@misc{StoltenowKoenigSchneideretal., author = {Stoltenow, Lara and K{\"o}nig, Barbara and Schneider, Sven and Corradini, Andrea and Lambers, Leen and Orejas, Fernando}, title = {Coinductive techniques for checking satisfiability of generalized nested conditions}, series = {35th International Conference on Concurrency Theory (CONCUR 2024), Leibniz International Proceedings in Informatics (LIPIcs)}, journal = {35th International Conference on Concurrency Theory (CONCUR 2024), Leibniz International Proceedings in Informatics (LIPIcs)}, number = {311}, publisher = {Leibniz-Zentrum f{\"u}r Informatik}, address = {Schloss Dagstuhl}, doi = {10.4230/LIPIcs.CONCUR.2024.39}, pages = {39:1 -- 39:20}, abstract = {We study nested conditions, a generalization of first-order logic to a categorical setting, and provide a tableau-based (semi-decision) procedure for checking (un)satisfiability and finite model generation. This generalizes earlier results on graph conditions. Furthermore we introduce a notion of witnesses, allowing the detection of infinite models in some cases. To ensure completeness, paths in a tableau must be fair, where fairness requires that all parts of a condition are processed eventually. Since the correctness arguments are non-trivial, we rely on coinductive proof methods and up-to techniques that structure the arguments. We distinguish between two types of categories: categories where all sections are isomorphisms, allowing for a simpler tableau calculus that includes finite model generation; in categories where this requirement does not hold, model generation does not work, but we still obtain a sound and complete calculus.}, language = {en} }