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Truth functionality and measurebased logics
 Fuzzy Sets, Logics and Reasoning about Knowledge
, 1999
"... We present a truthfunctional semantics for necessityvalued logics, based on the forcing technique. We interpret possibility distributions (which correspond to necessity measures) as informational states, and introduce a suitable language (basically, an extension of classical logic, similar to Pave ..."
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Cited by 5 (4 self)
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We present a truthfunctional semantics for necessityvalued logics, based on the forcing technique. We interpret possibility distributions (which correspond to necessity measures) as informational states, and introduce a suitable language (basically, an extension of classical logic, similar to Pavelka’s language). Then we define the relation of “forcing ” between an informational state and a formula, meaning that the state contains enough information to support the validity of the formula. The subsequent step is the definition of a manyvalued truthfunctional semantics, by simply taking the truth value of a formula to be the set of all informational states that force the truth of the formula. A proof system in sequent calculus form is provided, and validity and completeness theorems are proved. 1
Sequent Calculus and Data Fusion
, 2001
"... We present a formal method for data fusion, based on possibilistic logic. The method has been applied to a realworld problem of noisy sensordata fusion: the position estimation of an autonomous mobile robot navigating in an approximately and partially known office environment using a topological m ..."
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Cited by 4 (4 self)
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We present a formal method for data fusion, based on possibilistic logic. The method has been applied to a realworld problem of noisy sensordata fusion: the position estimation of an autonomous mobile robot navigating in an approximately and partially known office environment using a topological map. Each place in the map is characterized by a set of logical formulae axiomatizing both symbolic knowledge and uncertain information from the sensors. At each time instant during navigation, the necessity for each place is calculated using a function generated by a proof system based on sequent calculus. Several test runs using a real robot have shown the adequacy of the approach in interpreting and disambiguating the information coming from independent perceptual sources, in combination with symbolic knowledge.
Coherent Functions in Autonomous Systems
, 2002
"... INTRODUCTION Advanced sensorimotor devices, like mobile robots, are often referred to as autonomous systems. The expression is used to intentionally remark on the difference between these systems and those of traditional industrial automation. Although no rigorous definition is easily available, a ..."
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INTRODUCTION Advanced sensorimotor devices, like mobile robots, are often referred to as autonomous systems. The expression is used to intentionally remark on the difference between these systems and those of traditional industrial automation. Although no rigorous definition is easily available, a general informal consensus seems to exist on the features that denote autonomy: a system is considered the more autonomous the more reliably it can survive and perform tasks in the real world, without the need for human intervention. 171 ____________________________ *email: claudio.sossai@isib.cnr.it J. of Mult.Valued Logic & Soft Computing., Vol. 9, pp. 171194 2003 Old City Publishing, Inc. Reprints available directly from the publisher Published by license under the OCP Science imprint, Photocopying permitted by license only a member of the Old City Publishing Group In the literature different ideas and techniques have been proposed and investigated to achieve these results, nonethe
A possibilistic approach to sensor fusion in mobile robotics
 In 2nd Euromicro Workshop on Advanced Mobile Robots (Eurobot’97
, 1997
"... We present a formal method, based on the Logic of Possibility, to fuse uncertain senso y information and to produce an estimate of the position of a mobile robot. The robot navigates in an ofice environment, using a topological map, with the assistance of a “slave ” robot acting as a portable local ..."
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Cited by 2 (1 self)
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We present a formal method, based on the Logic of Possibility, to fuse uncertain senso y information and to produce an estimate of the position of a mobile robot. The robot navigates in an ofice environment, using a topological map, with the assistance of a “slave ” robot acting as a portable local landmark. Each relevant place in the map is characterized by a set of logical formulae axiomatizing both “crisp ” knowledge and uncertain information from the sensors. At each time instant during navigation, the necessity degree of each place is calculated using a purely syntactical method based on, sequent calculus. 1
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 Modal Logic for Fusing Partial Belief of Multiple Reasoners
, 1999
"... We present n , a multiagent epistemic logic where each agent can perform uncertain (possibilistic) reasoning. The original feature of this logic is the presence of a distributed belief operator, with the purpose of merging the belief of different agents. Unlike the corresponding operator in the ..."
