Solving Flexible Planning Problems In Fuzzy Description Logic ALC～*

The representation of uncertainty and imprecision has received a considerableattention in the Artificial Intelligence community in an attempt to extendexisting knowledge representation systems to deal with the imperfect natureof real world information (which is likely the rule rather than an exception).An impressive work has been carried out in the last decades, resulting in anumber of concepts being investigated, a number of problems beingidentified and a number of solutions being developed..For most knowledge representation formalisms, First-Order Logic (FOL)has been the basis: its basic units {individuals, their properties, and therelationship between them }naturally capture the way in which people encodetheir knowledge. Unfortunately, it is severely limited both (i) by its ability torepresent our uncertainty about the world due to lack of knowledge about thereal world a fact can only estimated to be true to e.g. a probability degree;and (ii) by its ability to represent inherently imprecise knowledge indeed,there are concepts, like tall, for which no exact definition exists and, thus, afact like"175cm is tall", rather being true or false, has a truth-value inbetween true and false.In the last decade a substantial amount of work has been carried out in thecontext of Description Logics (DLs). DLs are a logical reconstruction of theso-called frame-based knowledge representation languages, with the aim ofproviding a simple well-established Tarski-style declarative semantics tocapture the meaning of the most popular features of structured representationof knowledge. A main point is that DLs are considered as to be attractivelogics in knowledge based applications as they are a good compromisebetween expressive power and computational complexity.Experience in using DLs in applications has also shown that in manycases we would like to extend the representational and reasoning capabilitiesof them. In particular, the use of DLs in the context of MultimediaInformation Retrieval (MIR) points out the necessity of extending DLs withcapabilities which allow the treatment of the inherent imprecision inmultimedia object representation and retrieval In fact, classical DLs areinsufficient for describing real multimedia retrieval situations, as the retrievalis usually not only a yes-no question: (i) there presentations of multimediaobjects' content and queries which the system (and the logic) have access toare inherently imperfect;and (ii) the relevance of a multimedia object to aquery can thus be established only up to a limited degree. Because of this, weneed a logic in which, rather than deciding tout court whether a multimediaobject satisfies a query or not, we are able to rank the retrieved objectsaccording to how strongly the system believesin their relevance to a queryDescription logics have been applied to several areas of planning,including plan analysis, plan generation, plan recognition, and planevaluation and critiquing. The applications range from military planning totelephony systems, to mobile robot control. Subsumption reasoning andclassification support sophisticated reasoning about general types of actionsand plans than other planning research. In comparison with other planningresearch, these systems support more sophisticated reasoning about generaltypes of actions and plans through subsumption reasoning and classification.Another advantage is that their plan representations are integrated with thedescription logic representations of the objects in the domain, in comparisonwith the more impoverished representations used in other planning research.Our contributions lie in:(1) We presented a fuzzy extension of ALC*, combining Zadeh's fuzzy logicwith an expressive DL. In particular, concepts and roles become fuzzy, thus,reasoning about imprecise concepts is supported.(2) We defined the syntax and semantics of fuzzy ALC*, described itsproperties and presented a constraint propagation calculus for reasoning in it.(3) We encoded Flexible Planning problems within the framework of fuzzyALC*, and gave a algorithm for reasoning about actions and plans.