  We consider a multi-user semantic communications system in which agents
(transmitters and receivers) interact through the exchange of semantic messages
to convey meanings. In this context, languages are instrumental in structuring
the construction and consolidation of knowledge, influencing conceptual
representation and semantic extraction and interpretation. Yet, the crucial
role of languages in semantic communications is often overlooked. When this is
not the case, agent languages are assumed compatible and unambiguously
interoperable, ignoring practical limitations that may arise due to language
mismatching. This is the focus of this work. When agents use distinct
languages, message interpretation is prone to semantic noise resulting from
critical distortion introduced by semantic channels. To address this problem,
this paper proposes a new semantic channel equalizer to counteract and limit
the critical ambiguity in message interpretation. Our proposed solution models
the mismatch of languages with measurable transformations over semantic
representation spaces. We achieve this using optimal transport theory, where we
model such transformations as transportation maps. Then, to recover at the
receiver the meaning intended by the teacher we operate semantic equalization
to compensate for the transformation introduced by the semantic channel, either
before transmission and/or after the reception of semantic messages. We
implement the proposed approach as an operation over a codebook of
transformations specifically designed for successful communication. Numerical
results show that the proposed semantic channel equalizer outperforms
traditional approaches in terms of operational complexity and transmission
accuracy.
