pith. sign in

arxiv: 2604.20944 · v1 · submitted 2026-04-22 · 💻 cs.LG · cs.AI

LAF-Based Evaluation and UTTL-Based Learning Strategies with MIATTs

Yongquan Yang This is my paper

Pith reviewed 2026-05-10 01:19 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords machine learninguncertain supervisionmultiple inaccurate true targetslogical assessmentundefinable true target learningevaluation algorithmslearning strategies
0
0 comments X

The pith

LAF evaluation algorithms and UTTL learning strategies enable coherent machine learning modeling when true targets are ambiguous or subjective.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops practical mechanisms for machine learning tasks where the true target cannot be precisely defined because of ambiguity or subjectivity. It first examines how the coverage and diversity of multiple inaccurate true targets shape their structural properties and affect evaluation and training. From this, it formulates LAF-based evaluation algorithms that work on the original targets or on synthesized ternary versions, balancing interpretability with soundness and completeness. For training, it introduces UTTL-based strategies that apply Dice and cross-entropy losses either per target or in aggregated form. Together these components implement the broader EL-MIATTs framework, supplying a pathway for logically consistent and feasible modeling under uncertain supervision.

Core claim

Under the premise that a true target need not exist objectively, task-specific multiple inaccurate true targets can be analyzed for coverage and diversity, then used to ground LAF-based evaluation algorithms (operating on raw or ternary targets) and UTTL-based learning strategies (using per-target or aggregated Dice and cross-entropy optimization); their integration bridges logical semantics and statistical optimization to produce coherent, practical models.

What carries the argument

LAF (Logical Assessment Formula) for evaluation and UTTL (Undefinable True Target Learning) strategies for training, both operating on MIATTs (Multiple Inaccurate True Targets).

If this is right

  • Evaluation can be performed directly on MIATTs or on derived ternary targets while preserving soundness and completeness.
  • Training can optimize either per inaccurate target or via aggregated loss, using Dice or cross-entropy.
  • Logical semantics from LAF can be combined with statistical optimization from UTTL to guide model development.
  • The resulting systems support ML applications where ground truth is inherently uncertain rather than assumed fixed.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach could extend to domains such as medical imaging or opinion mining where labels naturally vary by expert or rater.
  • Comparing per-target versus aggregated optimization on large-scale ambiguous datasets would test which scheme scales better in practice.
  • If the framework succeeds, it suggests rethinking standard supervised-learning pipelines that presuppose a single objective target.

Load-bearing premise

The true target for a given ML task is not assumed to exist objectively in the real world.

What would settle it

Apply the LAF and UTTL methods to a benchmark dataset that has a single, objectively verifiable ground truth and measure whether performance degrades relative to standard supervised training on the same data.

Figures

Figures reproduced from arXiv: 2604.20944 by Yongquan Yang.

Figure 1
Figure 1. Figure 1: Possible patterns of task-specific MIATTs. Blue circles represent the underlying true target, while [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Geometric visualization of task-specific MIATTs. The relationship depicted by Formula (8) and [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
read the original abstract

