A search for a logic suitable for reasoning about Artificial Neural Networks (ANNs) has led to the introduction of times linear logic. There are graphical representations of timed linear proofs called timed proofnets, which are ideally suited for reasoning about ANNs. The logic introduced in this paper is limited to a metricized multiplicative linear logic, which is cryptically named 2mll. A brief introduction to linear logic, which provides the conceptual basis for 2mll and timed proofnets is presented. The correspondence between concurrent timed automata and timed proofnets is explored. Examples of the use of 2mll in reasoning about ANNs, are presented. Finally, an overview of a 2mll-based desing methodology for ANNs is given.
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