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We present n , a multiagent epistemic logic where each agent can perform uncertain (possibilistic) reasoning. The original feature of this logic is the presence of a distributed belief operator, with the purpose of merging the belief of different agents. Unlike the corresponding operator in the categorical (nonuncertain) case, our distributed belief operator accumulates support for the same fact coming from different agents. This means that opinions shared by different agents can be combined into a stronger distributed belief. This feature is useful in problems like pooling expert opinions and combining information from multiple unreliable sources. We provide a possible worlds semantics and an axiomatic calculus for our logic, and prove soundness, completeness and decidability results. We hint at some possible applications n in the conclusions.
LogicBased Algorithms for Data Interpretation With Application to Robotics
, 1998
"... We present a formal method, based on possibilistic logic, to fuse uncertain sensory information. The basic concepts underlying the approach are summarized and discussed. The method has been applied to a realworld problem of noisy sensordata fusion: the position estimation of an autonomous mobile r ..."
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We present a formal method, based on possibilistic logic, to fuse uncertain sensory information. The basic concepts underlying the approach are summarized and discussed. The method has been applied to a realworld problem of noisy sensordata fusion: the position estimation of an autonomous mobile robot navigating in an approximately and partially known o#ce environment, using a topological map. Each place in the map is characterized by a set of logical formulae axiomatizing both abstract knowledge and uncertain information from the sensors. At each time instant during navigation, the necessity value for each place is calculated using a purely syntactical method, based on sequent calculus. Several test runs on a real robot have evidenced the adequacy of the approach in interpreting and disambiguating the information coming from independent perceptual sources, in combination with abstract knowledge. Keywords: Reasoning with Uncertainty, Possibilistic Logic, Sequent Calculus, Sensor Fus...
Merging Probability and Possibility for Robot Localization
 In Proceedings of the Workshop on Reasoning with Uncertainty in Robot Navigation (RUR99
, 1999
"... A mobile robot localization system based on sensor fusion is described. Data coming from various sensors can require di#erent and often complementary uncertainty models: some are better described by possibility theory, others are intrinsically probabilistic. A logic for belief functions is int ..."
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A mobile robot localization system based on sensor fusion is described. Data coming from various sensors can require di#erent 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. For each place in a map of the environment, a set of logical rules allows to calculate the belief of the robot's presence, as a function of the partial evidences provided by the individual sensors. Various experimental runs have shown promising results. 1 Introduction The aim of this work is to apply to robotics a logical framework where di#erent uncertainty models, like belief functions, possibilities (i.e. consonant belief functions) and probabilities (i.e. additive belief functions) can be uniformly axiomatized. 1.1 Uncertainty models Although probability theory has a leading position in the description of uncertainty, in th...
Epistemic logics for information fusion
 Proc of the 7th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, LNAI 2711
, 2003
"... Abstract. In this paper, we propose some extensions of epistemic logic for reasoning about information fusion. The fusion operators considered in this paper include majority merging, arbitration, and general merging. Some modalities corresponding to these fusion operators are added to epistemic logi ..."
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Abstract. In this paper, we propose some extensions of epistemic logic for reasoning about information fusion. The fusion operators considered in this paper include majority merging, arbitration, and general merging. Some modalities corresponding to these fusion operators are added to epistemic logics and the Kripke semantics of these extended logics are presented. While most existing approaches treat information fusion operators as metalevel constructs, these operators are directly incorporated into our object logic language. Thus it is possible to reason about not only the merged results but also the fusion process in our logics.
Possibilistic Residuated Implication Logics with Applications
"... this paper, we will develop a class of logics for reasoning about qualitative and quantitative uncertainty. The semantics of the logics is uniformly based on possibility theory. Each logic in the class is parameterizedby a tnorm operation on [0,1], and we express the degree of implication between t ..."
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this paper, we will develop a class of logics for reasoning about qualitative and quantitative uncertainty. The semantics of the logics is uniformly based on possibility theory. Each logic in the class is parameterizedby a tnorm operation on [0,1], and we express the degree of implication between the possibilities of two formulas explicitly by using residuated implication with respect to the tnorm. The logics are then shown to be applicable to possibilistic reasoning, approximate reasoning, and nonmonotonic reasoning.