## Reasoning about epistemic states of agents by modal logic programming (2006)

Venue: | Proceedings of CLIMA VI, LNAI 3900 |

Citations: | 6 - 6 self |

### BibTeX

@INPROCEEDINGS{Nguyen06reasoningabout,

author = {Linh Anh Nguyen},

title = {Reasoning about epistemic states of agents by modal logic programming},

booktitle = {Proceedings of CLIMA VI, LNAI 3900},

year = {2006},

pages = {37--56},

publisher = {Springer-Verlag}

}

### OpenURL

### Abstract

Abstract. Modal logic programming is one of appropriate approaches to deal with reasoning about epistemic states of agents. We specify here the least model semantics, the fixpoint semantics, and an SLD-resolution calculus for modal logic programs in the multimodal logic KD4Ig5a, which is intended for reasoning about belief and common belief of agents. We prove that the presented SLD-resolution calculus is sound and complete. We also present a formalization of the wise men puzzle using a modal logic program in KD4Ig5a. This shows that it is worth to study modal logic programming for multi-agent systems. 1

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Citation Context ...tion 3. Modal logics and logic programming are useful instruments for multi-agent systems. Using modal logics is a natural way to represent and reason about knowledge and belief of agents (see, e.g., =-=[11, 33, 32, 17, 8, 1]-=-). Logic programming is also useful because logical implication is probably the inference form humans use most and want to adopt for multi-agent systems. Thus, one can think about modal logic programm... |

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Citation Context ...inger-Verlag, 2006.sModal logic programming has been studied in a number of works (see the earlier surveys [29, 13] and the later works [28, 5, 22, 26]). There are two approaches: the direct approach =-=[12, 3, 5, 22, 26]-=- and the translation approach [9, 28]. The first approach directly uses modalities, while the second one translates modal logic programs to classical logic programs. In this paper we will use the dire... |

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Citation Context ...s what it is. All know that this will happen. The room is silent; then, after a while, wise man A says “My card is white!”.sThe wise men puzzle has been previously studied in a number of works (e.g., =-=[20, 18, 10, 7, 2, 28, 4]-=-). McCarthy [20] directly used possible worlds to formalize the puzzle. Konolige [18], Nonnengart [28], and Baldoni [4] also used modal logics for the puzzle. Konolige [18] focused on limited reasonin... |

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Citation Context ...i-agent systems. In particular, we did not consider temporal dimension, actions, and events. Thus the current version of MProlog is not yet an agent programming language like AgentSpeak(L) [30], 3APL =-=[16]-=-, and KARO [21]. In this work, we concentrated on reasoning about common/mutual belief, which was also considered in the paper [21] on KARO, but neglected in [31, 30, 16]. To deal with actions and tim... |

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Citation Context ...roni (eds), Proceedings of CLIMA VI, LNAI 3900, pages 37-56, Springer-Verlag, 2006.sModal logic programming has been studied in a number of works (see the earlier surveys [29, 13] and the later works =-=[28, 5, 22, 26]-=-). There are two approaches: the direct approach [12, 3, 5, 22, 26] and the translation approach [9, 28]. The first approach directly uses modalities, while the second one translates modal logic progr... |

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Citation Context ...roni (eds), Proceedings of CLIMA VI, LNAI 3900, pages 37-56, Springer-Verlag, 2006.sModal logic programming has been studied in a number of works (see the earlier surveys [29, 13] and the later works =-=[28, 5, 22, 26]-=-). There are two approaches: the direct approach [12, 3, 5, 22, 26] and the translation approach [9, 28]. The first approach directly uses modalities, while the second one translates modal logic progr... |

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Citation Context ...nsist of the conditions of seriality and some classical first-order Horn formulas. In this work, we instantiate the above mentioned framework for the multimodal logic KD4Ig5a, which was introduced in =-=[23]-=- for reasoning about belief and common belief. We prove that the obtained SLD-resolution calculus is sound and complete. We also give a purely logical formalization of the wise men puzzle using a moda... |

