发表机构
State University of New York at Buffalo（纽约州立大学布法罗分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文将量子信息论与经典分体论结合，研究从经典RCC5形式主义衍生的量化分体论，论证该方法可推广到更复杂的定性推理形式主义，且量子比特更适合封装模糊现象信息。
AI 中文摘要
本文研究量化分体论，它将量子信息论与经典分体论（对部分-整体关系的形式分析）相结合。本文强调，清晰分体论关系的信息由经典比特捕获，而分体论模糊性则用量子比特（即qubits）来捕获分体论信息。从经典比特过渡到量子比特，为受分体论模糊性影响的实体之间的部分-整体关系提供了新的理解。本文系统研究了由经典RCC5形式主义产生的量化分体论，RCC5是定性推理（QR）中最广泛研究的形式主义之一，定性推理是人工智能的一个子领域。本文论证该方法可扩展以量化更复杂的定性推理形式主义，与物理学中从经典系统过渡到量子系统的策略相呼应。本研究探讨：（i）比特到量子比特的转换，同时理解这些（量子）比特传递分体论信息；（ii）通过集合划分表示量子比特状态，认识到集合论与经典逻辑的契合度高于量子物理中使用的复向量空间；（iii）证明经典定性推理形式主义可视为量化形式主义的特殊情况；（iv）表明量子比特能更有效地封装模糊现象的信息。
英文摘要
This paper investigates quantized mereology, which merges quantum information theory with classical mereology, the formal analysis of the part-whole relationship. It emphasizes that information about crisp mereological relations is captured by classical bits, whereas mereological vagueness involves the use of quantum bits, or qubits, to capture mereological information. Transitioning from classical bits to qubits offers a new understanding of part-whole relations among entities that are subject to mereological vagueness. This paper methodically studies the quantized mereology that arises from the classical RCC5 formalism, one of the most widely studied formalisms in Qualitative Reasoning (QR), a subfield of Artificial Intelligence. The argument is made that this method can be extended to quantize more sophisticated QR formalisms, mirroring how strategies are used in physics to transition from classical to quantum systems. The study explores: (i) the conversion of bits to qubits while understanding that these (qu)bits convey mereological information; (ii) the representation of qubit states via set partitions, acknowledging that set theory aligns more closely with classical logic than with the complex vector spaces employed in quantum physics; (iii) demonstrating that classical QR formalisms can be seen as special cases within quantized formalisms; and (iv) showing that qubits more effectively encapsulate information about vague phenomena.
