The LLM Proposes. The Logic Decides. Neurosymbolic agents, higher-order logic, and the AI we almost forgot [ukr]

A language model is fluent, and sometimes it is wrong and sure. In a chat that costs one bad answer. In an agent with a memory it costs more: the agent stores the mistake, reasons from it, and repeats it tomorrow. Retrieval cannot tell which of two contradictory notes is right, and a second model asked to judge only predicts a plausible verdict.

The fix is not new. Before deep learning, expert systems such as MYCIN and XCON kept knowledge as rules, applied them the same way every time, and answered "why?" and "how?". They failed at one thing: getting knowledge in, because every rule was typed by hand. LLMs are very good at exactly that. Neurosymbolic AI puts the two halves back together.

The talk follows that reunion through one running example: an assistant whose LLM "remembers" a meeting in Berlin while its calendar has the same person in Lisbon at the same hour. We cover deduction, induction and abduction, and why LLMs are good at the last; reasoning over a knowledge graph with Prolog and Datalog; and why higher-order logic programming (λProlog) fits agents well, with types that reject malformed LLM output, relations as values, scoped what-if assumptions, rules about rules, and proofs that a small kernel can check. We end with a working agent whose LLM writes λProlog behind six guards, and with honest numbers on what the logic layer catches and what it cannot.

For AI and agent engineers who know Python and LLMs. No background in logic or mathematics is assumed.