Quantification Of Resource Production Incompleteness

In a situation where an agent has to produce specific resources using the available ones, it may not be possible to achieve the complete goal, but only obtaining some of its parts. This incompleteness problem calls for reasoning models to make rational decisions. In this paper, we introduce a logic-based framework for measuring resource production incompleteness: the greater the value returned by a measure, the greater is the intensity of incompleteness. After motivating our work by describing situations where the incompleteness measures can be applied, we introduce our framework by using a postulate-based approach. To some extent, the incompleteness measures can be seen as a counterpart of inconsistency measures in resource logics. Here, intuitionistic affine logic is used for representing and reasoning about resource consummation and production. Besides, we propose different notions that are useful for defining different types of incompleteness measures. We also present several measures to illustrate the introduced concepts and notions.