{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T12:05:31Z","timestamp":1784203531551,"version":"3.55.0"},"publisher-location":"California","reference-count":0,"publisher":"International Joint Conferences on Artificial Intelligence Organization","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,7]]},"abstract":"<jats:p>Neuro-symbolic AI aims to integrate learning-based and symbolic reasoning components within a unified framework. While most existing work focuses on single-agent settings and engineering architectures, formal foundations for neuro-symbolic multi-agent systems remain limited. In this paper, we introduce a game-theoretic formal model capturing the interaction between probabilistic neural evaluation and symbolic strategic reasoning in multi-agent environments. The framework extends logical models of strategic reasoning while embedding probabilistic propositional inference into a distributed setting. We establish basic properties of the model and provide a comprehensive complexity-theoretic analysis of optimally stable strategic behaviour. In particular, for one-shot games, we show that utility evaluation corresponds to weighted model counting and characterise the complexity of the main associated Nash equilibrium problems, ranging from FP and #P to PP and Sigma^PP_2. We further study an iterated variant of the core model, showing PSPACE-completeness for the main decision problem in such a class of multi-player games. These results provide formal foundations for reasoning about neuro-symbolic multi-agent systems and clarify the computational limits of combining learning, uncertainty, and strategic interaction within the same formal reasoning framework.<\/jats:p>","DOI":"10.24963\/kr.2026\/88","type":"proceedings-article","created":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T11:15:53Z","timestamp":1784200553000},"page":"940-950","source":"Crossref","is-referenced-by-count":0,"title":["Semantic Foundations of Neuro-Symbolic Multi-Agent Systems"],"prefix":"10.24963","author":[{"given":"Julian","family":"Gutierrez","sequence":"first","affiliation":[{"name":"University of Sussex"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"10584","event":{"name":"23nd International Conference on Principles of Knowledge Representation and Reasoning {KR-2026}","theme":"Artificial Intelligence","location":"Lisbon, Portuagal","acronym":"KR-2026","number":"23","sponsor":["Artificial Intelligence Journal","Principles of Knowledge Representation and Reasoning Inc.","European Association for Artificial Intelligence"],"start":{"date-parts":[[2026,7,20]]},"end":{"date-parts":[[2026,7,18]]}},"container-title":["Proceedings of the TwentyThird International Conference on Principles of Knowledge Representation and Reasoning"],"original-title":[],"deposited":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T11:16:17Z","timestamp":1784200577000},"score":1,"resource":{"primary":{"URL":"https:\/\/proceedings.kr.org\/2026\/88"}},"subtitle":[],"proceedings-subject":"Artificial Intelligence Research Articles","short-title":[],"issued":{"date-parts":[[2026,7]]},"references-count":0,"URL":"https:\/\/doi.org\/10.24963\/kr.2026\/88","relation":{},"subject":[],"published":{"date-parts":[[2026,7]]}}}