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Abstract: 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. [Copyright &y& Elsevier]

Neural-Symbolic Systems concern the integration of the symbolic and connectionist paradigms of Artificial Intelligence. Distributed knowledge representation is traditionally seen under a symbolic perspective. In this paper, we show how neural networks can represent distributed symbolic knowledge, acting as multi-agent systems with learning capability (a key feature of neural networks). We apply the framework of Connectionist Modal Logics to well-known testbeds for distributed knowledge representation formalisms, namely the muddy children and the wise men puzzles. Finally, we sketch a full solution to these problems by extending our approach to deal with knowledge evolution over time. [ABSTRACT FROM AUTHOR]