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.
Journal reference
Journal of Artificial Intelligence Research 87, Article 12 (2026)
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.
Qualitative representations of mereological structures in Artificial Intelligence are generally based on a set of mutually exclusive and collectively exhaustive crisp (RCC5) relations. The amount of information carried by each element in this set of (crisp) relations is determined by the number of bits (N) required to distinguish all members of the set. This paper posits that mereological vagueness can arise if mereological relations are limited in the amount of information they can carry. Consequently, a comprehensive set of vague mereological relations is introduced, where each relation in this set can only carry 0 < n < N bits of information. In this framework, mereological information is treated as quantum information, with quantum bits (qubits) distinguishing relations subject to ontic vagueness. The main contribution is the thorough examination of mereological relations within a 3 qubit quantum system. Quantum bits are not represented as vectors in a Hilbert space but as cells in (granular) partitions. This paper is the companion to the author's quantized-mereology framework and develops its entangled-state layer: the combination of three simultaneous elementary questions, the families of entangled information states, the probability distribution for possible observations and the dynamics induced by sequences of non-simultaneous questions.
The successful application of quantum probability in cognitive science has been persistently challenged by the foundational 'why quantum?' question. In this paper, a novel answer is proposed through the development of an ontological grounding for the quantum-like structures observed in human judgment. It is argued that these cognitive structures may be a direct reflection of an objective, information-theoretic vagueness inherent in the macroscopic world. To formalize this, 'Quantized Mereology' is developed - a framework inspired by Rovelli's Relational Quantum Mechanics (RQM), where determinate mereological facts about vague entities like forests and clouds are established relationally through an act of judgment. The framework uses a real-valued Hilbert space as a precise object language, which is given meaning by a partition-theoretic meta-language. A key contribution is a defense of the real-valued structure, in which it is argued that the physical constraints necessitating complex numbers in microphysics constitute a category error when applied to the conceptual systems modeled herein. The result is a generative model for objective vagueness that provides a candidate ontological foundation for quantum cognition.
Abstract The emerging field of quantum mereology considers part-whole relations in quantum systems. Entangled quantum systems pose a peculiar problem in the field, since their total states are not reducible to that of their parts. While there exist several established proposals for modelling entangled systems, like monistic holism or relational holism, there is considerable unclarity, which further positions are available. Using the lambda operator and plural logic as formal tools, we review and develop conceivable models and evaluate their consistency and distinctness. The main result is an exhaustive taxonomy of six distinct and precise models that both provide information about the mereological features as well as about the entangled property. The taxonomy is well-suited to serve as the basis for future systematic investigations.
A composite quantum system has properties that are incompatible with every property of its parts. The existence of such global properties incompatible with all local properties constitutes what I call "mereological holism"--the distinctive holism of Quantum Theory. Mereological holism has the dramatic conceptual consequence of making untenable the usual understanding of the "quantum system" as being a "physical object", since composed objects have properties compatible with those of its parts. The notion of "property" can be extended in a unique way to the whole class of operational probabilistic theories (shortly OPTs), of which the most relevant cases are Quantum Theory and Classical Theory. Whereas Classical Theory is not mereologically holistic, we can now search for other OPTs that are so. Within the OPT framework the role of the "system" is that of an input-output connection between two objective events. In non holistic theories, such as Classical Theory, the system can still be regarded as an "object". On the contrary, in holistic theories interpreting "system" as "object" constitutes an hypostatization of a theoretical notion.
Quantum theory describes our universe incredibly successfully. To our classically-inclined brains, however, it is a bizarre description that requires a reimagining of what fundamental reality, or “ontology”, could look like. This thesis examines different ontological features in light of the success of quantum theory, what it requires, and what it rules out. While these investigations are primarily foundational, they also have relevance to quantum information, quantum communication, and experiments on quantum systems. The way that quantum theory describes the state of a system is one of its most unintuitive features. It is natural, therefore, to ask whether a similarly strange description of states is required on an ontological level. This thesis proves that almost all quantum superposition states for d > 3 dimensions must be real—that is, present in the ontology in a well-defined sense. This is a strong requirement which prevents intuitive explanations of the many quantum phenomena which are based on superpositions. A new theorem is also presented showing that quantum theory is incompatible with macro-realist ontologies, where certain physical quantities must always have definite values. This improves on the Leggett-Garg argument, which also aims to prove incompatibility with macro-realism but contains loopholes. Variations on both of these results that are error-tolerant (and therefore amenable to experimentation) are presented, as well as numerous related theorems showing that the ontology of quantum states must be somewhat similar to the quantum states themselves in various specific ways. Extending these same methods to quantum communication, a simple proof is found showing that an exponential number of classical bits are required to communicate a linear number of qubits. That is, classical systems are exponentially bad at storing quantum data. Causal influences are another part of ontology where quantum theory demands a revision of our classical notions. This follows from the outcomes of Bell experiments, as rigorously shown in recent analyses. Here, the task of constructing a native quantum framework for reasoning about causal influences is tackled. This is done by first analysing the simple example of a common cause, from which a quantum version of Reichenbach’s principle is identified. This quantum principle relies on an identification of quantum conditional independence which can be defined in four ways, each naturally generalising a corresponding definition for classical conditional independence. Not only does this allow one to reason about common causes in a quantum experiments, but it can also be generalised to a full framework of quantum causal models (mirroring how classical causal models generalise Reichenbach’s principle). This new definition of quantum causal models is illustrated by examples and strengthened by it’s foundation on a robust quantum Reichenbach’s principle. An unusual, but surprisingly fruitful, setting for considering quantum ontology is found by considering time travel to the past. This provides a testbed for different ontological concepts in quantum theory and new ways to compare classical and quantum frameworks. It is especially useful for comparing computational properties. In particular, time travel introduces non-linearity to quantum theory, which brings (sometimes implicit) ontological assumptions to the fore while introducing strange new abilities. Here, a model for quantum time travel is presented which arguably has fewer objectionable features than previous attempts, while remaining similarly well-motivated. This model is discussed and compared with previous quantum models, as well as with the classical case. Together, these threads of investigation develop a better understanding of how quantum theory affects possible ontologies and how ontological prejudices influence quantum theory.
We propose a rigorous synthesis of the ancient Indra’s Net metaphor with Relational Quantum Dynamics (RQD), casting quantum reality as a web of relationships formalized in category-theoretic and information-theoretic terms. Drawing on enriched category theory and measures like quantum mutual information and integrated information Φ, we develop a formal framework in which quantum systems (observers) and their states emerge only through relations – “jewels” reflecting one another. We define the mathematical structure of RQD as a category of relational contexts, proving that each quantum object is fully characterized by its morphisms (relations) to all others, in accordance with the Yoneda lemma. This theorem formally mirrors Indra’s Net by showing that each part reflects the whole, with no observer-independent properties. We further enrich the category with information metrics, demonstrating how quantum mutual information quantifies the “reflections” (correlations) between nodes, and how the integrated information Φ of the whole exceeds the sum of parts. Key theorems establish the consistency of this relational ontology resolving Wigner’s-friend-type paradoxes without requiring a global collapse and providing bounds on information integration in a fully interconnected “Indra’s net” state. We explore applications of the framework to consciousness (modeling observer-awareness via Φ in a relational network), to artificial intelligence (multi-agent systems as Indra’s net of information-sharing observers), and to quantum computing (entangled qubit networks as physical instantiations of Indra’s net). This work unifies metaphysical insights with quantum foundations in a fully formal manner, suggesting that quantum mechanics, information, and consciousness coalesce into a single relational web.