# Linear Algebraic Semantics for Multi-agent Communication

### Ryo Hatano, Katsuhiko Sano, Satoshi Tojo

#### Abstract

When we study multi-agent communication system, it forces us to manage an existence of communication channels between agents, such as phone numbers or e-mail addresses, while ordinary modal logic for multi-agent system does not consider the notion of channel. This paper proposes a decidable and semantically complete logic of belief with communication channels, and then expands the logic with informing action operators to change agents’ beliefs via communication channels. Moreover, for a better formalism for handling these semantics efficiently, we propose a linear algebraic representation of these. That is, with the help of Fitting (2003) and van Benthem and Liu (2007), we reformulate our proposed semantics of the doxastic static logic and its dynamic extensions in terms of boolean matrices. We also implement and publicize a calculation system of our matrix reformulations as an open system on the web.

#### References

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#### Paper Citation

#### in Harvard Style

Hatano R., Sano K. and Tojo S. (2015). **Linear Algebraic Semantics for Multi-agent Communication** . In *Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,* ISBN 978-989-758-073-4, pages 174-181. DOI: 10.5220/0005219001740181

#### in Bibtex Style

@conference{icaart15,

author={Ryo Hatano and Katsuhiko Sano and Satoshi Tojo},

title={Linear Algebraic Semantics for Multi-agent Communication},

booktitle={Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},

year={2015},

pages={174-181},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005219001740181},

isbn={978-989-758-073-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,

TI - Linear Algebraic Semantics for Multi-agent Communication

SN - 978-989-758-073-4

AU - Hatano R.

AU - Sano K.

AU - Tojo S.

PY - 2015

SP - 174

EP - 181

DO - 10.5220/0005219001740181