Andrey M. Kuznetsov

Is the solid, predictable world we experience reality in its fundamental form, or is it a beautifully orchestrated interface, carefully carved out of a cosmic potential? For centuries, science and philosophy have tried to corner the mysteries of consciousness, logic, and the self by confining them to separate, rigid boxes. This book breaks those boxes open, inviting the reader on an extraordinary intellectual journey. Vessels of the Void is a multidisciplinary inquiry designed for intellectual gourmands—scientists, philosophers, and deep thinkers who refuse to settle for simplistic answers. It is an exploration of how the human mind handles the ultimate paradox: how Everything and Nothing collapse into a single identity, and how a stable universe emerges from this creative tension. Rather than offering a superficial glance at disparate topics, the author establishes a careful, unified bridge connecting seemingly incompatible realms: The Metaphysical Depths: The ancient paradoxes of Buddhist emptiness (Nāgārjuna’s Śūnyatā) and Eastern antinomies (Pavel Florensky) meet Western existentialism (Jean-Paul Sartre) to redefine the very nature of human subjectivity. The Quantum and Biological Hardware: John Wheeler’s Participatory Universe joins forces with modern cognitive neuroscience (Anil Seth’s "controlled hallucinations" and Donald Hoffman’s interface theory) to map how the brain stabilizes the infinite void into space and time. The Formal Framework: Drawing on Yuri Ivlev’s foundational work on quasi-matrix logic, the author explores an intriguing new direction: Resolution Matrix Semantics (RMS) and Quantum-Inspired Poly-Logic (QPL). This framework suggests that human intuition is not a mystical flaw, but an emergent inference born from a fluid superposition of multiple concurrent logics. The Future of Mind and Machine: The book applies these insights to the current crisis of Large Language Models (LLMs), explaining why modern AI faces fundamental limitations under Gödelian incompleteness, and how poly-logical models might pave the way for true Artificial Intuition and paradox-free machine ethics. Vessels of the Void is a quiet, rewarding, and deeply engaging meditation on the mechanics of observation. Whether you are a professional logician seeking a new semantic paradigm, a cognitive scientist exploring the boundaries of the mind, or a reader dedicated to deep self-development, this book will challenge you to look at the architecture of your own awareness through a beautifully multi-dimensional lens.

This article argues that the world available to perception is not reality in its final or immediate form, but a manifestation of a deeper unmanifest domain through observation, neural mediation, and selective stabilization. The unmanifest is understood not as nothingness, but as a prephenomenal field in which objects, spatial boundaries, temporal order, and determinate histories have not yet fully emerged. The argument proceeds along three lines: structural affinities between neural networks and the cosmic web; the relation between quantum indeterminacy and statistical regularity; and participatory approaches to observation associated with John Wheeler. On this basis, I propose Quantum-Inspired Poly-Logic (QPL) as a formal framework for modeling manifestation. QPL describes how competing logical possibilities may coexist prior to stabilization and how a determinate phenomenal order may emerge through their resolution. Space, time, form, and history are thus interpreted not as absolutely primitive features of being, but as emergent products of manifestation.

This paper is written in the form of a philosophical essay rather than a technical academic article. It examines the assumption of a separate subject as a structural feature of thought rather than as an established ontological fact. Beginning from the formulation “Everything is Nothing,” the essay explores how the idea of a centered subject emerges through language, abstraction, and narrative continuity, and how this assumption shapes experience, fear, control, and the understanding of knowledge. The text argues that subjectivity is not discovered but inferred, arising from linguistic and cultural habits that reify processes into entities. By analyzing themes such as human embeddedness in environment, the role of language in producing metaphysical illusions, the misdirection of self-care, and the fear of death as fear of dissolution, the essay develops a view of reality as process without a central owner or observer. Rather than proposing a method, practice, or metaphysical system, the essay offers a conceptual reorientation: an examination of what remains when the assumption of a separate subject is withdrawn, and how meaning, knowledge, and action appear in the absence of a center.

Intuition is often treated as an essentially non-formal faculty that resists logical modeling and algorithmic explanation. This paper challenges that view by introducing a quantum-inspired poly-logical framework in which intuition emerges as a formally definable inferential phenomenon. Indeterminacy is reinterpreted not as incomplete information but as logical superposition, and reasoning agents are modeled as operating in superpositions of incompatible logics. In this setting, inference is not confined to any single logic: emergent inference occurs when a conclusion is accepted at the superposed level even though it is derivable in none of the component logics. Such conclusions are defined as instances of artificial intuition, arising through logical interference and collapse. The framework provides a constructive account of insight, offers a non-monological perspective on Gödelian limitations, and suggests applications to artificial intelligence, normative reasoning, and models of rational agency.

