# Algebraic Structure of Recursively Constructed References and Its Application to Knowledge Base

### Susumu Yamasaki, Mariko Sasakura

#### 2024

#### Abstract

From management views on complex website page structures, we formulate an algebraic structure of recursively constructed page references as presenting situations of them to the website with 3-valued domain. Algebraic structure of references, abstracted from website page references, is here expressed as a finite or countably infinite set of rules, where each rule is defined, by representing the recursive relations among web page references. The situations of a reference with request to the website can be denoted as the acquisitive positive, rejective negative and suspended negative, respectively. With respect to algebraic structure, a fixed point of the mapping associated with the rule set may be a model denoting consistent evaluations to assign the situations of references to 3-valued domain. Model theory for representation of consistent evaluations of references and the rule set (constructed with references) is newly settled if a fixed point consistently exists. A retrieval derivation to detect acquisitive positives and rejective negatives can be presented, to be sound with respect to the model, based on the inference by negation as failure, which is related to the suspended negative. As multiple knowledge base formed by a tuple of rule sets, this paper next presents algebraic structure of a distributed knowledge system constrained by a state, and sequential applications of such systems, containing state transitions. Model theory can be defined with fixed point of the mapping associated with the distributed knowledge system, although the fixed point may not be always applied to modeling. If consistent fixed point modeling is available, we may have a model of the distributed knowledge system, constrained by a state. Then the application of such a distributed knowledge system may be considered as causing state transitions, following modeling and designed state transitions.

Download#### Paper Citation

#### in Harvard Style

Yamasaki S. and Sasakura M. (2024). **Algebraic Structure of Recursively Constructed References and Its Application to Knowledge Base**. In *Proceedings of the 9th International Conference on Complexity, Future Information Systems and Risk - Volume 1: COMPLEXIS*; ISBN 978-989-758-698-9, SciTePress, pages 83-90. DOI: 10.5220/0012544500003708

#### in Bibtex Style

@conference{complexis24,

author={Susumu Yamasaki and Mariko Sasakura},

title={Algebraic Structure of Recursively Constructed References and Its Application to Knowledge Base},

booktitle={Proceedings of the 9th International Conference on Complexity, Future Information Systems and Risk - Volume 1: COMPLEXIS},

year={2024},

pages={83-90},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0012544500003708},

isbn={978-989-758-698-9},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 9th International Conference on Complexity, Future Information Systems and Risk - Volume 1: COMPLEXIS

TI - Algebraic Structure of Recursively Constructed References and Its Application to Knowledge Base

SN - 978-989-758-698-9

AU - Yamasaki S.

AU - Sasakura M.

PY - 2024

SP - 83

EP - 90

DO - 10.5220/0012544500003708

PB - SciTePress