Strengthened Inhibitory Connections Between Neurons I'm reading Bio Inspired Artificial Intelligence which cites this passage about neuron plasticity: 


  "Spike time-dependent plasticity. The percentage of synaptic modification depends on the difference between presynaptic and postsynaptic spikes (tpre −tpost). The temporal difference in the figure ranges between -100 ms and +100 ms. When the postsynaptic neuron fires after arrival of the presynaptic pulse (positive difference, also known as causal relation), the synaptic weight is increased; instead, when the postsynaptic neuron fires before the arrival of the presynaptic pulse (negative differ- ence, also known as anticausal difference), the synaptic weight is depressed." From Gerstner and Kistler (2002) plotted on data from Bi and Poo (2001).


How do inhibitory neurons, which have successfully inhibited an activation spike of a neuron, strengthen their connections with such neurons, as the neurons they stop don't spike?
The learning rule you describe (i.e. the change of synaptic weights from source neuron to target neuron depending on the temporal difference between source and target activity) is often referred to as 'classical' or 'standard' STDP (spike-timing dependent plasticity) and is focused on connections between excitatory cells. However, this simple form of plasticity is not enough to explain all experimental observations and has also computational problems with respect to stability i.e. there is in fact no 'standard' STDP, because the weight change is not only dependent on the temporal difference, but also on the voltage, location of the synapse, firing rate, the cell-type and probably other factors, see e.g. this article from 2010 dealing with questions surrounding STDP by Lisman and Spruston.

In short, the form of the learning rule depends on several factors and synaptic plasticity works differently for inhibitory cells. 
As the question as to how plasticity works involving inhibitory cells is not an easy topic, I will refer to this review paper which deals with different induction protocols and potential functional implications (e.g. stability, homeostasis): 
Review paper on inhibitory synaptic plasticity by Vogels et al.

Very recently, there also has been a research topic in Frontiers of Cellular Neuroscience on this topic: The editorial article briefly summarizes the different contributions