Semantic simultaneous localization and mapping is a subject of increasing interest in robotics and AI that directly influences the autonomous vehicles industry, the army industries, and more. One of the challenges in this field is to obtain object classification jointly with robot trajectory estimation. Considering view-dependent semantic measurements, there is a coupling between different classes, resulting in a combinatorial number of hypotheses. A common solution is to prune hypotheses that have a sufficiently low probability and to retain only a limited number of hypotheses. However, after pruning and renormalization, the updated probability is overconfident with respect to the original probability. This is especially problematic for systems that require high accuracy. If the prior probability of the classes is independent, the original normalization factor can be computed efficiently without pruning hypotheses. To the best of our knowledge, this is the first work to present these results. If the prior probability of the classes is dependent, we propose a lower bound on the normalization factor that ensures cautious results. The bound is calculated incrementally and with similar efficiency as in the independent case. After pruning and updating based on the bound, this belief is shown empirically to be close to the original belief.