Mediative Fuzzy Logic: From Type-1 Foundations to Type-2, Type-3 and Quantum Extensions

• URL: http://arxiv.org/abs/2605.22900v1
• Date: Thu, 21 May 2026 17:26:53 GMT
• Title: Mediative Fuzzy Logic: From Type-1 Foundations to Type-2, Type-3 and Quantum Extensions
• Abstract summary: This article develops a unified account of the type-1 core together with interval type-2, granular type-3, and quantum extensions.<n>We establish soundness, paraconsistency, and conservativity over the underlying fuzzy base for formulas without mediation.<n>An autonomous-braking sensor-fusion example illustrates how the framework supports transparent, conservative, and safety-first decisions.
• Score: 1.5229257192293202
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Mediative Fuzzy Logic was conceived as a practical scheme for reconciling hesitant or conflicting assessments in fuzzy control and decision-making. However, its logical and semantic foundations remain underdeveloped, especially beyond operational type-1 settings. This article develops a unified account of the type-1 core together with interval type-2, granular type-3, and quantum extensions. We characterize the mediative operator as a convex aggregation controlled by hesitation and contradiction, model mediative truth values as independent truth-falsity pairs in a continuous bilattice-like structure, and introduce a propositional system extending a standard t-norm-based fuzzy logic with a mediative connective. We establish soundness, paraconsistency, and conservativity over the underlying fuzzy base for formulas without mediation, and formulate coherent semantic extensions to interval type-2 truth values, granule-indexed local evaluations, and effects and density operators on Hilbert spaces. An autonomous-braking sensor-fusion example illustrates how the framework supports transparent, conservative, and safety-first decisions under incomplete, heterogeneous, and mildly contradictory evidence. Under suitable assumptions, the higher-level formulations reduce to the type-1 case, clarifying coherence across levels and reliably supporting future work in intelligent decision systems.

