in this paper, various elementary properties of vague rings are obtained. furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.

An important part of explaining how people communicate is to understand how people relate language to entities in the world. In describing measurements, people prefer to use qualitative words like ‘tall’ without precise applicability conditions, also known as vague words. The use of vague language varies widely across contexts, individuals, and tasks (single reference vs. comparisons between ta...

Disagreeing with Williamson on vagueness, the author proposes a solution that he calls “three-valued plurivaluationism” to the age-old sorites paradox. In essence, it is a three-valued semantics for a first-order language with identity with the additional suggestion that a vague language has more than one correct interpretation. Unlike the traditional three-valued approach to a vague language, ...

In the area of computer science focusing on creating machines that can engage on behaviors that humans consider intelligent. The ability to create intelligent machines has intrigued humans since ancient times and today with the advent of the computer and 50 years of research into various programming techniques, the dream of smart machines is becoming a reality. Researchers are creating systems ...

Many knowledge-based systems need to represent vague concepts. Although the practical approach of representing vague concepts as precise intervals over numbers is well-accepted in AI, there is no systematic method to delimit the boundaries of intervals, only ad hoc methods. We present a framework to reason precisely with vague concepts based on the observation that the vague concepts and their ...

This paper analyzes communication with a language that is vague in the sense that identical messages do not always result in identical interpretations. It is shown that strategic agents frequently add to this vagueness by being intentionally vague, i.e. they deliberately choose less precise messages than they have to among the ones available to them in equilibrium. Having to communicate with a ...