The mathematics of inheritance systems
The mathematics of inheritance systems
A logical framework for default reasoning
Artificial Intelligence
Learning and relearning in Boltzmann machines
Parallel distributed processing: explorations in the microstructure of cognition, vol. 1
Symmetric neural networks and propositional logic satisfiability
Neural Computation
What does a conditional knowledge base entail?
Proceedings of the first international conference on Principles of knowledge representation and reasoning
A mathematical treatment of defeasible reasoning and its implementation
Artificial Intelligence
Evidential reasoning in semantic networks: a formal theory and its parallel implementation (inheritance, categorization, connectionism, knowledge representation)
Mundane reasoning by parallel constraint satisfaction
Mundane reasoning by parallel constraint satisfaction
Default reasoning: causal and conditional theories
Default reasoning: causal and conditional theories
ECSQARU '01 Proceedings of the 6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Weighted Description Logics Preference Formulas for Multiattribute Negotiation
SUM '09 Proceedings of the 3rd International Conference on Scalable Uncertainty Management
Sequential inference with reliable observations: Learning to construct force-dynamic models
Artificial Intelligence
Connectionist Models for Formal Knowledge Adaptation
ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part II
Compactly representing utility functions using weighted goals and the max aggregator
Artificial Intelligence
Solving conflicts in information merging by a flexible interpretation of atomic propositions
Artificial Intelligence
Transformations around quantitative possibilistic logic
SUM'11 Proceedings of the 5th international conference on Scalable uncertainty management
Belief functions and default reasoning
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Penalty logic and its link with Dempster-Shafer theory
UAI'94 Proceedings of the Tenth international conference on Uncertainty in artificial intelligence
Computing utility from weighted description logic preference formulas
DALT'09 Proceedings of the 7th international conference on Declarative Agent Languages and Technologies
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We define a model-theoretic reasoning formalism that is naturally implemented on symmetric neural networks (like Hopfield networks or Boltzman machines). We show that every symmetric neural network, can be seen as performing a search for a satisfying model of some knowledge that is wired into the network's weights. Several equivalent languages are then shown to describe the knowledge embedded in these networks. Among them is propositional calculus extended by augmenting propositional assumptions with penalties. The extended calculus is useful in expressing default knowledge, preference between arguments, and reliability of assumptions in an inconsistent knowledge base. Every symmetric network can be described by this language and any sentence in the language is translatable into such a network, A sound and complete proof procedure supplements the model-theoretic definition and gives an intuitive understanding of the nonmonotonic behavior of the reasoning mechanism. Finally, we sketch a connectionist inference engine that implements this reasoning paradigm.