In many real-world machine learning (ML) applications, the true target cannot be precisely defined due to ambiguity or subjectivity information. To address this challenge, under the assumption that the true target for a given ML task is not assumed to exist objectively in the real world, the EL-MIATTs (Evaluation and Learning with Multiple Inaccurate True Targets) framework has been proposed. Bridging theory and practice in implementing EL-MIATTs, in this paper, we develop two complementary mechanisms: LAF (Logical Assessment Formula)-based evaluation algorithms and UTTL (Undefinable True Target Learning)-based learning strategies with MIATTs, which together enable logically coherent and practically feasible modeling under uncertain supervision. We first analyze task-specific MIATTs, examining how their coverage and diversity determine their structural property and influence downstream evaluation and learning. Based on this understanding, we formulate LAF-grounded evaluation algorithms that operate either on original MIATTs or on ternary targets synthesized from them, balancing interpretability, soundness, and completeness. For model training, we introduce UTTL-grounded learning strategies using Dice and cross-entropy loss functions, comparing per-target and aggregated optimization schemes. We also discuss how the integration of LAF and UTTL bridges the gap between logical semantics and statistical optimization. Together, these components provide a coherent pathway for implementing EL-MIATTs, offering a principled foundation for developing ML systems in scenarios where the notion of "ground truth" is inherently uncertain. An application of this work's results is presented as part of the study available at https://www.qeios.com/read/EZWLSN.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes the EL-MIATTs framework for machine learning tasks where the true target cannot be precisely defined due to ambiguity, under the explicit assumption that the true target does not exist objectively in the real world. It develops LAF-based evaluation algorithms operating on original MIATTs or synthesized ternary targets, and UTTL-based learning strategies employing Dice and cross-entropy losses with per-target versus aggregated optimization. The work analyzes how MIATT coverage and diversity influence structural properties, discusses bridging logical semantics with statistical optimization, and references an external application study.

Significance. If the framework were substantiated with derivations and validation, it could offer a conceptual bridge for ML in domains with inherent uncertainty, such as subjective labeling or ambiguous supervision, by linking logical assessment formulas to optimization schemes. However, the current manuscript provides no empirical results, theoretical proofs, or comparisons, so its potential significance remains speculative and unverified.

major comments (3)
  1. [Abstract and sections describing LAF and UTTL mechanisms] Abstract and the sections on LAF-based evaluation algorithms and UTTL-based learning strategies: No equations, pseudocode, or explicit formulations are given for the LAF-grounded algorithms (including how they balance interpretability, soundness, and completeness on original vs. ternary targets) or for the UTTL strategies (including adaptation of Dice and cross-entropy losses). This absence is load-bearing, as the central claim of logical coherence and practical feasibility cannot be evaluated without these details.
  2. [Sections on MIATT analysis and LAF-UTTL integration] The analysis of task-specific MIATTs and the discussion of LAF-UTTL integration: The manuscript describes how coverage and diversity determine structural properties and how logical semantics integrate with statistical optimization, but provides no quantitative measures, examples, or derivations showing the influence on downstream evaluation and learning. This undermines verification of the framework's soundness.
  3. [Application section and overall results] The manuscript contains no empirical results, ablation studies, error analysis, or comparisons to existing methods for uncertain supervision. Claims of practical feasibility therefore rest solely on high-level description rather than evidence.
minor comments (2)
  1. [Title and Abstract] The title refers to 'LAF-Based Evaluation and UTTL-Based Learning Strategies with MIATTs' while the abstract introduces the broader 'EL-MIATTs' acronym; consistent definition and usage of acronyms across title, abstract, and body would improve readability.
  2. [Abstract] The link to the application study (https://www.qeios.com/read/EZWLSN) is provided without any summary of its key findings or how it demonstrates the proposed mechanisms.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the detailed and constructive report. We agree that the manuscript requires additional concrete details to allow proper evaluation of the proposed framework. We will revise to incorporate explicit formulations, examples, and a discussion of the referenced application. Our responses to the major comments are provided below.

read point-by-point responses

  1. Referee: Abstract and the sections on LAF-based evaluation algorithms and UTTL-based learning strategies: No equations, pseudocode, or explicit formulations are given for the LAF-grounded algorithms (including how they balance interpretability, soundness, and completeness on original vs. ternary targets) or for the UTTL strategies (including adaptation of Dice and cross-entropy losses). This absence is load-bearing, as the central claim of logical coherence and practical feasibility cannot be evaluated without these details.

    Authors: We agree that the absence of explicit formulations limits evaluability. The manuscript presented the framework at a conceptual level. In revision, we will add the mathematical definitions of the LAF-based evaluation algorithms, including formulas that operationalize the balance among interpretability, soundness, and completeness for both original MIATTs and synthesized ternary targets. Pseudocode for the algorithms will be included. For the UTTL strategies, we will specify the adapted Dice and cross-entropy loss functions and detail the per-target versus aggregated optimization schemes. revision: yes

  2. Referee: The analysis of task-specific MIATTs and the discussion of LAF-UTTL integration: The manuscript describes how coverage and diversity determine structural properties and how logical semantics integrate with statistical optimization, but provides no quantitative measures, examples, or derivations showing the influence on downstream evaluation and learning. This undermines verification of the framework's soundness.

