## Epistemic logics, probability, and the calculus of evidence (1987)

Venue: | In Proceedings of the 10 th International Joint Conference on Artificial Intelligence |

Citations: | 31 - 0 self |

### BibTeX

@INPROCEEDINGS{Ruspini87epistemiclogics,,

author = {Enrique H. Ruspini},

title = {Epistemic logics, probability, and the calculus of evidence},

booktitle = {In Proceedings of the 10 th International Joint Conference on Artificial Intelligence},

year = {1987},

pages = {924--931},

publisher = {Morgan}

}

### OpenURL

### Abstract

This paper presents results of the application to epistemic logic structures of the method proposed by Carnap for the development of logical foundations of probability theory. These results, which provide firm conceptual bases

### Citations

2272 |
A Mathematical Theory of Evidence
- Shafer
- 1976
(Show Context)
Citation Context ... probability function defined on the algebra of epistemic sets. This probability is then shown to have the structure of the basic functions of the Dempster-Shafer calculus of evidence (Dempster 1967, =-=Shafer 1976-=-). Furthermore, if such an epistemic probability is extended to the sigma algebra of the truth sets (representing probabilities of the truth of propositions that describe the world), then the extensio... |

595 |
Upper and lower probabilities induced by a multivalued mapping
- Dempster
- 1967
(Show Context)
Citation Context ... conventional 1 probability function defined on the algebra of epistemic sets. This probability is then shown to have the structure of the basic functions of the Dempster-Shafer calculus of evidence (=-=Dempster 1967-=-, Shafer 1976). Furthermore, if such an epistemic probability is extended to the sigma algebra of the truth sets (representing probabilities of the truth of propositions that describe the world), then... |

438 |
Knowledge and Belief
- Hintikka
- 1962
(Show Context)
Citation Context ...ttention to epistemic logics — a form of modal logics developed to deal with problems of representation and manipulation of the states of knowledge of rationalsagents. Originally studied by Hintikka (=-=Hintikka 1962-=-), their use in artificial intelligence problems was proposed by Moore (Moore 1980). Recently epistemic logics have also been applied to the design of intelligent robots (Rosenschein and Kaelbling 198... |

420 |
Probabilistic logic
- Nilsson
- 1986
(Show Context)
Citation Context ...on in determining the probability distribution values that underlie rational choices in decision problems. Our approach is also related in several ways to the probabilistic logic approach of Nilsson (=-=Nilsson 1986-=-) — the major differences being in the use of epistemic concepts and the derivation of global conditions for probability extension, in contrast to formulas derived from interval probability theory or ... |

266 | Logical Foundations of Probability - Carnap - 1950 |

152 |
Reasoning about knowledge and action
- Moore
- 1980
(Show Context)
Citation Context ... of representation and manipulation of the states of knowledge of rationalsagents. Originally studied by Hintikka (Hintikka 1962), their use in artificial intelligence problems was proposed by Moore (=-=Moore 1980-=-). Recently epistemic logics have also been applied to the design of intelligent robots (Rosenschein and Kaelbling 1986). In our extension of the Carnapian ideas the starting point is a generalization... |

132 |
Meaning and Necessity
- Carnap
- 1947
(Show Context)
Citation Context ... an understanding by examining the basic concepts, structures, and ideas relevant to the characterization of imprecise and uncertain knowledge. Our approach is strongly based on Carnap's methodology (=-=Carnap 1956-=-, 1962) for the development of logical foundations of probability theory. In his formulation, Carnap developed an universe of possible worlds that encompasses all possible valid states of a real-world... |

130 |
The synthesis of digital machines with provable epistemic properties
- Rosenschein, Kaelbling
- 1986
(Show Context)
Citation Context ...ed by Hintikka (Hintikka 1962), their use in artificial intelligence problems was proposed by Moore (Moore 1980). Recently epistemic logics have also been applied to the design of intelligent robots (=-=Rosenschein and Kaelbling 1986-=-). In our extension of the Carnapian ideas the starting point is a generalization of Carnap's space of possible worlds, or universe. This generalization, obtained by considering representations of bot... |

52 | Indeterminate probabilities
- WILLIAMS
- 1976
(Show Context)
Citation Context ...ilities. These considerations have led to the development of schemes to represent uncertain information as constraints on the values of valid probability distributions. Interval probability theories (=-=Williams 1976-=-), of which the DempsterShafer calculus is a particular case, are important examples of this technique. The approach we have followed here, however, proceds from a different logical foundation. Starti... |

36 |
The logical foundations of evidential reasoning
- RUSPINI
- 1986
(Show Context)
Citation Context ...obtained in the research being discussed, as such extensive discussion is well outside the scope of this paper. The reader interested in the actual details will find them discussed in a related work (=-=Ruspini 1986-=-a). II The Epistemic Universe A. The Carnapian Universe Carnap's logical approach to probability starts with the construction of a space of possible worlds that encompasses all valid states of a syste... |

25 |
The measurement of belief
- SUPPES
- 1974
(Show Context)
Citation Context ...ory. These bounds correspond to the well-known concepts of lower and upper probability functions and, in this particular regard, our results are in agreement with the characterization made by Suppes (=-=Suppes 1974-=-) of the role of uncertain information in determining the probability distribution values that underlie rational choices in decision problems. Our approach is also related in several ways to the proba... |

24 |
Jr.) Combinatorial Theory (Second Edition
- Hall
- 1986
(Show Context)
Citation Context ...ions and mass functions are related by the equation which is valid for every objective proposition p in the frame of discernment. From this basic equation, by using results from combinatorial theory (=-=Hall 1986-=-), it is possible 6 Sigma algebras are families of subsets that are closed under the settheoretic operations of complementation, countable union, and countable intersection.sFigure 3: Relations Betwee... |

2 |
Approximate deduction in single evidential bodies
- Ruspini
- 1986
(Show Context)
Citation Context ...obtained in the research being discussed, as such extensive discussion is well outside the scope of this paper. The reader interested in the actual details will find them discussed in a related work (=-=Ruspini 1986-=-a). II The Epistemic Universe A. The Carnapian Universe Carnap's logical approach to probability starts with the construction of a space of possible worlds that encompasses all valid states of a syste... |

1 |
Bases Mathimatiques du Calcul des Probability
- Neveu
- 1964
(Show Context)
Citation Context ... epistemic probability to a probability function defined over the truth algebra. The problem of probability extension has received a great deal of attention in probability theory (see, for ex ample, =-=Neveu, 1964-=-). The standard procedure for its solu tion is to define lower and upper probabilities for sets not included in the domain of definition (i.e., sigma algebra) of the probability function being extend... |

1 | A Hester, "Likelihood, Probability, and Knowledge - Ralpern, Mc - 1984 |