  Constructing responses in task-oriented dialogue systems typically relies on
information sources such the current dialogue state or external databases. This
paper presents a novel approach to knowledge-grounded response generation that
combines retrieval-augmented language models with logical reasoning. The
approach revolves around a knowledge graph representing the current dialogue
state and background information, and proceeds in three steps. The knowledge
graph is first enriched with logically derived facts inferred using
probabilistic logical programming. A neural model is then employed at each turn
to score the conversational relevance of each node and edge of this extended
graph. Finally, the elements with highest relevance scores are converted to a
natural language form, and are integrated into the prompt for the neural
conversational model employed to generate the system response.
  We investigate the benefits of the proposed approach on two datasets (KVRET
and GraphWOZ) along with a human evaluation. Experimental results show that the
combination of (probabilistic) logical reasoning with conversational relevance
scoring does increase both the factuality and fluency of the responses.
