ALCLM: A Description Logic over Lattice with Concept Modifiers

We extend the description logic ALC to the description logic over lattice with concept modifiers ALC
_LM
. We define the syntax, semantics for ALC
_LM
and present a tableau decision procedure for the ABox consistency problem. Our logic ALC
_LM
is able to handle vagueness on primitive concepts, primitive concepts modified by stressers or depressers, complex concepts, as well as concept assertions and role assertions of an ontology.