In principle, First Order Logic and equivalent languages can represent anything that can be represented in natural language. The problem is that in practice it is very hard to transfer into a logic language all the knowledge you might need for a useful system.
In fact, this was one motivation for at least one branch of machine learning- the work from Ryszard Michalski, Claude Sammut, Ranan Banerji, Steven Vere, Brian Cohen and later rule-learners like Quinlan's decision tree learners and of course all the later work in Inductive Logic Programming by Plotkin, Shapiro, Muggleton etc. These are all rule-learning systems, that can avoid the knowledge acquisition bottleneck that probably did in for purely rule-based expert systems in the '90s (i.e. getting experts to transfer their knowledge into rules).
I rather agree that further progress in AI will require a, let's say, synchretistic approach- like I say in another comment, the obvious thing for me is to use deep learning for perception, logic for inference and probabilistic modelling to deal with the noisy world. There are some people working in that sort of direction, with different amounts of emphasis on each of the three approaches. For instance, Josh Tenenbaum at MIT, Evans and Grefenstette at DeepMind, Luc De Raedt at KU Leuven, Kristian Kersting at Dortmund, Lise Getoor also at MIT, Pedro Domingos at Washington, and many others.
Apologies for all the name-dropping without links. Let me know and I can provide them if required.