## 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

### Citations

1497 |
Reasoning about Knowledge
- Fagin, Halpern, et al.
- 1995
(Show Context)
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... |

811 | Modeling rational agents within a BDI architecture
- Rao, George
- 1991
(Show Context)
Citation Context ...anguage 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 solutions are to adopt CTL like the BDI-architecture [31], (concurrent) dynamic logic like the KARO system [21], or discrete linear temporal logic. Extending ... |

393 | AgentSpeak(L): BDI agents speak out in a logical computable language
- Rao
- 1996
(Show Context)
Citation Context ...cts of multi-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 acti... |

70 | First order theories of individual concepts and propositions
- McCarthy
- 1979
(Show Context)
Citation Context ...ave all information it wants or can reason exactly as the others, but at least it can simulate epistemic states of the other agents, using some assumptions. The wise men puzzle introduced by McCarthy =-=[20]-=- is an example of reasoning about epistemic states of agents. We will study it in Section 3. Modal logics and logic programming are useful instruments for multi-agent systems. Using modal logics is a ... |

60 | An Overview of Temporal and Modal Logic Programming
- Orgun, Ma
- 1994
(Show Context)
Citation Context ...amming. In F. Toni and P. Torroni (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 sec... |

51 | Multi-Agent Reasoning with Belief Contexts II: Elaboration Tolerance
- Cimatti, Serafini
- 1996
(Show Context)
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... |

42 |
Belief and Incompleteness
- Konolige
- 1985
(Show Context)
Citation Context ...of semantics of KD4Ig5a-MProlog, we give a formalization of the three wise men puzzle in MProlog. The puzzle is a famous benchmark introduced by McCarthy [20] for AI. It can be stated as follows (cf. =-=[18]-=-). A king wishes to know whether his three advisors (A, B, C) are as wise as they claim to be. Three chairs are lined up, all facing the same direction, with one behind the other. The wise men are ins... |

32 |
Multimodal logic programming using equational and order-sorted logic. Theoretical Computer Science
- Debart, Enjalbert, et al.
- 1992
(Show Context)
Citation Context ...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 direct approach. This approach is justifi... |

27 | Proofs in context
- Attardi, Simi
- 1994
(Show Context)
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... |

26 |
editors. Executable Modal and Temporal Logics
- Fisher, Owens
- 1995
(Show Context)
Citation Context ...amming. In F. Toni and P. Torroni (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 sec... |

25 |
Foundations of Logical Programming, 2nd Ed
- Lloyd
- 1987
(Show Context)
Citation Context ...ε (the empty substitution) and Gi is derived from Gi−1 and (the rSatL rule variant) ϕi. Each ϕi is called an input clause/rule of the derivation. We assume standardizing variables apart as usual (see =-=[19]-=-). An SLD-refutation of P ∪ {G} in L is a finite SLD-derivation from P ∪ {G} in L with the empty clause as the last goal in the derivation. Let P be an L-MProlog program and G a goal. A computed answe... |

24 |
del Cerro. MOLOG: A system that extends PROLOG with modal logic
- Fariñas
- 1986
(Show Context)
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... |

18 |
Declarative semantics for modal logic programs
- Balbiani, Herzig
- 1988
(Show Context)
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... |

18 | Normal multimodal logics with interaction axioms
- Baldoni
- 2000
(Show Context)
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... |

18 | A framework for modal logic programming
- Baldoni, Giordano, et al.
- 1996
(Show Context)
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... |

15 |
Agent programming
- Meyer
- 1999
(Show Context)
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... |

15 | A fixpoint semantics and an SLD-resolution calculus for modal logic programs
- Nguyen
(Show Context)
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... |

14 | Step-logic and the three-wise-men problem
- Elgot-Drapkin
- 1991
(Show Context)
Citation Context |

14 |
How to use modalities and sorts in Prolog
- Nonnengart
(Show Context)
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... |

13 | Multimodal logic programming and its applications to modal deductive databases. Manuscript (served as a technical report), available at http://www.mimuw.edu
- Nguyen
- 2004
(Show Context)
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... |

10 | The modal logic programming system mprolog
- Nguyen
(Show Context)
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... |

10 | Foundations of modal deductive databases
- Nguyen
- 2007
(Show Context)
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... |

9 |
Rational teams: Logical aspects of multi-agent systems
- Meyer
- 2004
(Show Context)
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... |

8 |
Inheritance and Hypothetical Reasoning in Logic Programming
- Brogi, Lamma, et al.
- 1990
(Show Context)
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 ... |

8 |
A tableau system with automaton-labelled formulae for regular grammar logics
- Goré, Nguyen
- 2005
(Show Context)
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 ... |

6 | On programming KARO agents
- Meyer, Eijk, et al.
- 2001
(Show Context)
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... |

3 | An SLD-resolution calculus for basic serial multimodal logics
- Nguyen
- 2005
(Show Context)
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... |

3 | D.: Multi-Agent Logic of Dynamic Belief and Knowledge
- Schmidt, Tishkovsky
(Show Context)
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... |

3 |
Modalities for reasoning about knowledge and uncertainties
- Hoek, Meyer
- 1996
(Show Context)
Citation Context |

2 |
Tableaux for regular grammar logics of agents using automaton-modal formulae
- Goré, Nguyen
- 2006
(Show Context)
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... |

2 |
Practical Reasoning for Uncertain Agents
- Ferreira, Fisher, et al.
- 2004
(Show Context)
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... |

1 |
der Hoek. Practical reasoning for uncertain agents
- Ferreira, Fisher, et al.
- 2004
(Show Context)
Citation Context |

1 | Bounded versus unbounded model checking for interpreted systems (invited talk at FAAMAS’03
- Kacprzak, Lomuscio, et al.
- 2003
(Show Context)
Citation Context |