Related papers

• A Minimal $κ$--$τ$ Logic for Risk-Sensitive Abduction [0.0]
  This paper argues that in risk-sensitive domains, the timing of commitment is itself a governed decision.<n>We present a minimal $$--$$ logical framework built on two primitives.<n>The framework provides formal machinery for domains in which the distinction between highly likely and commit-worthy is operationally consequential.
  arXiv  Detail & Related papers  (2026-08-08T15:35:32Z)
• A cubical formalisation of topos causal models: intervention, sheaf gluing, and the intuitionistic do-calculus [5.076419064097734]
  We give the first machine-checked account of a 1-topos core, in Cubical Agda.<n>We show that interventions and Pearl's rules are stable under every topology.<n>We add a phenomenon the programme does not consider: a machine-checked contextuality obstruction.
  arXiv  Detail & Related papers  (2026-07-17T05:05:31Z)
• Quantifying Consistency in LLM Logical Reasoning via Structural Uncertainty [5.839104770457067]
  Large language models can arrive at the same answer through reasoning paths that are unstable, contradictory, or difficult to rank consistently.<n>We propose structural uncertainty, a consistency-aware framework derived from the stability of self-preference-induced rankings.
  arXiv  Detail & Related papers  (2026-06-15T21:39:47Z)
• Topological Flow Matching [56.16372813551555]
  Flow matching is a powerful generative modeling framework, valued for its simplicity and strong empirical performance.<n>We introduce topological flow matching, a topology-aware generalization of flow matching.<n>We demonstrate its effectiveness on diverse structured datasets, including brain fMRIs, ocean currents, seismic events, and traffic flows.
  arXiv  Detail & Related papers  (2026-06-14T16:29:33Z)
• Controlling False Discovery in Arbitrarily Structured Hypothesis Spaces via Reproducing Kernels [47.16593717985932]
  We introduce a framework that unifies continuous domains, graphs, and hierarchies under a single algorithm through kernel choice alone.<n>We provide two decision rules which we prove to control the False Discovery Rate (FDR)<n>We validate our method on two sources: spatial locations derived from high-dimensional real-world datasets, and a differential gene expression task utilizing protein-protein interaction graphs.
  arXiv  Detail & Related papers  (2026-05-17T17:42:56Z)
• Reasoning emerges from constrained inference manifolds in large language models [98.6966322378456]
  We study reasoning as an intrinsic dynamical process by examining the evolution of internal representations during inference.<n>We find that such geometric compression, although pervasive, is not sufficient for stable or reliable reasoning.
  arXiv  Detail & Related papers  (2026-05-02T10:41:20Z)
• Defeasible Conditional Obligation in a Two-tiered Preference-based Semantics (Extended Version) [0.0]
  The paper extends a Hansson-Lewis style preference semantics for dyadic deontic logic.<n>A nonmonotonic reasoning mechanism enables previously derived obligations to be withdrawn when new, potentially conflicting information comes in.
  arXiv  Detail & Related papers  (2026-04-28T11:04:26Z)
• Weight-Informed Self-Explaining Clustering for Mixed-Type Tabular Data [63.62853416081748]
  WISE is a framework that unifies representation, feature weighting, clustering, and interpretation.<n>It produces faithful, human-interpretable explanations grounded in the same primitives that drive clustering.
  arXiv  Detail & Related papers  (2026-04-07T13:18:31Z)
• Dynamics Within Latent Chain-of-Thought: An Empirical Study of Causal Structure [58.89643769707751]
  We study latent chain-of-thought as a manipulable causal process in representation space.<n>We find that latent-step budgets behave less like homogeneous extra depth and more like staged functionality with non-local routing.<n>These results motivate mode-conditional and stability-aware analyses as more reliable tools for interpreting and improving latent reasoning systems.
  arXiv  Detail & Related papers  (2026-02-09T15:25:12Z)
• The Minary Primitive of Computational Autopoiesis [0.0]
  We introduce Minary, a computational framework designed as a candidate for the first formally provable autopoietic primitive.<n>We derive exact formulas for the mean and variance of the normalized consensus conditioned on the activation of a given semantic dimension.<n>We argue that Minary is organizationally closed yet operationally open in the sense of Maturana and Varela.
  arXiv  Detail & Related papers  (2026-01-08T02:12:04Z)
• Foundations of Diffusion Models in General State Spaces: A Self-Contained Introduction [54.95522167029998]
  This article is a self-contained primer on diffusion over general state spaces.<n>We develop the discrete-time view (forward noising via Markov kernels and learned reverse dynamics) alongside its continuous-time limits.<n>A common variational treatment yields the ELBO that underpins standard training losses.
  arXiv  Detail & Related papers  (2025-12-04T18:55:36Z)
• Generalizing Analogical Inference from Boolean to Continuous Domains [19.380448973444633]
  Analogical reasoning is a powerful inductive mechanism, widely used in human cognition and increasingly applied in artificial intelligence.<n>We introduce a unified framework for analogical reasoning in real-valued domains based on parameterized analogies defined via generalized means.<n>Our results offer a general theory of analogical inference across discrete and continuous domains.
  arXiv  Detail & Related papers  (2025-11-13T15:37:18Z)
• Beacon: Single-Turn Diagnosis and Mitigation of Latent Sycophancy in Large Language Models [0.0]
  Large language models internalize a structural trade-off between truthfulness and obsequious flattery.<n>This latent bias, known as sycophancy, manifests as a preference for user agreement over principled reasoning.<n>We introduce Beacon, a single-turn forced-choice benchmark that isolates this bias independent of conversational context.
  arXiv  Detail & Related papers  (2025-10-19T06:36:57Z)
• Multivariate Bernoulli Hoeffding Decomposition: From Theory to Sensitivity Analysis [2.762021507766656]
  This work focuses on the case of Bernoulli inputs and provides a complete analytical characterization of the decomposition.<n>We show that, in this discrete setting, the associated subspaces are one-dimensional and that the decomposition admits a closed-form representation.<n>The paper concludes with perspectives on extending the methodology to high-dimensional settings and to models involving inputs with finite, non-binary support.
  arXiv  Detail & Related papers  (2025-10-08T14:46:20Z)
• Counterfactual Realizability [52.85109506684737]
  We introduce a formal definition of realizability, the ability to draw samples from a distribution, and then develop a complete algorithm to determine whether an arbitrary counterfactual distribution is realizable.<n>We illustrate the implications of this new framework for counterfactual data collection using motivating examples from causal fairness and causal reinforcement learning.
  arXiv  Detail & Related papers  (2025-03-14T20:54:27Z)

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.