    Authors: We acknowledge that the current analysis remains qualitative. The revised manuscript will define quantitative measures of MIATT coverage and diversity, supply concrete examples of task-specific MIATTs, and provide derivations demonstrating their effects on evaluation outcomes and learning objectives. These additions will make explicit the links between structural properties and the integration of logical semantics with statistical optimization. revision: yes

  3. Referee: The manuscript contains no empirical results, ablation studies, error analysis, or comparisons to existing methods for uncertain supervision. Claims of practical feasibility therefore rest solely on high-level description rather than evidence.

    Authors: The manuscript develops a theoretical framework, with an external application study referenced at https://www.qeios.com/read/EZWLSN. We agree that internal evidence would strengthen the presentation. In revision we will add a concise summary of the application outcomes and a discussion of how the framework relates to existing uncertain-supervision methods, while clarifying the conceptual scope of the current work. revision: partial

standing simulated objections not resolved
  • Comprehensive empirical results, ablation studies, error analysis, and direct comparisons, as these were outside the original scope of the conceptual framework paper and would require new experimental work.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper proposes the EL-MIATTs framework along with LAF-based evaluation algorithms and UTTL-based learning strategies as new conceptual mechanisms for ML under uncertain supervision, conditional on the explicit assumption that no objective true target exists. The derivation consists of analyzing MIATT coverage/diversity, formulating evaluation algorithms on original or synthesized ternary targets, and defining training strategies that apply standard Dice and cross-entropy losses in per-target or aggregated modes. No equations, fitted parameters, or predictions are presented that reduce by construction to the inputs; the claims of logical coherence and practical feasibility follow directly from the introduced components without self-citation chains, uniqueness theorems, or ansatzes imported from prior work. The framework is therefore self-contained as a high-level proposal.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 3 invented entities

The central claim rests on the stated domain assumption about non-objective true targets and introduces new framework components without independent evidence or external benchmarks in the abstract.

axioms (1)
  • domain assumption The true target for a given ML task is not assumed to exist objectively in the real world.
    Explicitly stated in the abstract as the foundation for the EL-MIATTs framework.
invented entities (3)
  • MIATTs (Multiple Inaccurate True Targets) no independent evidence
    purpose: Represent ambiguous or subjective targets for evaluation and learning.
    Core construct of the proposed framework.
  • LAF (Logical Assessment Formula) no independent evidence
    purpose: Ground evaluation algorithms that operate on MIATTs or synthesized ternary targets.
    New mechanism for balancing interpretability, soundness, and completeness.
  • UTTL (Undefinable True Target Learning) no independent evidence
    purpose: Ground learning strategies using Dice and cross-entropy losses with per-target or aggregated optimization.
    New mechanism for model training under uncertain supervision.

pith-pipeline@v0.9.0 · 5589 in / 1464 out tokens · 52065 ms · 2026-05-10T01:19:31.075468+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Negative Ontology of True Target for Machine Learning: Towards Evaluation and Learning under Democratic Supervision

    cs.LG 2026-04 unverdicted novelty 6.0

    By adopting a negative ontology where the true target does not objectively exist, the paper defines Democratic Supervision and derives the EL-MIATTs framework for ML evaluation and learning with Multiple Inaccurate Tr...

  2. Negative Ontology of True Target for Machine Learning: Towards Evaluation and Learning under Democratic Supervision

    cs.LG 2026-04 unverdicted novelty 4.0

    The true target does not objectively exist in ML, so models should use multiple inaccurate true targets under democratic supervision via the EL-MIATTs framework for evaluation and learning.

