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In a two-way relay channel (TWRC), physical-layer network coding (PNC) doubles the system throughput by turning superimposed signals transmitted simultaneously by different end nodes into useful network-coded information (known as PNC decoding). Prior works indicated that the PNC decoding performance is affected by the relative phase offset between the received signals from different nodes. In particular, some "bad" relative phase offsets could lead to huge performance degradation. Previous solutions to mitigate the relative phase offset effect were limited to the conventional bit-oriented communication paradigm, aiming at delivering a given information stream as quickly and reliably as possible. In contrast, this paper puts forth the first semantic communication-empowered PNC-enabled TWRC to address the relative phase offset issue, referred to as SC-PNC. Despite the bad relative phase offsets, SC-PNC directly extracts the semantic meaning of transmitted messages rather than ensuring accurate bit stream transmission. We jointly design deep neural network (DNN)-based transceivers at the end nodes and propose a semantic PNC decoder at the relay. Taking image delivery as an example, experimental results show that the SC-PNC TWRC achieves high and stable reconstruction quality for images under different channel conditions and relative phase offsets, compared with the conventional bit-oriented counterparts.