Human thinking does not proceed within a single logic. It stabilizes meaning at the intersection of multiple, partially incompatible logics while tolerating indeterminacy. This paper develops quantum-inspired polylogical systems - formal framework in which this cognitive fact becomes a principle of inference. Building on Resolution Matrix Semantics, indeterminate truth values are interpreted as semantic superpositions, and logical systems themselves form a space of interacting constraints. Inference is reconceived not as derivation within a fixed logic, but as the emergence of stable semantic configurations through interference and suppression. Unlike conventional quantum AI, which accelerates classical reasoning, the proposed model alters the semantics of inference itself. Poly-Logic Quantum AI thus offers a structural model of human reasoning—one that explains coherence without certainty, context sensitivity without logic switching, and the emergence of new ideas without randomness. The result is a theory of artificial reasoning closer to human thinking than to calculation.

This paper explores an alternative non-relational semantics for modal logic, framing modal systems as "poly-logics"—intersections of simpler, foundational logics. Building on pioneering work by J. Kearns and subsequent developments, we demonstrate how established systems such as K series (K, K4, K5, K45), KD series (KD, KD4, KD5, KD45), KB series (KDB, KB, KB4, KB5, KB45) emerge as intersections of logics like KT, KTB, FN, TR, and their extensions. Utilizing Resolution Matrix Semantics (RMS), we establish soundness and completeness for key systems with sketched proofs and introduce an innovative tableau-based proof procedure tailored to RMS. This approach not only unifies disparate modal frameworks but also yields efficient algorithmic tools for validity checking, offering fresh insights into the algebraic structure of modal deduction. Examples illustrate the method's efficacy, highlighting its advantages over traditional Kripke-style model checking.

This paper develops formal semantics and tableau-based proof procedures for several modal logics using Resolution Matrix Semantics (RMS), a non-relational approach that employs determinate truth values (tn, tc, fc, fn) alongside indeterminate values (true t, false f, both t/f). Unlike Kripke's relational models, which excel in relational contexts, RMS offers a productive alternative for modeling elusive precision, akin to quantum indeterminacy, while preserving modal distinctions. A tableau method is introduced, extending classical decomposition rules to RMS truth values. Branching rules for connectives and □ handle determinate and indeterminate cases, with dual algorithms (FA for f, TFA for t/f) for KD and K. Examples demonstrate validity (e.g., □p → p in KT, □p → ¬□¬p in KD) and non-validity (e.g., p → □◇p in KT), closing all branches for theorems. These contributions enhance RMS's applicability, providing efficient, non-relational tools for modal reasoning without worlds.

The paper examines the interplay of classical concept theory, Buddhist philosophy, and Russian metaphysics, focusing on the inverse relationship between a concept’s content and extension. It shows that a concept with infinite content, including contradictory attributes, has a null extension, making it “empty.” This is interpreted through Buddhist śūnyatā (Madhyamaka, Diamond Sutra) and linked to Solovyov’s “all-unity” and Florensky’s “antinomy.” Using non-classical logic (dialectical, multi-valued, quantum), it establishes the equivalence of “everything” and “nothing.” The analysis connects these ideas across philosophical traditions and highlights their relevance to modern science, including ecology, AI, and complex systems.

The paper explores consciousness as a projection of an "unmanifest world"—a primordial medium of "all and nothing"—onto human perception, drawing on Buddhist philosophy, Plato’s allegory of the cave, and contemporary science. Inspired by Nāgārjuna’s śūnyatā, Yogācāra’s vijñāna, and Plato’s depiction of shadows as perceived reality, it posits that neurons filter this indeterminate potential into a perceived reality of objects, time, and dualities, rendering the world an illusion (māyā) with conditional legitimacy (saṃvṛti-satya). Neuroscience supports this, revealing perception as an active neural construct, while quantum mechanics and Hoffman’s interface theory suggest a deeper, unmanifest substrate. The paper speculates on constructing consciousness as a modular system, leveraging bioengineering (e.g., CRISPR, organoids), neurotechnology (e.g., BCIs, artificial neurons), and quantum engineering to perceive alternate realities—novel objects, altered time, multidimensionality. As understanding consciousness as a complex interference grid advances, its construction may become routine, potentially democratizing the creation of conscious entities and reshaping societal views on the self, aligning with Buddhist notions of emptiness and interconnectedness. Critical reflections contrast materialist reductions with panpsychist possibilities, questioning whether such engineering accesses the unmanifest or crafts new illusions. Bridging metaphysics, science, and technology, this synthesis envisions humans as architects of perception, illuminating consciousness’s paradoxical nature: a shadow that both "is and is not," uniting ancient wisdom with future potential.