Reference graph

Works this paper leans on

52 extracted references · 23 canonical work pages · cited by 1 Pith paper

  1. [1]

    Introduction Modern machine learning (ML) systems are increasingly deployed in real -world environments where the notion of a single, precisely defined true target is often ill-posed or even nonexistent. In many practical domains , such as medical diagnosis, social behavior analysis, and open-world perception, ground truth labels arise from subjective, in...

  2. [2]

    Preliminary In this section, building on previous studies [11, 12], we briefly introduce the definition and core concept of MIATTs, their task-specific generation and evaluation processes, as well as LAF [13] and UTTL [14] for evaluation and learning of predictive models with MIATTS. 2.1 Definition and essence of MIATTs Building on the core premise that t...

  3. [3]

    Analysis of Task-Specific MIATTs Regarding the generation and assessment of MIATTs for a specific task, this section analyzes the possible qualities and structural patterns of task-specific MIATTs, along with their downstream influence on evaluation and learning. 3.1 Possible qualities of task-specific MIATTs with respect to assessment indicators Based on...

  4. [4]

    Accordingly, this section presents LAF -grounded evaluation algorithms employing logical operators such as conjunction, disjunction, and fuzzy aggregation

    Evaluation with MIATTs: LAF-Grounded Strategies Assuming that the true target for a given ML task is not assumed to exist as a well-defined object in the real world [11], LAF provides a principled framework that, based on MIATTs, can approximate ATT-based evaluation effectively in complex settings but may diverge in simpler ones [11, 13] . Accordingly, th...

  5. [5]

    decidable

    Formula level (fact-level): • K3 semantics: ¬𝑎 = 1 − 𝑎; Conjunction (∧) uses Gödel t-norm: 𝑎 ∧ 𝑏 = 𝑚𝑖𝑛(𝑎, 𝑏); Disjunction (∨) using t-conorm: 𝑎 ∨ 𝑏 = 𝑚𝑎𝑥(𝑎, 𝑏); Implication: 𝑎 ⇒ 𝑏 = 𝑚𝑎𝑥(1 − 𝑎, 𝑏). • Applicability 𝐴(𝜑): Whether the fact is “decidable” for the sample. In practice: 𝐴(𝜑) = 1[𝑣 ≠ 1/2]

  6. [6]

    partial representations

    Satisfaction of a single IATT 𝒕𝒏 ∗: • Intra-fact Aggregation (emphasizing that "partial representations" must be satisfied simultaneously): 𝑆𝑛(𝑖) = min 𝜑∈𝛷𝑛 𝑣𝜑(𝑖, 𝑡̃). (9) Or a weighted version 𝑆𝑛(𝑖) = min𝜑(𝛼𝜑 ⊙ 𝑣𝜑) (default is equal weighting, ⊙ is the weighting rule; simpler options include weighted minimum or weighted geometric mean). • Applicability c...

  7. [7]

    collectively covering more true target facts

    Collective coverage of aggregation across multiple MIATTs: • We want to reflect "collectively covering more true target facts." Aggregation using t-conorm: 𝑆𝑀𝐼𝐴𝑇𝑇𝑠(𝑖) = max 𝑛=1… 𝑁 𝑆𝑛(𝑖). (11) Explanation: As long as all the core facts of a model are satisfied, the model is correct in that aspect. • Alternatively, a probabilistic "at least one aspect is co...

  8. [8]

    satisfied

    Paraconsistency penalty: When two facts (possibly across MIATTs) with mutually exclusive requirements on the same sample are both "satisfied" to 1 (or close to 1), this is counted as a contradictory hit. • Define a set of mutually exclusive pairs 𝑀 = {(𝜑𝑚, 𝜑𝑛)}. • Sample-level contradiction rate: 𝐾𝑀𝐼𝐴𝑇𝑇𝑠(𝑖) = 1 |𝑀| ∑ 1[𝑣𝜑𝑚 = 1 ∧ 𝑣𝜑𝑛 = 1](𝜑𝑚,𝜑𝑛)∈𝑀 . (14)

