Computability and logic
The Z notation: a reference manual
The Z notation: a reference manual
Alloy: a lightweight object modelling notation
ACM Transactions on Software Engineering and Methodology (TOSEM)
Decidable verification for reducible timed automata specified in a first order logic with time
Theoretical Computer Science
Back to the future: revisiting precise program verification using SMT solvers
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Towards a Small Model Theorem for Data Independent Systems in Alloy
Electronic Notes in Theoretical Computer Science (ENTCS)
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
Decidable fragments of many-sorted logic
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Instantiation of SMT problems modulo integers
AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
Relational reasoning via SMT solving
FM'11 Proceedings of the 17th international conference on Formal methods
Information Processing Letters
The representation of inconsistent knowledge in advanced knowledge based systems
KES'11 Proceedings of the 15th international conference on Knowledge-based and intelligent information and engineering systems - Volume Part II
An Instantiation Scheme for Satisfiability Modulo Theories
Journal of Automated Reasoning
ABZ'12 Proceedings of the Third international conference on Abstract State Machines, Alloy, B, VDM, and Z
Instantiation Schemes for Nested Theories
ACM Transactions on Computational Logic (TOCL)
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Many natural specifications use types. We investigate the decidability of fragments of many-sorted first-order logic. We identified some decidable fragments and illustrated their usefulness by formalizing specifications considered in the literature. Often the intended interpretations of specifications are finite. We prove that the formulas in these fragments are valid iff they are valid over the finite structures. We extend these results to logics that allow a restricted form of transitive closure. We tried to extend the classical classification of the quantifier prefixes into decidable/undecidable classes to the many-sorted logic. However, our results indicate that a naive extension fails and more subtle classification is needed.