N. Vasiliev’s early 20th-century concept of multidimensional logic, developed alongside L. Brouwer and J. Lukasiewicz, proposes a non-Aristotelian framework. It distinguishes logical laws into external (gussiological) and internal levels. The external level follows multidimensional principles and the law of the excluded middle, while the internal level depends on endalogous assumptions about the cognizable world. In a one-dimensional world, only positive statements are atomic, with negative statements arising from inference, underscoring the constraints of directly expressing negation.

Resolution Matrix Semantics (RMS) proposes a new modal logic approach to model poly-logic cognition—the capacity to reason through multiple logical perspectives concurrently—leveraging indeterminate truth values and sub-interpretations. Inspired by Vladimir Bibler’s dialogic logic, RMS captures the pluralistic, dynamic essence of human thought, blending logical, emotional, and contextual dimensions to address ambiguity. In contrast to conventional education’s mono-logic, textbook-centric methods, RMS advocates for poly-logic pedagogical strategies, such as Socratic dialogues, exploratory discussions, and open-ended inquiries, to align with natural cognitive processes. Empirical support from dialogic teaching studies underscores RMS’s potential to foster critical thinking, cognitive adaptability, and student engagement, equipping learners for complex real-world issues. Furthermore, RMS informs the development of educational technologies, enabling adaptive systems to process diverse interpretive threads, thus reimagining learning as a dynamic, dialogic process.

This paper introduces Resolution Matrix Semantics (RMS), a novel framework for modal logic that prioritizes indeterminate truth values and sub-interpretations over traditional relational structures, offering a poly-logic model that mirrors human cognition. Drawing on Vladimir Bibler’s concept of poly-logic substantive control, RMS captures the pluralistic, concurrent nature of human reasoning by evaluating logical formulas across multiple interpretive threads, resolving ambiguities akin to quantum cognitive processes. By integrating insights from quantum cognition, neuroscience, and parallel computing, the paper argues that RMS reflects the brain’s intrinsic ability to navigate uncertainty through superposition-like states and entangled judgments. Philosophically, RMS challenges classical mono-logic assumptions, aligning with non-classical logics and pluralistic epistemologies. Its implications extend to AI, NLP, and quantum computing, promising rapid, precise decision-making under uncertainty. RMS thus redefines rationality as a dynamic, dialogic process, bridging logic, cognition, and the fundamental indeterminacy of reality.

The use of a quasi-functional approach to formalize a system of five-valued deontic logic is one of the central objectives of the dissertation research. The aim of the dissertation is to investigate a system of five-valued deontic logic, whose language includes, in addition to modal operators describing "official" norms, denoted as О ("obligatory") and Р ("permitted"), operators representing unofficial, "moral" attitudes, denoted as Оm ("morally approved") and Рm ("morally permitted"). In accordance with the stated objective, the dissertation addresses the following tasks: - Formalize a system of five-valued deontic logic using the quasi-functional method. - Relevatize the resulting system. - Drawing on the analogy between alethic and deontic logic systems, formalize a semantically defined system based on the natural system of relevant implication Еп. - Construct five-valued quasi-functional logics based on other non-standard semantics, in particular, the semantics of truth gaps and the semantics of saturated valuations, and formalize the systems defined semantically.

The Resolution Matrix Semantics (RMS) framework, inspired by Y. Ivlev’s quasi-matrix approach [Ivlev, 1997], formalizes deontic logic using a truth-value-based system. It employs normative values—mandatory (m), indifferent (i), and forbidden (b)—for acts, and true (t) or false (f) for formulas, distinguishing normative and propositional domains. RMS incorporates indeterminate truth values (m/i, “either m or i”) and an interpretation mechanism to resolve them, enabling precise normative evaluations. The deontic system SDLm mirrors Standard Deontic Logic (SDL) axiomatically but avoids paradoxes like Chisholm and Gentle Murderer. SDLm’s soundness and completeness are proven, with tableau rules for automated theorem verification. By focusing on normative status, SDLm provides a paradox-free framework for reasoning about obligations, permissions, and prohibitions, applicable in ethics, law, and artificial intelligence.