  9. [9]

    strict correct ness in one aspect

    Final sample score (with coverage correction and consistency penalty): The final sample score can be expressed as 𝑆𝑐𝑜𝑟𝑒𝑀𝐼𝐴𝑇𝑇𝑠(𝑖) = (𝜆𝑆𝑀𝐼𝐴𝑇𝑇𝑠(𝑖) + (1 − 𝜆)𝑆𝑀𝐼𝐴𝑇𝑇𝑠 𝑁𝑜𝑖𝑠𝑦𝑂𝑅) ∙ 𝐶𝑀𝐼𝐴𝑇𝑇𝑠(𝑖) ∙ (1 − 𝛾𝐾𝑀𝐼𝐴𝑇𝑇𝑠(𝑖)), (15) where 𝜆 ∈ [0,1] controls "strict correct ness in one aspect" vs. "correct ness in at least one aspect"; 𝛾 ∈ [0,1] controls the intensity of the cont...

  10. [10]

    decidability

    Dataset-level metrics: • Average: 𝑆𝑐𝑜𝑟𝑒̅̅̅̅̅̅̅̅𝑀𝐼𝐴𝑇𝑇𝑠 = 1 |𝐷| ∑ 𝑆𝑐𝑜𝑟𝑒𝑀𝐼𝐴𝑇𝑇𝑠(𝑖)𝑖∈𝐷 . (16) • Simultaneously output 𝐶̅𝑀𝐼𝐴𝑇𝑇𝑠 = 1 |𝐷| ∑ 𝐶𝑀𝐼𝐴𝑇𝑇𝑠(𝑖)𝑖∈𝐷 ("decidability" of the evaluation), 𝐾̅𝑀𝐼𝐴𝑇𝑇𝑠 = 1 |𝐷| ∑ 𝐾𝑀𝐼𝐴𝑇𝑇𝑠(𝑖)𝑖∈𝐷 (overall contradiction rate). 4.1.2 Methodological key points and scalability This logic-based metric design method for evaluation with origin...

  11. [11]

    Partial representation

    Aligned with the definition: • "Partial representation" → Use conjunction (min) within a single IATT to force the key facts in that aspect to hold simultaneously. • "Collective coverage" → Use disjunction (max / NoisyOR) between MIATTs to indicate that "together they cover more aspects of the truth."

  12. [12]

    how many facts were used

    Unknown/Not applicable: Use 𝑈𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑= 0.5 to maintain the good algebraic properties of K3; the coverage 𝐶 allows you to determine "how many facts were used" in the evaluation

  13. [13]

    quasi-parallel consistency

    Conflict resolution: Mutually Exclusive Group + Penalty Term (1 − 𝛾𝐾𝑀𝐼𝐴𝑇𝑇𝑠) is a simple "quasi-parallel consistency" approach; complex scenarios can be replaced with Belnap four -valued logic ({⊥, ⊤, 𝑏𝑜𝑡ℎ, 𝑛𝑒𝑖𝑡ℎ𝑒𝑟}) or a constraint solver [26, 27]

  14. [14]

    Weight learning: Weights can be given by an expert or meta-learned using a validation set (e.g., using the 𝑆𝑐𝑜𝑟𝑒̅̅̅̅̅̅̅̅𝑀𝐼𝐴𝑇𝑇𝑠 as the target and using Bayesian Optimization/Differential Evolution to find weights)

  15. [15]

    where it satisfies/does not satisfy

    Interpretability: Each sample has a corresponding set of multiple true targets (MIATTs) for evaluation, which naturally provides an explanation of the hotspots of "where it satisfies/does not satisfy." 4.2 Evaluation with ternary target synthesized from MIATTs We combine MIATTs into a three -valued logical "synthetic true target" 𝑡† via logical merging, t...

