We propose a fragment of many-sorted second order logic called EQSMT and show that checking satisfiability of sentences in this fragment is decidable. EQSMT formulae have an exists^*forall^* quantifier prefix (over variables, functions and relations) making EQSMT conducive for modeling synthesis problems. Moreover, EQSMT allows reasoning using a combination of background theories provided that they have a decidable satisfiability problem for the exists^*forall^* FO-fragment (e.g., linear arithmetic). Our decision procedure reduces the satisfiability of EQSMT formulae to satisfiability queries of exists^*forall^* formulae of each individual background theory, allowing us to use existing efficient SMT solvers supporting exists^*forall^* reasoning for these theories; hence our procedure can be seen as effectively quantified SMT (EQSMT) reasoning.
@InProceedings{madhusudan_et_al:LIPIcs.CSL.2018.31, author = {Madhusudan, P. and Mathur, Umang and Saha, Shambwaditya and Viswanathan, Mahesh}, title = {{A Decidable Fragment of Second Order Logic With Applications to Synthesis}}, booktitle = {27th EACSL Annual Conference on Computer Science Logic (CSL 2018)}, pages = {31:1--31:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-088-0}, ISSN = {1868-8969}, year = {2018}, volume = {119}, editor = {Ghica, Dan R. and Jung, Achim}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.31}, URN = {urn:nbn:de:0030-drops-96987}, doi = {10.4230/LIPIcs.CSL.2018.31}, annote = {Keywords: second order logic, synthesis, decidable fragment} }
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