Markov logic is a widely used tool in statistical relational learning, which uses a weighted first-order logic knowledge base to specify a Markov random field (MRF) or a conditional random field (CRF). In many applications, a Markov logic network (MLN) is trained in one domain, but used in a different one. This paper focuses on dynamic Markov logic networks, where the domain of time points typically varies between training and testing. It has been previously pointed out that the marginal probabilities of truth assignments to ground atoms can change if one extends or reduces the domains of predicates in an MLN. We show that in addition to this problem, the standard way of unrolling a Markov logic theory into a MRF may result in time-inhomogeneity of the underlying Markov chain. Furthermore, even if these representational problems are not significant for a given domain, we show that the more practical problem of generating samples in a sequential conditional random field for the next slice relying on the samples from the previous slice has high computational cost in the general case, due to the need to estimate a normalization factor for each sample. We propose a new discriminative model, slice normalized dynamic Markov logic networks (SN-DMLN), that suffers from none of these issues. It supports efficient online inference, and can directly model influences between variables within a time slice that do not have a causal direction, in contrast with fully directed models (e.g., DBNs). Experimental results show an improvement in accuracy over previous approaches to online inference in dynamic Markov logic networks.