  16. [16]

    Fact computation • For each sample (𝑖, 𝑡̃), calculate the true value of all MIATTs {𝑣𝑛}; • Use the above rules to generate the composite truth value 𝑡†(𝑖, 𝑡̃)

  17. [17]

    uncertain/insufficient

    Model score definition • For a sample, the score is: 𝑆𝑐𝑜𝑟𝑒𝑡†(𝑖) = 𝑡†(𝑖, 𝑡̃). (18) That is:  If target = 1, the prediction is completely correct → score 1;  If target = 0, the prediction is completely wrong → score 0;  If target = ½, the prediction is "uncertain/insufficient" given the partial true target → score 0.5. • Overall score for the dataset: 𝑆𝑐...

  18. [18]

    Accordingly, this section introduces UTTL-grounded learning strategies constructed upon two commonly used loss functions—Dice [20] and Cross Entropy (CE) [21]

    Learning with MIATTs: UTTL-Grounded Strategies Assuming that the true target for a given ML task is not assumed to exist as a well-defined object in the real world [11], UTTL provides a principled framework for learning from MIATTs, which indicates that UTTL can be effectively implemented through a multi -target learning paradigm [11, 14]. Accordingly, th...

  19. [19]

    Instead, MIATTs represent diverse, partially correct, and complementary views derived from task -specific AI models (AIM)

    Discussion The concept of MIATTs provides a pragmatic response to the epistemological limitation that the true target of a ML task is not assumed to exist as a well -defined object in the real world. Instead, MIATTs represent diverse, partially correct, and complementary views derived from task -specific AI models (AIM). The quality of a task -specific MI...

  20. [20]

    By grounding the evaluation process in the LAF and the learning process in the UTTL paradigm [13, 14] , we operationalize EL -MIATTs into two coherent, complementary mechanisms

    Conclusion, Limitation, and Future Work This paper presents a systematic effort to bridge the theoretical formulation and practical implementation of the EL -MIATTs framework [11], emphasizing how LAF -based evaluation algorithms and UTTL-based learning strategies enable reliable model assessment and training under epistemic uncertainty. By grounding the ...

  21. [21]

    and its downstream influence on evaluation and learning, proposed two LAF-grounded evaluation schemes (parallel multi-perspective and ternary synthesized), and developed two UTTL-grounded learning strategies (Per-target then Aggregate and Aggregate then Single Loss) applicable to common loss functions such as Dice and Cross Entropy. Together, these develo...

  22. [22]

    Are Labels Always Necessary for Classifier Accuracy Evaluation? Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

    Deng W, Zheng L. Are Labels Always Necessary for Classifier Accuracy Evaluation? Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). 2021. pp. 15069–78

    2021

  23. [23]

    Evaluating Classifiers Without Expert Labels

    Jung HJ, Lease M. Evaluating Classifiers Without Expert Labels. 2012. https://doi.org/10.48550/arxiv.1212.0960

    work page doi:10.48550/arxiv.1212.0960 2012

  24. [24]

    Performance measure characterization for evaluating neuroimage segmentation algorithms

    Chang HH, Zhuang AH, Valentino DJ, Chu WC. Performance measure characterization for evaluating neuroimage segmentation algorithms. NeuroImage. 2009. https://doi.org/10.1016/j.neuroimage.2009.03.068

    work page doi:10.1016/j.neuroimage.2009.03.068 2009

  25. [25]

    Metrics for evaluating 3D medical image segmentation: analysis, selection, and tool

    Taha AA, Hanbury A. Metrics for evaluating 3D medical image segmentation: analysis, selection, and tool. BMC Medical Imaging. 2015;15:29. https://doi.org/10.1186/s12880 - 015-0068-x

    work page doi:10.1186/s12880 2015

  26. [26]

    A Review on Evaluation Metrics for Data Classification Evaluations

    M H, M.N S. A Review on Evaluation Metrics for Data Classification Evaluations. International Journal of Data Mining & Knowledge Management Process. 2015;5:01 –11. https://doi.org/10.5121/ijdkp.2015.5201

    work page doi:10.5121/ijdkp.2015.5201 2015

  27. [27]

