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Fusion of Symbolic Knowledge and Uncertain Information in Robotics
 International Journal of Intelligent Systems
, 2001
"... The interpretation of data coming from the real world may require different and often complementary uncertainty models: some are better described by possibility theory, others are intrinsically probabilistic. A logic for belief functions is introduced to axiomatize both semantics as special cases. A ..."
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The interpretation of data coming from the real world may require different and often complementary uncertainty models: some are better described by possibility theory, others are intrinsically probabilistic. A logic for belief functions is introduced to axiomatize both semantics as special cases. As it properly extends classical logic, it also allows the fusion of data with different semantics and symbolic knowledge. The approach has been applied to the problem of mobile robot localization. For each place in the environment, a set of logical propositions allows the system to calculate the belief of the robot's presence as a function of the partial evidences provided by the individual sensors.
A Categorical Approach to Data Fusion
"... Abstract Using suitable topoi of presheaves, a categorical definition of measure is given. When the general definition is specialized to particular categories made of sets of possibility, probability or imprecise probability measures, the internal language of the corresponding topos gives a valid a ..."
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Abstract Using suitable topoi of presheaves, a categorical definition of measure is given. When the general definition is specialized to particular categories made of sets of possibility, probability or imprecise probability measures, the internal language of the corresponding topos gives a valid and complete proof system for the corresponding semantics. An application of this method to data fusion in mobile robotics is presented.
Fuzzy control and coherent functions
"... A fuzzy controller can be seen as an algorithm that, given a fuzzy set (input) and a set of linguistic rules, computes the degree of possibility of every control value. Using a valid and complete proof system for possibilistic logic, we prove that fuzzy controllers enjoy the following property: ever ..."
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A fuzzy controller can be seen as an algorithm that, given a fuzzy set (input) and a set of linguistic rules, computes the degree of possibility of every control value. Using a valid and complete proof system for possibilistic logic, we prove that fuzzy controllers enjoy the following property: every possibility measure that satisfies the degrees of possibility of input and linguistic rules also satisfies, for every control value, the degree of possibility computed by the fuzzy controller. We call such a property coherence between input, task description and output. We give a general definition of coherent function and we show that coherent functions form a class of functions that properly contains fuzzy controllers. Moreover, we present an application of coherent functions to a task different from control, namely localization in mobile robotics. 1