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Citation Context ...en puzzle given below uses KD4Ig5aMProlog. It is more elegant than the above-mentioned formalizations, as it uses a modal logic with a clear semantics of common belief in a direct way. As reported in =-=[21]-=-, we have designed and implemented a modal logic programming system, also called MProlog. In that system, SLD-resolution calculi for MProlog can be specified according to the theoretical framework giv... |

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Citation Context ...ess to belief bases of each other. They are members of a united system and viewed as “friends”. An SLD-resolution for MProlog in KD4s5s is given in [23]. The following example is taken from our paper =-=[27]-=-. Let us consider the situation when a company has some branches and a central database. Each of the branches can access and update the database, and suppose that the company wants to distinguish data... |

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Citation Context ...tion 3. Modal logics and logic programming are useful instruments for multi-agent systems. Using modal logics is a natural way to represent and reason about knowledge and belief of agents (see, e.g., =-=[11, 33, 32, 17, 8, 1]-=-). Logic programming is also useful because logical implication is probably the inference form humans use most and want to adopt for multi-agent systems. Thus, one can think about modal logic programm... |

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Citation Context ...ive two more examples illustrating the usefulness of modal logic programming for multi-agent systems. 6.1 Inheritance in a Hierarchy of Classes In [5], Baldoni et al. formalizes an example taken from =-=[6]-=- of inheritance in a hierarchy of classes by a modal logic program. We adopt here their example with a small modification. Let us consider four classes: animal, horse, bird, and tweety. Since what is ... |

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Citation Context ...a was introduced in [23]. It is different in the nature from the well-known multimodal logic of common knowledge. It also differs from the modal logic with mutual belief [1]. In [15] (an extension of =-=[14]-=-), Goré and Nguyen show that the satisfiability problem in the propositional version of KD4Ig5a is in EXPTIME. Clearly, the problem is PSPACE-hard (as KD4Ig5a contains KD4). We guess that the problem ... |

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Citation Context .... In particular, we did not consider temporal dimension, actions, and events. Thus the current version of MProlog is not yet an agent programming language like AgentSpeak(L) [30], 3APL [16], and KARO =-=[21]-=-. In this work, we concentrated on reasoning about common/mutual belief, which was also considered in the paper [21] on KARO, but neglected in [31, 30, 16]. To deal with actions and time, possible sol... |

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Citation Context ...al logics of belief and common/mutual belief that can be used to formalize the wise men puzzle. Our framework for modal logic programming [26] is applicable for a wide class of multimodal logics (see =-=[23, 25]-=-) and it can be extended for other versions of Kripke semantics, e.g. with varying domain or flexible terms (see a discussion in [26]). In summary, this paper is on reasoning about common/mutual belie... |

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Citation Context ...tion 3. Modal logics and logic programming are useful instruments for multi-agent systems. Using modal logics is a natural way to represent and reason about knowledge and belief of agents (see, e.g., =-=[11, 33, 32, 17, 8, 1]-=-). Logic programming is also useful because logical implication is probably the inference form humans use most and want to adopt for multi-agent systems. Thus, one can think about modal logic programm... |

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Citation Context ...lief. The logic KD4Ig5a was introduced in [23]. It is different in the nature from the well-known multimodal logic of common knowledge. It also differs from the modal logic with mutual belief [1]. In =-=[15]-=- (an extension of [14]), Goré and Nguyen show that the satisfiability problem in the propositional version of KD4Ig5a is in EXPTIME. Clearly, the problem is PSPACE-hard (as KD4Ig5a contains KD4). We g... |

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Citation Context ...tion 3. Modal logics and logic programming are useful instruments for multi-agent systems. Using modal logics is a natural way to represent and reason about knowledge and belief of agents (see, e.g., =-=[10, 28, 27, 14, 7, 1]-=-). Logic programming is also useful because logical implication is probably the inference form humans use most and want to adopt for multi-agent systems. Thus, one can think about modal logic programm... |

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