# Modal Mu-calculus Extension with Description of Autonomy and Its Algebraic Structure

### Susumu Yamasaki, Mariko Sasakura

#### Abstract

This paper deals with complex abstract state machinery, clearly represented by modal logic with fixed point operator. The logic is well known as modal mu-calculus, which is extended to the version involving human computer interaction as well as involving awareness, communication and behavioral predicates of propositional variables as in autonomy systems. The extended version contains complexity for human machine interaction, whose meaning is represented by Heyting algebra but not by Boolean algebra. In the sense of Heyting algebra, human computer interaction of complexity can be described such that related predicates of communication and behavior may be simplified. Then the extended version can be applied to some process by means of awareness to an expertise, communication and behavior processes, and repetitions represented with fixed point operator (that is, mu-operator). This version is also concerned with model theory caused by postfix modal operator, where composition and alternation of modal operators may be organized into an algebraic structure.

Download#### Paper Citation

#### in Harvard Style

Yamasaki S. and Sasakura M. (2020). **Modal Mu-calculus Extension with Description of Autonomy and Its Algebraic Structure**.In *Proceedings of the 5th International Conference on Complexity, Future Information Systems and Risk - Volume 1: COMPLEXIS,* ISBN 978-989-758-427-5, pages 63-71. DOI: 10.5220/0009322300630071

#### in Bibtex Style

@conference{complexis20,

author={Susumu Yamasaki and Mariko Sasakura},

title={Modal Mu-calculus Extension with Description of Autonomy and Its Algebraic Structure},

booktitle={Proceedings of the 5th International Conference on Complexity, Future Information Systems and Risk - Volume 1: COMPLEXIS,},

year={2020},

pages={63-71},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0009322300630071},

isbn={978-989-758-427-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 5th International Conference on Complexity, Future Information Systems and Risk - Volume 1: COMPLEXIS,

TI - Modal Mu-calculus Extension with Description of Autonomy and Its Algebraic Structure

SN - 978-989-758-427-5

AU - Yamasaki S.

AU - Sasakura M.

PY - 2020

SP - 63

EP - 71

DO - 10.5220/0009322300630071