We use non-relational semantics for the formalization of the systems S3d, S3dp and S3dq of deontic logic. The system S3d is weaker than the standard logic SDL. The semantics for S3dp represents combination of quasi-matrix semantics and the semantics of truth value gluts, which allows S3dp to avoid deontic explosion OA ∧ O¬A ⊃ OB. The system S3dq rejects both deontic explosion and the formula OA ∧ O¬A ⊃ OA ∧ ¬OA, thus it allows to consider deontic dilemmas without classical contradictions. The systems S5d, S5dp and S5dq in which the two types of deontic operators are used, namely, strong and weak obligation (permission), can be built as an extension of the correspondent systems S3d, S3dp and S3dq.

A multidimensional pseudo-Boolean algebra is constructed based on generalized sequences of classes, drawing on N.A. Vasiliev's philosophical ideas and V.A. Smirnov's formalizations. Vasiliev's non-Aristotelian logics, which challenge the laws of non-contradiction and the excluded middle, are extended to n-dimensional logics where atomic statements represent positive, negative, or indifferent states. Finite linear sequences are generalized into partially ordered sequences, forming an implicative lattice with defined intersection and union operations. This structure satisfies the properties of a pseudo-Boolean algebra, providing a formal framework for multidimensional logics applicable to imaginary and normative scenarios, such as deontic logic. The approach parallels non-Euclidean geometry, offering a novel perspective on logical systems and their ontological implications.

A decision procedure for the Guarded Fragment (GF) of First-Order Logic (FOL) is introduced, based on Deduction Chains (DC) and inspired by K. Schütte's completeness proof for FOL. The DCL algorithm, a DC-like method tailored for GF, mirrors the tableau algorithm while using a blocking technique to ensure termination. Defined by Andréka, van Benthem, and Németi, GF generalizes modal, temporal, and description logics, maintaining decidability and finite model properties. Operating on formulas in negation normal form, the DCL algorithm handles guarded quantifiers and equality, and is proven sound and complete. Termination is established through bounds on the completion tree's nodes, demonstrating effectiveness in determining GF formula validity, with satisfiability being 2EXPTIME-complete. The approach extends to weaker variants, such as loosely guarded and clique guarded fragments, and their fixed-point extensions.

This paper explores the philosophical implications of Resolution Matrix Semantics (RMS) as an alternative foundation for modal logic. Unlike traditional Kripkean models, which interpret modality through relations between multiple possible worlds governed by classical logic, RMS treats indeterminate truth values as fundamental, operating within a single world. RMS introduces "blinking" truth assignments and sub-interpretations to resolve uncertainty, capturing the inherently poly-logical nature of human thought. Drawing a parallel to quantum physics, we argue that Kripke models resemble Everett’s Many-Worlds interpretation, while RMS aligns with the Copenhagen interpretation’s emphasis on intrinsic uncertainty. RMS offers a new view of modal reasoning—not as a proliferation of worlds, but as a diversification of perspectives within one world. The framework’s philosophical significance is examined through connections to poly-logic thinking, quantum cognitive models, and potential applications in artificial intelligence and parallel computing. RMS ultimately provides a dynamic, pluralistic model for rationality that better reflects the complexity of human cognition and decision-making under uncertainty.

Resolution Matrix Semantics (RMS) introduces the alternative truth-value-based framework for modal logic, providing a substantive alternative to Kripke’s relational semantics of possible worlds. Drawing inspiration from Y. Ivlev’s substantive semantics, RMS utilizes a 4-valued structure—necessary truth (tn), contingent truth (tc), contingent false (fc), and necessary false (fn)—augmented by indeterminate values (t, f, t/f) to define modal systems Km, KDm, KTm, S4m, and S5m, analogous to Kripke’s K, KD, T, S4, and S5. By directly assigning determined and indeterminate truth values via an interpretation function, RMS validates formulas without relying on accessibility relations, as demonstrated through soundness and completeness proofs and a tailored tableau method. The framework’s versatility extends to applications in deontic logic, artificial intelligence, and quantum computing, enabling context-dependent reasoning with computational efficiency. RMS thus bridges philosophical logic and practical domains, offering a truth-centric perspective on modal reasoning’s complexities.