    Learning From Noisy Labels With Deep Neural Networks: A Survey

    Song H, Kim M, Park D, Shin Y, Lee J -G. Learning From Noisy Labels With Deep Neural Networks: A Survey. IEEE Trans Neural Netw Learning Syst. 2023;34:8135 –53. https://doi.org/10.1109/TNNLS.2022.3152527

    work page doi:10.1109/tnnls.2022.3152527 2023

  28. [28]

    A Comprehensive Review on Multiple Instance Learning

    Fatima S, Ali S, Kim H -C. A Comprehensive Review on Multiple Instance Learning. Electronics. 2023;12:4323. https://doi.org/10.3390/electronics12204323

    work page doi:10.3390/electronics12204323 2023

  29. [29]

    A Survey on Deep Semi -Supervised Learning

    Yang X, Song Z, King I, Xu Z. A Survey on Deep Semi -Supervised Learning. IEEE Trans Knowl Data Eng. 2023;35:8934–54. https://doi.org/10.1109/tkde.2022.3220219

    work page doi:10.1109/tkde.2022.3220219 2023

  30. [30]

    Web Data Mining

    Supervised Learning. Web Data Mining. Berlin, Heidelberg: Springer Berlin Heidelberg

  31. [31]

    pp. 63–132. https://doi.org/10.1007/978-3-642-19460-3_3

    work page doi:10.1007/978-3-642-19460-3_3

  32. [32]

    Moderately supervised learning: definition, framework and generality

    Yang Y. Moderately supervised learning: definition, framework and generality. Artif Intell Rev. 2024;57:37. https://doi.org/10.1007/s10462-023-10654-6

    work page doi:10.1007/s10462-023-10654-6 2024

  33. [33]

    EL-MIATTs: Evaluation and Learning with Multiple Inaccurate True Targets

    Yang Y. EL-MIATTs: Evaluation and Learning with Multiple Inaccurate True Targets. 2026. https://doi.org/10.32388/UMHEFG.4

    work page doi:10.32388/umhefg.4 2026

  34. [34]

    Bridging Theory and Practice in Implementing EL -MIATTs: Logic -Driven Algorithms for MIATTs Generation and Assessment

    Yang Y. Bridging Theory and Practice in Implementing EL -MIATTs: Logic -Driven Algorithms for MIATTs Generation and Assessment. 2025. https://doi.org/10.32388/0UD1AN

    work page doi:10.32388/0ud1an 2025

  35. [35]

    Logical assessment formula and its principles for evaluations with inaccurate ground-truth labels

    Yang Y. Logical assessment formula and its principles for evaluations with inaccurate ground-truth labels. Knowl Inf Syst. 2024. https://doi.org/10.1007/s10115-023-02047-6

    work page doi:10.1007/s10115-023-02047-6 2024

  36. [36]

    Undefinable True Target Learning: Towards Learning with Democratic Supervision

    Yang Y. Undefinable True Target Learning: Towards Learning with Democratic Supervision. 2025. https://doi.org/10.32388/KBK3P8.5

    work page doi:10.32388/kbk3p8.5 2025

  37. [37]

    T-norms and T-conorms hesitant fuzzy Einstein aggregation operator and its application to decision making

    Fahmi A, Amin F, Aslam M, Yaqoob N, Shaukat S. T-norms and T-conorms hesitant fuzzy Einstein aggregation operator and its application to decision making. Soft Comput. 2021;25:47–71. https://doi.org/10.1007/s00500-020-05426-1

    work page doi:10.1007/s00500-020-05426-1 2021

  38. [38]

    Vague and fuzzy t -norms and t -conorms

    Boixader D, Recasens J. Vague and fuzzy t -norms and t -conorms. Fuzzy Sets and Systems. 2022;433:156–75. https://doi.org/10.1016/j.fss.2021.07.008

    work page doi:10.1016/j.fss.2021.07.008 2022

  39. [39]

    An algebraic completeness proof for Kleene’s 3 -valued logic

    Negri M. An algebraic completeness proof for Kleene’s 3 -valued logic. Bollettino Dell’Unione Matematica Italiana. 2002;5-B:447–67

