## Modal Logics for Representing Incoherent Knowledge (1995)

Venue: | In Handbook of Defeasible Reasoning and Uncertainty Management |

Citations: | 5 - 0 self |

### BibTeX

@INPROCEEDINGS{Meyer95modallogics,

author = {J.J.Ch. Meyer and W. Van Der Hoek},

title = {Modal Logics for Representing Incoherent Knowledge},

booktitle = {In Handbook of Defeasible Reasoning and Uncertainty Management},

year = {1995},

pages = {37--75},

publisher = {Kluwer}

}

### OpenURL

### Abstract

In this paper we review ways of representing incoherent 'knowledge' in a consistent way, where the use of modal logic and Kripke-style semantics is put central. Starting with a presentation of the basic modal framework, we discuss the basic modal systems K, KD (with an excursion to the representation of conflicting norms in deontic logic) and Chellas' minimal modal logic D. Next we look at the epistemic logics KD45, S4 and S5, including the logical omniscience problem and several non-standard modal logics to overcome this problem. After this we turn to the issue of reasoning by default, where a conflict of defaults (or default beliefs) may arise. We give an epistemic treatment of default reasoning, and treat the way conflicts of defaults can be solved viewed from the more general perspective of resolving conflicts in meta- level reasoning. Furthermore, special attention is paid to specificity in default reasoning as a principle to solve these conflicts, for which we develop an extension of Halpern & Moses' theory of honest formulas. Finally, we discuss several numerical modal logics in their capacity of ways of representation of incoherent information.

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Citation Context ...e not dealing with sources of information, but with a number of defaults, also known as the lottery paradox. The following example is well-known in the literature on probabilistic reasoning ([Kyb61], =-=[Pea88]-=-) and on non-monotonic reasoning ([Gin87]), where it is called the lottery paradox. It deals with the situation of a lottery with n tickets, numbered 1 ... n. Let wi denote 'ticket i will be the winni... |

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