Modal Logic for Stratified Becoming: Actualization Beyond Possible Worlds

• URL: http://arxiv.org/abs/2506.17276v1
• Date: Thu, 12 Jun 2025 18:35:01 GMT
• Title: Modal Logic for Stratified Becoming: Actualization Beyond Possible Worlds
• Abstract summary: This article develops a novel framework for modal logic based on the idea of stratified actualization.<n>Traditional Kripke semantics treat modal operators as quantification over fully determinate alternatives.<n>We propose a system Stratified Actualization Logic (SAL) in which modalities are indexed by levels of ontological stability, interpreted as admissibility.
• Score: 55.2480439325792
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This article develops a novel framework for modal logic based on the idea of stratified actualization, rather than the classical model of global possible worlds. Traditional Kripke semantics treat modal operators as quantification over fully determinate alternatives, neglecting the local, dynamic, and often asymmetric nature of actualization processes. We propose a system Stratified Actualization Logic (SAL) in which modalities are indexed by levels of ontological stability, interpreted as admissibility regimes. Each modality operates over a structured layer of possibility, grounded in the internal coherence of transitions between layers. We formally define the syntax and semantics of SAL, introduce its axioms, and prove soundness and completeness. Applications are discussed in connection with temporal becoming, quantum decoherence domains, and modal metaphysics. The result is a logic that captures the ontological structure of actualization without recourse to abstract possible worlds, offering a stratified alternative to standard modal realism.

