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Logical Neural Networks
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Logical Neural Networks
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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 omnidirectional rather than focused on predefined target variables, and corresponds to logical reasoning, including classical first-order logic theorem proving as a special case. The model is end-to-end differentiable, and learning minimizes a novel loss function capturing logical contradiction, yielding resilience to inconsistent knowledge. It also enables the open-world assumption by maintaining bounds on truth values which can have probabilistic semantics, yielding resilience to incomplete knowledge.
Forward citations
Cited by 15 Pith papers
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Explicit Fuzzy Logic in the Feed-Forward Layer: Self-Forgetting Quantifiers Discover Legible Grammatical-Licensing Detectors
A parameter-neutral fuzzy-logic FFN augmented with self-forgetting quantifiers produces legible grammatical-licensing detectors while matching baseline perplexity on OpenWebText.
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First-Order Temporal Logic Tensor Networks
FOT-LTN extends Logic Tensor Networks by integrating first-order linear temporal logic syntax with fuzzy differentiable semantics, supporting temporal operators and quantifiers, and shows improved performance over neu...
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Do Fair Models Reason Fairly? Counterfactual Explanation Consistency for Procedural Fairness in Credit Decisions
Outcome-fair credit models often exhibit hidden procedural bias through inconsistent reasoning across groups, which the CEC framework mitigates by enforcing consistent feature attributions via counterfactuals.
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Training, Reading, and Editing Legible Transformers
A variance-floor objective plus learned operator gates produce an end-to-end legible transformer whose crisp units are 50–184× more local to edit and can be reshaped from fan-out to fan-in circuits without quality loss.
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AttackPathGNN: Cross-function vulnerability detection in smart contracts using state interference graphs and conjunction pooling
AttackPathGNN introduces a State Interference Graph and conjunction pooling inside a GNN to detect cross-function vulnerabilities in Solidity contracts, reporting 92.3% F1 on SmartBugs Wild.
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Fairness of Explanations in Artificial Intelligence (AI): A Unifying Framework, Axioms, and Future Direction toward Responsible AI
A conditional invariance framework defines explanation fairness as explanations being statistically independent of protected attributes given task-relevant features, unifying existing metrics and enabling procedural b...
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Temporal Reasoning Is Not the Bottleneck: A Probabilistic Inconsistency Framework for Neuro-Symbolic QA
Temporal reasoning is not the core bottleneck for LLMs on time-based QA; the real issue is unstructured text-to-event mapping, addressed by a neuro-symbolic system with PIS that reaches 100% accuracy on benchmarks whe...
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Structured Abductive-Deductive-Inductive Reasoning for LLMs via Algebraic Invariants
A symbolic protocol operationalizes Peirce's tripartite reasoning for LLMs using five algebraic invariants including a Weakest Link bound to enforce logical consistency and prevent weak premises from supporting strong...
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THEIA: Learning Complete Kleene Three-Valued Logic in a Pure-Neural Modular Architecture
A modular neural architecture learns complete K3 logic and shows uncertainty-verdict asymmetric propagation plus a reliability spectrum for long discretized composition.
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THEIA: Learning Complete Kleene Three-Valued Logic in a Pure-Neural Modular Architecture
A modular neural architecture learns complete Kleene three-valued logic from task data and exhibits uncertainty-preserving propagation plus superior 500-step generalization under Gumbel-softmax training where flat MLP...
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Logic of Hypotheses: from Zero to Full Knowledge in Neurosymbolic Integration
LoH adds a learnable choice operator to propositional logic, compiles formulas to differentiable graphs via fuzzy logic, subsumes prior NeSy models, and supports discretization to Boolean functions via the Gödel trick.
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Algebraic Machine Learning for Small-to-Medium Datasets Is Competitive against Strong Standard Baselines
AML outperforms cross-validated baselines including CNNs on 50-2000 example image datasets and is comparable to XGBoost/LightGBM on tabular data using only training data and no task-dependent hyperparameters.
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Enabling topography-resolving structural dynamic contact simulation
A multi-scale FE–BEM method is extended to dynamic time integration and Harmonic Balance, enabling topography-resolved contact simulation of bolted joints and load-history-dependent equilibria on the S4 Beam.
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Overmind NSA: A Unified Neuro-Symbolic Computing Architecture with Approximate Nonlinear Activations and Preemptive Memory Bypass
Overmind is a neuro-symbolic architecture that uses adjustable Padé approximations and memory bypass to deliver 8.1 TOPS/W efficiency and 410 GOPS throughput on mixed workloads with minimal accuracy loss.
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Auto-Relational Reasoning
A system using auto-relational reasoning solves IQ test problems at 98.03% rate without any prior knowledge, reaching top 1% human performance.
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