Authors:
Susumu Yamasaki
1
and
Mariko Sasakura
2
Affiliations:
1
Okayama University, Tsushima-Naka, Okayama, Japan
;
2
IPDRE, Tottori University, Hamasaka, Tottori City, Japan
Keyword(s):
Algebraic Structure, Model Theory, Knowledge Base.
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 derivati
on 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.
(More)