Handling imperfect temporal relations
Published inJyväskylä studies in computing
PhD Vladimir Ryabov’in väitöskirja tarkastelee epätäydellisen ajallisentiedon esittämistä ja käsittelyä. Tavoitteenaan hänellä oli kehittääepätäydellisille aikarelaatioille sopiva formalismi. Ryabov keskittyytyössään kahteen seikkaan: 1) epätäydellisten aikarelaatioidenesittämiseen ja estimointiin sekä 2) niiden pohjalta tapahtuvaanpäättelyyn. Väitöskirjassa kehitetyssä esitystavassa epätäydellinenaikarelaatio kuvataan numeerisin arvoin. Koska nämä numeeriset arvot eivätuseinkaan ole välittömästi saatavissa, käytetään estimointia tarvittavienarvojen määrittämiseksi. Ryabov’in kuvaamaan päättelymekanismiinkuuluvilla operaatioilla johdetaan tunnettujen epätäydellistenaikarelaatioiden pohjalta uusia arvoltaan aikaisemmin tuntemattomiaepätäydellisiä aikarelaatioita mielenkiintoisten aikaprimitiivien välille.Representation and reasoning about time is important in modeling dynamicaspects of the world. Temporal formalisms are applied in all areas wherethe time course of events plays an important role, for example, intemporal databases, process control, planning, natural languageunderstanding, and in diagnostic systems. Imperfect information surroundsus everywhere - almost all that we know about the real world is not fullycertain, complete, precise, or consistent. In the area of temporalrepresentation and reasoning, we also need to deal with imperfectinformation.In this way, the research problem of this thesis is situated at theconvergence of the topic of temporal representation and reasoning withthat of handling imperfect information. The main problem considered is thedevelopment of formalism for handling imperfect temporal relations. Withinthis research problem we distinguish between two main issues: therepresentation and the estimation of imperfect temporal relations, andreasoning with imperfect relations. An imperfect temporal relation needsto be represented along with the numerical measures of imperfection ofthis relation. The estimation of imperfection suggests how these measurescan be obtained, because they are not readily available in manysituations. The reasoning mechanism defines the operations for reasoningabout imperfect temporal relations. These operations allow us to derivepreviously unknown imperfect temporal relations, taking as operands knownimperfect relations.In this thesis we propose a numerical formalism, based on probabilitytheory, for handling imperfect temporal relations. An imperfect temporalrelation between two primitives (points or intervals) is represented bythe probabilities of the basic relations (“<”, “=”, and “>” for points,and thirteen Allen’s relations for intervals) between these primitives.These probability values are calculated by the proposed formulas takinginto account the information about the primitives. We further assume thatthe measurements of the temporal values of two primitives may include somemeasurement error, which needs to be taken into consideration during theestimation. Taking into account the maximum value of this measurementerror, we derive the lower and the upper probabilities of the basicrelations between two primitives. The mechanism for reasoning aboutimperfect relations between temporal points includes four operations:inversion, composition, addition, and negation.In this thesis we also propose two possible application areas for theproposed formalism. These are medical and industrial diagnostics, whichare actually the two sub-areas of the big research field of automateddiagnostics. The main advantage of temporal diagnostics is that itconsiders not only a static set of symptoms, but together with the timethey were monitored, and which allows to have a broader view on thesituation. Moreover, sometimes only considering temporal evolution ofrelations between different symptoms can give us a hint to precisediagnostics.It is almost inconceivable to try to represent clinical data and reasonabout them without a temporal dimension. Monitoring clinical variablesover time often provides information that drives medical decision-making,and in some medical diagnostic applications, temporal information aboutthe occurrence of the symptoms is vital for correct diagnostics. We assumethat there exist a certain number of symptoms (events) that are criticalfor particular diseases that we are able to classify. The core of ourapproach to temporal diagnostics is generation and further use of temporalscenarios of known illnesses. Such scenario is a relational network, wherethe nodes are the symptoms from the set of possible symptoms, and the arcsare the temporal relations between the symptoms. We propose to representthese relations using the formal mechanism proposed in this thesis, i.e.these relations are imperfect temporal relations. A particular course ofillness for a particular patient is formalized using also a relationalnetwork with symptoms and relations between them. When we observed anumber of cases of this particular illness from a number of patients, wecan generate a temporal scenario. At this stage we combine the networksfor the illness into the one scenario.Temporal scenarios for known illnesses are stored in a database and can beaccessed when we try to put the diagnosis. In this situation, we cancompare a relational network, describing the particular course of illness,with known temporal scenarios using the mechanism proposed in this thesis.To perform this comparison we use original measures of distance betweendifferent imperfect relations, and between network and scenario. In thisway, we are able to provide a therapist with potential diagnoses (ifappropriate) and their probabilities.In industrial, as well as in medical, diagnostics we use the approach ofmodel-based diagnosis. The key idea of this approach is that we explicitlyrepresent the knowledge about the device monitored, its structure, andoperational behavior as a model. The diagnostics itself is organized as aninference process based on this model and the observed behavior. Ingeneral, the mechanism for industrial temporal diagnostics usinggeneration and recognition of uncertain temporal scenarios is similar tothe one already discussed regarding medical diagnostics. The conceptualschemas for our approach to industrial temporal diagnostics are proposedin the thesis.The main contribution of this work is a new formal technique for therepresentation of, estimation of, and reasoning with imperfect temporalrelations. The presented work has several limitations. The study is mainlytheoretical and we concentrated on the development of a formal approach tohandle imperfect temporal relations. The approach is limited to the use ofthe discrete time model. In the thesis we have considered only two typesof imperfection within temporal relations, that is, uncertainty andinconsistency. The proposed formalism is also limited to deal with thesetwo types of imperfection.We think that the proposed approach can be extended in the future to dealwith the continuous time model. Extending the formalism for dealing withimprecision, incompleteness, and ignorance might also be an interestingtopic. It is also planned to investigate further the application of themechanism in industrial temporal diagnostics. ...
PublisherUniversity of Jyväskylä
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