Foundations of logic programming
Foundations of logic programming
Learning internal representations by error propagation
Parallel distributed processing: explorations in the microstructure of cognition, vol. 1
Temporal logic (vol. 1): mathematical foundations and computational aspects
Temporal logic (vol. 1): mathematical foundations and computational aspects
Knowledge-based artificial neural networks
Artificial Intelligence
Reasoning about knowledge
Robust reasoning: integrating rule-based and similarity-based reasoning
Artificial Intelligence
Neural network fundamentals with graphs, algorithms, and applications
Neural network fundamentals with graphs, algorithms, and applications
Modal tableaux with propagation rules and structural rules
Fundamenta Informaticae
Preferred answer sets for extended logic programs
Artificial Intelligence
Logic in computer science: modelling and reasoning about systems
Logic in computer science: modelling and reasoning about systems
Knowledge-based neurocomputing
Knowledge-based neurocomputing
Symbolic knowledge extraction from trained neural networks: a sound approach
Artificial Intelligence
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Connectionist-Symbolic Integration: From Unified to Hybrid Approaches
Connectionist-Symbolic Integration: From Unified to Hybrid Approaches
The Connectionist Inductive Learning and Logic Programming System
Applied Intelligence
Three problems in computer science
Journal of the ACM (JACM)
An Overview of Temporal and Modal Logic Programming
ICTL '94 Proceedings of the First International Conference on Temporal Logic
Programming in Modal Logic: An Extension of PROLOG based on Modal Logic
Proceedings of the 5th Conference on Logic Programming '86
Extracting symbolic rules from trained neural network ensembles
AI Communications - Special issue on Artificial intelligence advances in China
Rule-based reasoning in connectionist networks
Rule-based reasoning in connectionist networks
Fewer epistemological challenges for connectionism
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
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Modal logics are amongst the most successful applied logical systems. Neural networks were proved to be effective learning systems. In this paper, we propose to combine the strengths of modal logics and neural networks by introducing Connectionist Modal Logics (CML). CML belongs to the domain of neural-symbolic integration, which concerns the application of problem-specific symbolic knowledge within the neurocomputing paradigm. In CML, one may represent, reason or learn modal logics using a neural network. This is achieved by a Modalities Algorithm that translates modal logic programs into neural network ensembles. We show that the translation is sound, i.e. the network ensemble computes a fixed-point meaning of the original modal program, acting as a distributed computational model for modal logic. We also show that the fixed-point computation terminates whenever the modal program is well-behaved. Finally, we validate CML as a computational model for integrated knowledge representation and learning by applying it to a well-known testbed for distributed knowledge representation. This paves the way for a range of applications on integrated knowledge representation and learning, from practical reasoning to evolving multi-agent systems.