In 1938, Tarski proved that a formula is not intuitionistically valid if, and only if, it has a counter-model in the Heyting algebra of open sets of some topological space. In fact, Tarski showed that any Euclidean space R^n with n >= 1 suffices, as does e.g. the Cantor space. In particular, intuitionistic logic cannot…
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48 results for “intuitionistic logic”
Deep RL for ATP in intuitionistic logic, outperforming existing methods.
problem Automated theorem proving in intuitionistic propositional logic.
method Deep reinforcement learning with novel data augmentation and graph neural networks.
result Our prover outperforms Coq's tauto tactic, solving 84% of the theorems in a benchmark library.
In category theory, logic and geometry cooperate with each other producing what is known under the name Synthetic Differential Geometry (SDG). The main difference between SDG and standard differential geometry is that the intuitionistic logic of SDG enforces the existence of infinitesimal objects which essentially modi…
The main objective is to present a some variant of the Black - Litterman model. We consider the canonical case when priori return is determined by means such excess return from the CAPM market portfolio which is derived using reverse optimization method. Then the a priori return is at risk quantified uncertainty. On th…
Study enhances financial forecasting with machine learning and fuzzy MCDM.
problem Increasing financial uncertainty and market complexity.
method Integrates machine learning (XGBoost, LSTM, GNN) and intuitionistic fuzzy MCDM.
result High forecasting accuracy with low MAPE and narrow confidence intervals.
F.: Good morning Hermann, I would like to talk with you about infinitesimals. G.: Tell me Pierre. F.: I'm fed up of all these slanders about my attitude to be non rigorous, so I've started to study nonstandard analysis (NSA) and synthetic differential geometry (SDG). G.: Yes, I've read something ... F.: Ok, no problem …
AlphaLogics mines market logic to generate interpretable alpha factors.
problem Complex, opaque alpha factors from factor mining overlook market logic.
method Market Logic Mining, Factor Generation and Optimization, Market Logic Generation and Optimization.
result AlphaLogics improves predictive metrics and risk-adjusted returns over baselines.
NLN learns logical reasoning from neural networks.
problem Lack of logical reasoning in deep neural networks.
method Dynamic neural architecture that builds computational graph based on logical expressions, learns logical operations as neural modules, conducts propositional logical reasoning.
result NLN significantly outperforms state-of-the-art models on collaborative filtering and personalized recommendation tasks.
Paper studies a universal logical operator for deep networks, improving interpretability.
problem Learning a universal logical operator for deep convolution networks without manual prescription.
method Exploration of different logical operators (AND, OR, XOR) and learning a universal one.
result Insightful observations lead to a novel logical interpretation of deep convolution networks.
NLM combines neural networks and logic programming for complex reasoning.
problem Complex reasoning tasks involving logic and properties.
method Neural-symbolic architecture combining neural networks and logic programming.
result NLM achieves perfect generalization on various tasks.
Polyhedral semantics for intermediate logics; Nerve Criterion ensures completeness.
problem Characterize polyhedrally-complete intermediate logics.
method Developed Nerve Criterion to characterize polyhedrally-complete logics combinatorially.
result Nerve Criterion provides a necessary and sufficient condition for polyhedrally-completeness.
Logical scaffolds enhance AI software quality.
problem Improving AI component quality in software.
method Logical scaffolds as a method to improve AI components.
result Logical scaffolds can improve AI beyond perception systems.
Boolean logic used for neural network training and inference, with convergence analysis.
problem Discrete optimization in neural networks with Boolean logic.
method Boolean logic backpropagation with convergence analysis.
result First convergence analysis for Boolean logic in neural networks.
Graph neural networks improve logic reasoning for large datasets.
problem Combining logic reasoning and probabilistic inference for large datasets.
method Exploring Graph Neural Networks (GNNs) for Markov Logic Networks (MLN) to improve probabilistic logic inference.
result ExpressGNN, a more expressive variant of GNN, can perform effective probabilistic logic inference and scale to large datasets.
Develops deep learning for logical code segmentation.
problem Lack of logically segmented source code.
method Novel deep learning approach to generate logical code segments.
result Improves software analysis tasks like commenting, bug detection, and code synthesis.
pLogicNet combines logic rules and embeddings for efficient knowledge graph reasoning.
problem Efficiently predicting missing facts in knowledge graphs.
method Combines Markov Logic Networks with knowledge graph embeddings using variational EM algorithm.
result pLogicNet outperforms traditional methods on multiple knowledge graphs.
