Computation-oriented reductions of predicate to propositional logic
Decision Support Systems
Proceedings of the workshop on Sorts and types in artificial intelligence
Partial Instantiation Methods for Inference in First-Order Logic
Journal of Automated Reasoning
Implementation and use of the PLT scheme Web server
Higher-Order and Symbolic Computation
Deciding Effectively Propositional Logic Using DPLL and Substitution Sets
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Complete Instantiation for Quantified Formulas in Satisfiabiliby Modulo Theories
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Decidable fragments of many-sorted logic
Journal of Symbolic Computation
Towards a Small Model Theorem for Data Independent Systems in Alloy
Electronic Notes in Theoretical Computer Science (ENTCS)
Kodkod: a relational model finder
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
Decidability of invariant validation for paramaterized systems
TACAS'03 Proceedings of the 9th international conference on Tools and algorithms for the construction and analysis of systems
Aluminum: principled scenario exploration through minimality
Proceedings of the 2013 International Conference on Software Engineering
Tierless programming and reasoning for software-defined networks
NSDI'14 Proceedings of the 11th USENIX Conference on Networked Systems Design and Implementation
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Many model-finding tools, such as Alloy, charge users with providing bounds on the sizes of models. It would be preferable to automatically compute sufficient upper-bounds whenever possible. The Bernays-Schönfinkel-Ramsey fragment of first-order logic can relieve users of this burden in some cases: its sentences are satisfiable iff they are satisfied in a finite model, whose size is computable from the input problem. Researchers have observed, however, that the class of sentences for which such a theorem holds is richer in a many-sorted framework--which Alloy inhabits--than in the one-sorted case. This paper studies this phenomenon in the general setting of order-sorted logic supporting overloading and empty sorts. We establish a syntactic condition generalizing the Bernays-Schönfinkel-Ramsey form that ensures the Finite Model Property. We give a linear-time algorithm for deciding this condition and a polynomial-time algorithm for computing the bound on model sizes. As a consequence, model-finding is a complete decision procedure for sentences in this class. Our work has been incorporated into Margrave, a tool for policy analysis, and applies in real-world situations.