We aim at improving reasoning on inconsistent and uncertain data. We focus on knowledge-graph data, extended with time intervals to specify their validity, as regularly found in historical sciences. We propose principles on semantics for efficient Maximum A-Posteriori inference on the new Temporal Markov Logic Networks (TMLN) which extend the Markov Logic Networks (MLN) by uncertain temporal facts and rules. We examine total and partial temporal (in)consistency relations between sets of temporal formulae. Then we propose a new Temporal Parametric Semantics, which may combine several sub-functions, allowing to use different assessment strategies. Finally, we expose the constraints that semantics must respect to satisfy our principles.