Graph neural networks struggle with proving unsatisfiability in complex logical formulas.
problem Proving unsatisfiability in complex logical formulas.
method Investigating the limitations of graph neural networks in logical reasoning tasks.
result Graph neural networks may fail in certifying unsatisfiability in Boolean formulae.
Neural Logic Reasoning integrates deep learning and symbolic logic for better prediction tasks.
problem Lack of cognitive reasoning in deep neural networks limits their ability to solve complex prediction tasks.
method Proposes Logic-Integrated Neural Network (LINN) that learns logical operations and conducts propositional logical reasoning.
result LINN significantly outperforms state-of-the-art recommendation models in Top-K recommendation.
Combines neural networks and logic circuits for interpretable, accurate, and cost-effective learning.
problem Lack of generalizability and interpretability in neural networks and high hardware cost in logic circuits.
method Trains a neural network, then translates it to random forests, and finally to AND-Inverter logic.
result The pipeline maintains greater accuracy and minimizes logic complexity.
FPGA-based logic architecture speeds up GBDT training 259x.
problem Training efficiency and power consumption in GBDT models.
method Implemented logic architecture on FPGA, compared with software libraries.
result Training speed 26-259x faster, power efficiency 90-1,104x higher.
Integrates deep learning and logic reasoning for intelligent agents.
problem Combining deep learning and logic reasoning for robust decision-making.
method Deep Logic Models integrating deep learners and logic reasoning.
result Proposed models outperform other approaches in joint learning and inference.
The purpose of this paper is to discuss how topology and geometry provide, in many instances, the connective tissue that enables logical comprehension. We illustrate this theme with many examples including Venn diagrams, knot diagrams, knot-logical diagrams and an arrow of reference that elucidates self-reference and G…
Kernel for STL formulae enables machine learning in temporal logic.
problem Lack of a kernel for STL formulae.
method Define a kernel for STL formulae and embed them into a Hilbert space.
result Kernel-based machine learning algorithms can now be applied to STL formulae.
Transformers learn to predict temporal logic solutions from classical solver outputs.
problem Training neural networks on logic problem solutions for verification.
method Training a Transformer on generated training data from classical solvers, focusing on one solution per formula.
result Transformers can predict correct solutions to temporal logic problems, even to unseen benchmarks.
Study logical generalization in GNNs using a new benchmark.
problem Understanding how GNNs adapt to new logical tasks.
method Developed GraphLog benchmark suite for logical tasks, evaluated GNNs in supervised, pretraining, and continual learning settings.
result Logical diversity during training affects GNNs' ability to generalize.
The logic of uncertainty as a logic of experience and chance and the co~event-based Bayes' theoremq-fin.GN
The logic of uncertainty is not the logic of experience and as well as it is not the logic of chance. It is the logic of experience and chance. Experience and chance are two inseparable poles. These are two dual reflections of one essence, which is called co~event. The theory of experience and chance is the theory of c…
2-simplicial Transformer enhances logical reasoning in reinforcement learning.
problem Logical reasoning in reinforcement learning.
method Introduces -simplicial Transformer with higher-dimensional attention and tensor product updates.
result Shows effectiveness of -simplicial Transformer for logical reasoning.
Proposes NLRL for enhancing neural networks' interpretability.
problem Deep neural networks lack interpretability for humans.
method Introduces neural logic rule layers (NLRL) to represent arbitrary logic rules.
result NLRL-enhanced neural networks can learn complex logic and arithmetic.
Paper introduces a new framework combining deep learning and logic for relational data.
problem Scalability and flexibility of deep learning methods for relational data.
method Combines auto-encoding principle with first-order logic and logic programs.
result Latent representations are more accurate, flexible, and interpretable.
NMLNs use neural networks to learn relational structure from data.
problem Learning implicit rules from data without explicit logic rules.
method Combines Markov logic with neural networks to learn relational structure.
result NMLNs can predict in settings without explicit logic rules.
Responds to comments on Bayesian Logic Regression algorithm, provides extensions and tutorial.
problem Improving Bayesian Logic Regression algorithm and its applications.
method Summarizes and responds to discussants' comments, provides extensions and tutorial.
result Extensions and tutorial for the Bayesian Logic Regression algorithm.
Tensor logic aims to unify AI types with scalable and transparent features.
problem Lack of a unified AI programming language with scalability and transparency.
method Introduces tensor logic, a new AI language based on tensor equations.
result Tensor logic enables key AI forms like transformers, formal reasoning, and graphical models.
Logical neural networks solve mazes by filling dead ends, but not all methods generalize well.
problem Understanding how logical neural networks extrapolate solutions to mazes.
method Examined recurrent and implicit neural networks trained on maze-solving tasks.
result Models fail to generalize well to diverse maze sizes, suggesting limitations in learning scalable algorithms.
