is tractable, so that every query about logical consequences of the theory can be answered in polynomial time. We map tractable satisfiability classes to tractable entailment classes, including hierarchies of tractable problems; and show that some initially promising conditions for tractability of entailment, proposed by Esghi [13] and del Val [10], surprisingly only identify a subset of renamable Horn. We then consider a potential application of tractable entailment, through a reduction due to Esghi [13] of certain abduction problems to a sequence of entailment problems. Besides clarifying the range of applicability of Esghi's results from the semantic point of view, we show that the reduction can almost trivially fail to be in any of the basic tractable classes discussed in the first part of the paper. We leave open the question of how to more broadly identify tractable entailment classes, as our examples ...

In this thesis we have developed novel methods for analyzing biological data, the primary sequences of the DNA and proteins, the microarray based gene expression data, and other functional genomics data. The main contribution is the development of the pattern discovery algorithm SPEXS, accompanied by several practical applications for analyzing real biological problems. For performing these biological studies that integrate different types of biological data we have developed a comprehensive web-based biological data analysis environment Expression Profiler (http://ep.ebi.ac.uk/)...