A connectionist model for 2-dimensional modal logic

The importance of bridging the gap between the connectionist and symbolic paradigms has been widely recognized. In this paper, we present a new connectionist model called CML2 for 2-dimensional modal logic program. After proposing a fix-point semantics of the logic program, we put forward an algorithm to build the CML2, which encodes the background knowledge represented by a 2-dimensional modal logic program into a recurrent neural network. We also prove the correctness of the algorithm.