Ontologies describe a conceptualization of a part of the world relevant to some application. What are the units of conceptualizations? Current ontologies often equate concepts with words from natural languages. Words are certainly not the smallest units of conceptualization, neither are the sets of synonyms of WordNet or other linguistically justified units. I suggest to take distinctions as basic units and to construct concepts from them whereas other approaches start with concepts and discover properties that distinguish them. Distinctions separate concepts and produce a taxonomic lattice, which contains the named concepts together with other potential conceptual units. The taxa are organized in a superclass/subclass (better supertaxa/subtaxa) relation and for any two taxa there is always a single least common supertaxon. Algorithms to maintain such a taxonomic structure and methods to combine different taxonomies are shown, using a four valued (relevance) logic as introduced by Belnap . The novel aspect of the method is that distinctions that are only meaningful in the context of other distinctions restrict the lattice of concepts to the meaningful subset.
The approach is restricted to the is_a relation between classes; it relates to Formal Concept Analysis, but replaces the “formal attributes” with (necessary) distinctions and uses a four-valued logic. It stresses the focus of recent ontological studies like DOLCE or WonderWeb on qualities; it is expected that distinctions as introduced here for the is_a hierarchy influence the mereological aspects of an ontology (i.e., the part_of relation) and connect to Gibson's affordances  and contribute to the classification of operations.
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