    2002

  40. [40]

    Natural implicative expansions of variants of Kleene’s strong 3 - valued logic with Gödel -type and dual Gödel -type negation

    Robles G, Méndez JM. Natural implicative expansions of variants of Kleene’s strong 3 - valued logic with Gödel -type and dual Gödel -type negation. Journal of Applied Non - Classical Logics. 2021;31:130–53. https://doi.org/10.1080/11663081.2021.1948285

    work page doi:10.1080/11663081.2021.1948285 2021

  41. [41]

    Stephen Cole Kleene

    Rasiowa H. Stephen Cole Kleene. Introduction to metamathematics. North -Holland Publishing Co., Amsterdam, and P. Noordhoff, Groningen, 1952; D. van Nostrand Company, New York and Toronto 1952; X + 550 pp. J Symb Log. 1954;19:215 –6. https://doi.org/10.2307/2268620

    work page doi:10.2307/2268620 1952

  42. [42]

    V -net: Fully convolutional neural networks for volumetric medical image segmentation

    Milletari F, Navab N, Ahmadi S -A. V -net: Fully convolutional neural networks for volumetric medical image segmentation. 2016 fourth international conference on 3D vision (3DV). Ieee; 2016. pp. 565–71

    2016

  43. [43]

    Cross -Entropy Loss Functions: Theoretical Analysis and Applications

    Mao A, Mohri M, Zhong Y. Cross -Entropy Loss Functions: Theoretical Analysis and Applications. In: Krause A, Brunskill E, Cho K, Engelhardt B, Sabato S, Scarlett J, editors. Proceedings of the 40th International Conference on Machine Learning, vol. 202. PM LR

  44. [44]

    Paraconsistency and its Philosophical Interpretations

    Barrio E, Da Re B. Paraconsistency and its Philosophical Interpretations. AJL. 2018;15:151–

    2018

  45. [45]

    https://doi.org/10.26686/ajl.v15i2.4860

    work page doi:10.26686/ajl.v15i2.4860

  46. [46]

    Literal and Controllable Paraconsistency

    Ciuciura J. Literal and Controllable Paraconsistency. LLP. 2024;1 –19. https://doi.org/10.12775/LLP.2024.027

    work page doi:10.12775/llp.2024.027 2024

  47. [47]

    An assessment of operational coverage as both an adequacy and a selection criterion for operational profile based testing

    Miranda B, Bertolino A. An assessment of operational coverage as both an adequacy and a selection criterion for operational profile based testing. Software Qual J. 2018;26:1571 –

    2018

  48. [48]

    https://doi.org/10.1007/s11219-017-9388-0

    work page doi:10.1007/s11219-017-9388-0

  49. [49]

    A Brief Survey on Oracle -based Test Adequacy Metrics

    Hossain SB, Dwyer MB. A Brief Survey on Oracle -based Test Adequacy Metrics. 2022. https://doi.org/10.48550/ARXIV.2212.06118

    work page doi:10.48550/arxiv.2212.06118 2022

  50. [50]

    Abductive Reasoning in a Paraconsistent Framework

    Bienvenu M, Inoue K, Kozhemiachenko D. Abductive Reasoning in a Paraconsistent Framework. Proceedings of the TwentyFirst International Conference on Principles of Knowledge Representation and Reasoning. Hanoi, Vietnam: International Joint Conferences on A rtificial Intelligence Organization; 2024. pp. 134 –44. https://doi.org/10.24963/kr.2024/13

    work page doi:10.24963/kr.2024/13 2024

  51. [51]

    How a Computer Should Think

    Belnap ND. How a Computer Should Think. In: Omori H, Wansing H, editors. New Essays on Belnap-­Dunn Logic, vol. 418. Cham: Springer International Publishing; 2019. pp. 35 –

    2019

  52. [52]

    https://doi.org/10.1007/978-3-030-31136-0_4

    work page doi:10.1007/978-3-030-31136-0_4