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Large Language Models (LLMs) can be used as repositories of biological and chemical information to generate pharmacological lead compounds. However, for LLMs to focus on specific drug targets typically requires experimentation with progressively more refined prompts. Results thus become dependent not just on what is known about the target, but also on what is known about the prompt- engineering. In this paper, we separate the prompt into domain-constraints that can be written in a standard logical form and a simple text-based query. We investigate whether LLMs can be guided, not by refining prompts manually, but by refining the logical component automatically, keeping the query unchanged. We describe an iterative procedure LMLF (“Language Model with Logical Feedback”) in which the constraints are progressively refined using a logical notion of generalisation. On any iteration, newly generated instances are verified against the constraint, providing "logical-feedback" for the next iteration's refinement of the constraints. We evaluate LMLF using two well-known targets (inhibition of the Janus Kinase 2; and Dopamine Receptor D2); and two different LLMs (GPT-3 and PaLM). We show that LMLF, starting with the same logical constraints and query text, can be used to guide both LLMs to generate potential leads. We find: (a) Binding affinities of LMLF-generated molecules are skewed towards higher binding affinities than those from existing baselines; (b) LMLF results in generating molecules that are skewed towards higher binding affinities than without logical feedback; (c) Assessment by a computational chemist suggests that LMLF generated compounds may be novel inhibitors. These findings suggest that LLMs with logical feedback may provide a mechanism for generating new leads without requiring the domain-specialist to acquire sophisticated skills in prompt-engineering.