Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this paper, we propose a formal framework unifying several forms of extensions and combinations of qualitative formalisms, including multi-scale reasoning, temporal sequences, and loose integrations. This framework makes it possible to reason in the context of each of these combinations and extensions, but also to study in a unified way the satisfiability decision and its complexity. In particular, we establish two complementary theorems guaranteeing that the satisfiability decision is polynomial, and we use them to recover the known results of the size-topology combination. We also generalize the main definition of qualitative formalism to include qualitative formalisms excluded from the definitions of the literature, important in the context of combinations.

翻译：在人工智能背景下研究的各种推理形式中，定性推理使得在缺乏精确数值的不完整信息背景下推断新知识成为可能。本文提出了一个统一多种定性形式体系扩展与组合形式的正式框架，包括多尺度推理、时间序列以及松散集成。该框架不仅使得在每种此类组合与扩展背景下进行推理成为可能，还能以统一方式研究可满足性判定及其复杂度。特别地，我们建立了两个保证可满足性判定为多项式复杂度的互补定理，并运用它们重新推导出尺寸-拓扑组合的已知结果。同时，我们将定性形式体系的核心定义推广至包含文献定义中排除的、在组合背景下具有重要意义的定性形式体系。