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Classical systems of mereology identify a maximuml set of jointly exhaustive and pairwise disjoint (RCC5) relations. The amount of information that is carried by each member of this set of (crisp) relations is determined by the number of bits of information that are required to distinguish all the members of the set. It is postulated in this paper, that vague mereological relations are limited in the amount of information they can carry. That is, if a crisp mereological relation can carry N bits of information, then a vague mereological relation can carry only 1 ⩽ n < N bits. The aim of this paper is it to explore these ideas in the context of various systems of vague mereological relations. The resulting formalism is non-classical in the sense of quantum information theory.

Vague predicates such as heap, tall, bald, near to, nicer than, etc., are characterized by their Sorites susceptibility and the existence of borderline cases. In attempting to develop a general theory, diverse vague predicates are often analyzed in rather broad natural language settings. Because this has proven to be rather difficult, the phenomenon of vagueness is studied here in a narrower and strictly formalized setting: Vague size predicates such as "roughly the same size" and "negligible in size with respect to" are studied within the framework of a formalized theory of parthood extended by size predicates. Such a restricted axiomatic framework has a number of advantages: (i) it is easier to analyze logical and semantical aspects of vagueness; (ii) it is possible to study the interrelations between precise quantitative facts and the interpretation of vague and qualitative predicates in a restricted class of models; (iii) it is possible to precisely analyze the logical properties of vague and qualitative size predicates which are fundamental to formalized deductive reasoning. All three aspects are critical for the representation and reasoning about many vague predicates as they are used in many sciences and in medicine.

Biomedical Ontologies integrate diverse biomedical data and enable intelligent data-mining and help translate basic research into useful clinical knowledge. We present the RNA Ontology (RNAO), an ontology for integrating diverse RNA data, including RNA sequences and sequence alignments, three-dimensional structures, and biochemical and functional data. For example, individual atomic resolution RNA structures have broader significance as representatives of classes of homologous molecules, which can differ significantly in sequence while sharing core structural features and common roles or functions. Thus, structural data gain value by being linked to homologous sequences in genomic data and databases of sequence alignments. Likewise, the value of genomic data is enhanced by annotation of shared structural features, especially when these can be linked to specific functions. Moreover, the significance of biochemical, functional and mutational analyses of RNA molecules are most fully understood when linked to molecular structures and phylogenies. To achieve these goals, RNAO provides logically rigorous definitions of the components of RNA primary, secondary and tertiary structure and the relations between these entities. RNAO is being developed to comply with the developing standards of the Open Biomedical Ontologies (OBO) Consortium. The RNAO can be accessed at http://code.google.com/p/rnao/.