## Logic-Based Algorithms for Data Interpretation With Application to Robotics (1998)

Citations: | 1 - 1 self |

### BibTeX

@TECHREPORT{Bison98logic-basedalgorithms,

author = {Paolo Bison and Gaetano Chemello and Claudio Sossai},

title = {Logic-Based Algorithms for Data Interpretation With Application to Robotics},

institution = {},

year = {1998}

}

### OpenURL

### Abstract

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 real-world problem of noisy sensor-data 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...

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Citation Context ...is similar to those in [36, 37, 44]. In these works, a coarse granularity is adopted: the map is a network of places or gateways connected by arcs, in contrast to finer-grain representations, like in =-=[53]-=- or in [34]. Each place is described by sentences, belonging to an enhanced version of the possibilistic logic [20], which relate an abstract description of the place with the perceptual picture provi... |

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Citation Context ...ompletely rules out the semantics of probabilities (in the frequentist frame). The possibilistic perspective [59] seems more appropriate because possibilities naturally capture the idea of similarity =-=[48, 25] -=-between actual percepts and prototypical configurations or expected observations. Assuming a more general point of view, δp1,...,pn can be seen as the degree of doubt about the fact that p1,...,pn co... |

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Citation Context ...a. In the style of current research, localization is made against a topological map, consisting of places connected by paths. Our map, with the addition of approximate metrics, is similar to those in =-=[36, 37, 44]-=-. In these works, a coarse granularity is adopted: the map is a network of places or gateways connected by arcs, in contrast to finer-grain representations, like in [53] or in [34]. Each place is desc... |

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Citation Context ...ence between the two classes lies in the presence vs absence of “complete information”: truth functionality appears when dealing with complete information, while it is absent in measure-based syst=-=ems [24]. Th-=-ese two classes are described by two different logical formalisms: • logics for vague reasoning: fuzzy logic in a narrow sense [60, 32] as a many-valued logic [40, 46, 31, 16, 17, 2, 45, 43]; • fu... |

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Citation Context ...erent logical formalisms: • logics for vague reasoning: fuzzy logic in a narrow sense [60, 32] as a many-valued logic [40, 46, 31, 16, 17, 2, 45, 43]; • fuzzy-measure based logics, i.e. possibilis=-=tic [12, 20, 27, 39]-=- and probabilistic [26, 29] logics. To our knowledge, no complete logics have been defined yet for belief functions [52, 54]. Due to the lack of truth functionality, the description of the logical str... |

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Citation Context ...14 in section 7.2); 3. code uncertain knowledge using weighted formulae (for example formulae 15, 16, 20 in section 7.2); 4. fuse the coded information using the rules for data fusion as presented in =-=[3, 21, 23], o-=-btaining a multiset of formulae Γ. Note that the formalism allows different fusion operations: at an elementary level we can fuse observations using different connectives (e.g. & and ⊗), but we can... |

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Citation Context ...r approach is a formalization of possibilistic reasoning, based on Girard’s linear logic [30], in the framework of algebraic semantics for substructural logics, called Local Possibilistic Logic (LPL=-=) [14]-=-, which has a valid and complete proof system in the sequent-calculus style. It is easy to show that LPL is an extension of usual possibilistic logic [20]. We will see how the intended semantics of LP... |

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Citation Context ...14 in section 7.2); 3. code uncertain knowledge using weighted formulae (for example formulae 15, 16, 20 in section 7.2); 4. fuse the coded information using the rules for data fusion as presented in =-=[3, 21, 23], o-=-btaining a multiset of formulae Γ. Note that the formalism allows different fusion operations: at an elementary level we can fuse observations using different connectives (e.g. & and ⊗), but we can... |

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Citation Context ...building a number of (fuzzy) hypotheses, one for each sensor, of the robot location. The various hypotheses are then fused using fuzzy intersection. A similar approach is proposed by Gasós and Martí=-=n [28]-=-, that perform localization by comparing a partial fuzzy map built during navigation with a pre-existing global map. 2 Why possibilities In our experimental work we have verified that data can be inte... |