Related papers

• iFuzz-Meta: An Interpretable Fuzzy Learning Framework Bridging Top-Down and Bottom-Up Knowledge Integration [25.176188581821112]
  iFuzz-Meta is an interpretable fuzzy rule-based learning framework.<n>It preserves human-understandable reasoning structures within modern neural architectures.
  arXiv  Detail & Related papers  (2026-07-30T02:44:54Z)
• From Application-Layer Simulation to Native Meta-Architecture: Structural Tension as an Endogenous Driver for Heterogeneous AI Evolution [0.0]
  Current large language models (LLMs) are stateless across inference sessions.<n>This paper proposes a theoretical framework for submerging such application-layer cognitive protocols into a native meta-architecture.
  arXiv  Detail & Related papers  (2026-07-07T13:34:27Z)
• Sheaf-Theoretic Planning: A Categorical Foundation for Resilient Multi-Agent Autonomous Systems [0.0]
  Sheaf-Theoretic Planning (STP) is a transformative alternative to traditional multi-agent system (MAS)<n>STP emerges as a transformative alternative, grounding the problem of multi-agent coordination under the mathematical structures of topos theory and sheaf semantics.<n>This report provides an exhaustive analysis, justification, and extension of the resilient framework, exploring its categorical foundations, implementation feasibility, and role in the future of autonomous systems.
  arXiv  Detail & Related papers  (2026-05-03T13:50:24Z)
• Chain of Modality: From Static Fusion to Dynamic Orchestration in Omni-MLLMs [84.3271821505699]
  Chain of Modality (CoM) is an agentic framework that transitions multimodal fusion from passive concatenation to dynamic orchestration.<n> operating in either a training-free or a data-efficient SFT setting, CoM achieves robust and consistent generalization across diverse benchmarks.
  arXiv  Detail & Related papers  (2026-04-16T01:21:14Z)
• OMNIFLOW: A Physics-Grounded Multimodal Agent for Generalized Scientific Reasoning [51.33849811496781]
  Large Language Models (LLMs) have demonstrated exceptional logical reasoning capabilities but frequently struggle with the continuous dynamics by Partial Differential Equations (PDEs)<n>We propose OMNIFLOW, a multimodal-symbolic architecture designed to ground frozen LLMs in fundamental physical laws without requiring domain-specific parameter updates.<n>We evaluate it on a benchmark spanning microscopic turbulence, theoretical Navier-Stokes, and macroscopic global weather forecasting.
  arXiv  Detail & Related papers  (2026-03-16T18:29:01Z)
• The Trinity of Consistency as a Defining Principle for General World Models [106.16462830681452]
  General World Models are capable of learning, simulating, and reasoning about objective physical laws.<n>We propose a principled theoretical framework that defines the essential properties requisite for a General World Model.<n>Our work establishes a principled pathway toward general world models, clarifying both the limitations of current systems and the architectural requirements for future progress.
  arXiv  Detail & Related papers  (2026-02-26T16:15:55Z)
• Continual learning and refinement of causal models through dynamic predicate invention [0.6198237241838559]
  We propose a framework for constructing symbolic causal world models entirely online.<n>We leverage the power of Meta-Interpretive Learning and predicate invention to find semantically meaningful and reusable abstractions.
  arXiv  Detail & Related papers  (2026-02-19T10:08:31Z)
• Aligning Agentic World Models via Knowledgeable Experience Learning [68.85843641222186]
  We introduce WorldMind, a framework that constructs a symbolic World Knowledge Repository by synthesizing environmental feedback.<n>WorldMind achieves superior performance compared to baselines with remarkable cross-model and cross-environment transferability.
  arXiv  Detail & Related papers  (2026-01-19T17:33:31Z)
• Modal Logical Neural Networks [0.15229257192293197]
  We propose Modal Logical Neural Networks (MLNNs), a neurosymbolic framework that integrates deep learning with the formal semantics of modal logic.<n>We show how enforcing or learning accessibility can increase logical consistency and interpretability without changing the underlying task architecture.
  arXiv  Detail & Related papers  (2025-12-03T06:38:29Z)
• Explainable Chain-of-Thought Reasoning: An Empirical Analysis on State-Aware Reasoning Dynamics [69.00587226225232]
  We introduce a state-aware transition framework that abstracts CoT trajectories into structured latent dynamics.<n>To characterize the global structure of reasoning, we model their progression as a Markov chain.<n>This abstraction supports a range of analyses, including semantic role identification, temporal pattern visualization, and consistency evaluation.
  arXiv  Detail & Related papers  (2025-08-29T18:53:31Z)
• Dynamics-Aligned Latent Imagination in Contextual World Models for Zero-Shot Generalization [1.6332728502735252]
  We introduce Dynamics-Aligned Latent Imagination (DALI), a framework that infers latent context representations from agent-environment interactions.<n>DALI generates actionable representations conditioning the world model and policy, bridging perception and control.<n>On challenging cMDP benchmarks, DALI achieves significant gains over context-unaware baselines.
  arXiv  Detail & Related papers  (2025-08-27T22:02:56Z)
• CTRLS: Chain-of-Thought Reasoning via Latent State-Transition [57.51370433303236]
  Chain-of-thought (CoT) reasoning enables large language models to break down complex problems into interpretable intermediate steps.<n>We introduce groundingS, a framework that formulates CoT reasoning as a Markov decision process (MDP) with latent state transitions.<n>We show improvements in reasoning accuracy, diversity, and exploration efficiency across benchmark reasoning tasks.
  arXiv  Detail & Related papers  (2025-07-10T21:32:18Z)
• Policy Regularization on Globally Accessible States in Cross-Dynamics Reinforcement Learning [53.9544543607396]
  We propose a novel framework that integrates reward rendering with Imitation from Observation (IfO)<n>By instantiating F-distance in different ways, we derive two theoretical analysis and develop a practical algorithm called Accessible State Oriented Policy Regularization (ASOR)<n>ASOR serves as a general add-on module that can be incorporated into various approaches RL, including offline RL and off-policy RL.
  arXiv  Detail & Related papers  (2025-03-10T03:50:20Z)
• Standard Neural Computation Alone Is Insufficient for Logical Intelligence [3.230778132936486]
  We argue that standard neural layers must be fundamentally rethought to integrate logical reasoning.<n>We advocate for Logical Neural Units (LNUs)-modular components that embed differentiable approximations of logical operations.
  arXiv  Detail & Related papers  (2025-02-04T09:07:45Z)
• Advancing Interactive Explainable AI via Belief Change Theory [5.842480645870251]
  We argue that this type of formalisation provides a framework and a methodology to develop interactive explanations. We first define a novel, logic-based formalism to represent explanatory information shared between humans and machines. We then consider real world scenarios for interactive XAI, with different prioritisations of new and existing knowledge, where our formalism may be instantiated.
  arXiv  Detail & Related papers  (2024-08-13T13:11:56Z)
• Unifying different notions of quantum incompatibility into a strict hierarchy of resource theories of communication [60.18814584837969]
  We introduce the notion of q-compatibility, which unifies different notions of POVMs, channels, and instruments incompatibility. We are able to pinpoint exactly what each notion of incompatibility consists of, in terms of information-theoretic resources.
  arXiv  Detail & Related papers  (2022-11-16T21:33:31Z)
• Provable Hierarchy-Based Meta-Reinforcement Learning [50.17896588738377]
  We analyze HRL in the meta-RL setting, where learner learns latent hierarchical structure during meta-training for use in a downstream task. We provide "diversity conditions" which, together with a tractable optimism-based algorithm, guarantee sample-efficient recovery of this natural hierarchy. Our bounds incorporate common notions in HRL literature such as temporal and state/action abstractions, suggesting that our setting and analysis capture important features of HRL in practice.
  arXiv  Detail & Related papers  (2021-10-18T17:56:02Z)
• Functoriality of Quantum Resource Theory and Variable-Domain Modal Logic [0.0]
  I show that quantum resource theories may be functorially translated into models of variable-domain S4 modal logic. I then extend this functorial relationship to an injective one by adding structure to these logical models.
  arXiv  Detail & Related papers  (2020-06-29T20:11:32Z)
• Logical Neural Networks [51.46602187496816]
  We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning) Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a highly intepretable disentangled representation. Inference is omni rather than focused on predefined target variables, and corresponds to logical reasoning.
  arXiv  Detail & Related papers  (2020-06-23T16:55:45Z)
• Solvable Criterion for the Contextuality of any Prepare-and-Measure Scenario [0.0]
  An operationally noncontextual ontological model of the quantum statistics associated with the prepare-and-measure scenario is constructed. A mathematical criterion, called unit separability, is formulated as the relevant classicality criterion. We reformulate our results in the framework of generalized probabilistic theories.
  arXiv  Detail & Related papers  (2020-03-13T18:00:05Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.