A Categorical Approach to Data Fusion

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

[1]  Gai CarSO.  A Logic for Reasoning about Probabilities * , 2004 .

[2]  Lotfi A. Zadeh,et al.  A Theory of Approximate Reasoning , 1979 .

[3]  Paolo Bison,et al.  Sequent calculus and data fusion , 2001, Fuzzy Sets Syst..

[4]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[5]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[6]  P. Walley.  Statistical Reasoning with Imprecise Probabilities , 1990 .

[7]  Benjamin Kuipers,et al.  A Hierarchy of Qualitative Representations for Space , 1998, Spatial Cognition.

[8]  Patrick Lincoln,et al.  Linear logic , 1992, SIGA.

[9]  Paolo Bison,et al.  Fusion of symbolic knowledge and uncertain information in robotics , 2001, Int. J. Intell. Syst..

[10]  Didier Dubois,et al.  The three semantics of fuzzy sets , 1997, Fuzzy Sets Syst..

[11]  Claudio Sossai,et al.  Reasoning with uncertainty and context-dependent languages , 2005, EUSFLAT Conf..

[12]  I. Moerdijk,et al.  Sheaves in geometry and logic: a first introduction to topos theory , 1992 .

[13]  George J. Klir,et al.  Fuzzy sets and fuzzy logic , 1995 .

[14]  Claudio Sossai,et al.  U-Sets as a possibilistic set theory , 2004, Fuzzy Sets Syst..

[15]  Didier Dubois,et al.  Possibility Theory: Qualitative and Quantitative Aspects , 1998 .

[16]  Illah R. Nourbakhsh,et al.  DERVISH - An Office-Navigating Robot , 1995, AI Mag..

[17]  Gaetano Chemello,et al.  Coherent Functions in Autonomous Systems , 2003, J. Multiple Valued Log. Soft Comput..

[18]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

[19]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[20]  C. Sossai.  U − Sets as probabilistic sets , 2003 .

[21]  David Kortenkamp,et al.  Topological Mapping for Mobile Robots Using a Combination of Sonar and Vision Sensing , 1994, AAAI.

[22]  Luca Boldrin,et al.  Local Possibilistic Logic , 1997, J. Appl. Non Class. Logics.

[23]  Enrique H. Ruspini,et al.  On the semantics of fuzzy logic , 1991, Int. J. Approx. Reason..

[24]  Joseph Y. Halpern,et al.  A Logic for Reasoning about Upper Probabilities , 2001, UAI.

[25]  Alessandro Saffiotti,et al.  Integrating Fuzzy Geometric Maps and Topological Maps for Robot Navigation , 1999, IIA/SOCO.