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Citation Context ...l to expect that they provide an exact copy of first-order logic embedded inside the language L. In the case of ̷Lukasiewicz T-norm, i.e. α ×̷L β = max(α + β − 1,0), some more properties can =-=be shown [13]. For example-=-, for negation we have that �¬A� =1−�A�. 8s4.3 Proof system We present the calculus in a sequent form, since we are dealing with a connective (⊗, corresponding to a T-norm) which in gener... |

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Citation Context ...erent logical formalisms: • logics for vague reasoning: fuzzy logic in a narrow sense [60, 32] as a many-valued logic [40, 46, 31, 16, 17, 2, 45, 43]; • fuzzy-measure based logics, i.e. possibilis=-=tic [12, 20, 27, 39]-=- and probabilistic [26, 29] logics. To our knowledge, no complete logics have been defined yet for belief functions [52, 54]. Due to the lack of truth functionality, the description of the logical str... |

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Citation Context ...a. In the style of current research, localization is made against a topological map, consisting of places connected by paths. Our map, with the addition of approximate metrics, is similar to those in =-=[36, 37, 44]-=-. In these works, a coarse granularity is adopted: the map is a network of places or gateways connected by arcs, in contrast to finer-grain representations, like in [53] or in [34]. Each place is desc... |

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Citation Context ...omplete information, while it is absent in measure-based systems [24]. These two classes are described by two different logical formalisms: • logics for vague reasoning: fuzzy logic in a narrow sens=-=e [60, 32] a-=-s a many-valued logic [40, 46, 31, 16, 17, 2, 45, 43]; • fuzzy-measure based logics, i.e. possibilistic [12, 20, 27, 39] and probabilistic [26, 29] logics. To our knowledge, no complete logics have ... |

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Citation Context ...14 in section 7.2); 3. code uncertain knowledge using weighted formulae (for example formulae 15, 16, 20 in section 7.2); 4. fuse the coded information using the rules for data fusion as presented in =-=[3, 21, 23], o-=-btaining a multiset of formulae Γ. Note that the formalism allows different fusion operations: at an elementary level we can fuse observations using different connectives (e.g. & and ⊗), but we can... |

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Citation Context ...ilistic Logic, Sequent Calculus, Sensor Fusion, Mobile Robotics, Localization. 1 Introduction In this paper, which extends and supersedes work already presented both in Logic and in Robotics contexts =-=[5, 6, 7, 8]-=-, we will use a syntactical approach to data fusion to solve a localization problem in robotics. In our experiments we use a robot equipped with three different sensor systems (see figure 1): a belt o... |

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Citation Context ...hat sequent 27 introduces a degree of noise due to the fact that, as soon as we know ⊢ α ⊕ enter room(r, t) we can deduce (α &(1−α)) ⊕⊥ This situation can be handled using the techniques =-=described in [15]. We ha-=-ve experimented that α is always close to either 0 or 1, since the robot recognizes very well the door crossing, hence ɛ = α &(1−α) remains always small. In the case that ɛ is almost equal to 0... |

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Citation Context ...erent logical formalisms: • logics for vague reasoning: fuzzy logic in a narrow sense [60, 32] as a many-valued logic [40, 46, 31, 16, 17, 2, 45, 43]; • fuzzy-measure based logics, i.e. possibilis=-=tic [12, 20, 27, 39]-=- and probabilistic [26, 29] logics. To our knowledge, no complete logics have been defined yet for belief functions [52, 54]. Due to the lack of truth functionality, the description of the logical str... |

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Citation Context ...omplete information, while it is absent in measure-based systems [24]. These two classes are described by two different logical formalisms: • logics for vague reasoning: fuzzy logic in a narrow sens=-=e [60, 32] a-=-s a many-valued logic [40, 46, 31, 16, 17, 2, 45, 43]; • fuzzy-measure based logics, i.e. possibilistic [12, 20, 27, 39] and probabilistic [26, 29] logics. To our knowledge, no complete logics have ... |

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