Algebraic and relational models for a system based on a poset of two elements

TL;DR

This paper introduces a formal system and semantic models for managing knowledge in a two-agent poset system, utilizing algebraic structures related to three-valued Heyting algebras with Boolean operators.

Contribution

It presents a simple set of conditions for knowledge management in a two-agent poset system and develops related algebraic and semantic models.

Findings

Formal system for two-agent knowledge management

Semantic models based on algebraic structures

Connection to three-valued Heyting algebras

Abstract

The aim of this paper is to present a very simple set of conditions, necessary for the management of knowledge of a poset $T$ of two agents, which are partially ordered by the capabilities available in the system. We build up a formal system and we elaborate suitable semantic models in order to derive information from the poset. The system is related to three-valued Heyting algebras with Boolean operators.