Intermediate logic of all convex polyhedra is axiomatized.
problem Defining and axiomatizing intermediate logic for convex polyhedra.
method Using Jankov-Fine formulas, classical polyhedral geometry, and p-morphic images to establish completeness.
result A finite axiomatisation of PL for all convex polyhedra.
Paper improves robustness certification by integrating ML and logical reasoning.
problem Limited robustness certification under perturbation radius.
method Integrates statistical ML models with logical reasoning using Markov logic networks.
result First certified robustness bound for MLN derived and experimentally validated.
SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solvercs.LG
SATNet integrates logical reasoning into deep learning with a differentiable MAXSAT solver.
problem Integrating logical reasoning into deep learning architectures.
method Differentiable MAXSAT solver based on fast coordinate descent for SDP.
result Minimally supervised learning of logical structures in deep learning systems.
Safe reinforcement learning with logical constraints for optimal policy synthesis.
problem Ensuring safety during reinforcement learning while maximizing goal satisfaction.
method Adaptive safe padding that synthesizes optimal control policies satisfying temporal logic formulas.
result The proposed method handles the trade-off between exploration and safety with theoretical guarantees.
Graphs improve theorem proving in higher-order logic.
problem Challenges in converting higher-order logic formulas into graph-based representations.
method Used graph neural networks (GNNs) to represent and search higher-order logic.
result GNNs outperform state-of-the-art methods in higher-order theorem proving.
Proposes using logical specifications for multi-objective reinforcement learning to improve agent behavior.
problem Difficulties in controlling reinforcement learning agents and the need for better generalization.
method Uses propositional logic to specify the importance of multiple objectives, encoding these specifications using a recurrent neural network.
result MORL agents parameterized by logical specifications can generalize to novel combinations of objectives and achieve comparable performance.
ENN neural network learns logical syllogisms using Euler diagrams.
problem Traditional neural networks struggle with logical reasoning, especially syllogisms.
method ENN represents logical relations as Euler diagrams, optimizing syllogism structures with a novel back-propagation algorithm.
result ENN can precisely represent and reason with all 24 syllogism structures.
Combining deep neural networks with structured logic rules is desirable to harness flexibility and reduce uninterpretability of the neural models. We propose a general framework capable of enhancing various types of neural networks (e.g., CNNs and RNNs) with declarative first-order logic rules. Specifically, we develop…
The paper uses temporal logic to guide safe reinforcement learning for complex tasks.
problem Learning safe control policies for complex, long-horizon tasks in physical systems.
method Combines temporal logic, control barrier functions, and control Lyapunov functions to facilitate safe exploration and learning.
result Developed a flexible system that allows users to specify task objectives and constraints in various forms and levels.
Learning low-dimensional embeddings of knowledge graphs is a powerful approach used to predict unobserved or missing edges between entities. However, an open challenge in this area is developing techniques that can go beyond simple edge prediction and handle more complex logical queries, which might involve multiple un…
This paper presents a stochastic logic time delay reservoir design. The reservoir is analyzed using a number of metrics, such as kernel quality, generalization rank, performance on simple benchmarks, and is also compared to a deterministic design. A novel re-seeding method is introduced to reduce the adverse effects of…
Improves deep learning interpretability through logical network construction.
problem Difficulty in understanding and explaining deep neural networks, especially convolution neural networks.
method Proposes a method to construct a logical network based on fully connected layers to improve interpretability.
result Improves the interpretability of deep learning processes and models.
Paper uses subjective logic to estimate uncertainty in multi-armed bandit problems.
problem Estimating uncertainty in multi-armed bandit problems.
method Formalism of subjective logic applied to multi-armed bandits, proposing new algorithms.
result Subjective logic quantities enable useful assessment of uncertainty.
RDLI integrates domain logic and context grounding to detect crypto anomalies under scarce labels.
problem Extreme label scarcity and evasion strategies in crypto networks.
method Relational Domain Logic Integration (RDLI) with Retrieval Grounded Context (RGC).
result RDLI outperforms GNN baselines by 28.9% in F1 score under 0.01% label scarcity.
Causal Razorscs.LG
The study examines causal razors and their logical relations, highlighting a dilemma in causal discovery.
problem Selecting a reasonable scoring criterion for causal discovery algorithms.
method Review and logical comparison of numerous causal razors, focusing on parameter minimality in multinomial models.
result Parameter minimality poses a dilemma in selecting a reasonable scoring criterion for causal discovery algorithms.