Programming with sets; an introduction to SETL
Programming with sets; an introduction to SETL
The automation of syllogistic I. Syllogistic normal forms
Journal of Symbolic Computation
The automation of syllogistic. II. optimization and complexity issues
Journal of Automated Reasoning
Symbolic model checking: 1020 states and beyond
Information and Computation - Special issue: Selections from 1990 IEEE symposium on logic in computer science
A derived algorithm for evaluating ε-expressions over abstract sets
Journal of Symbolic Computation - Special issue on automatic programming
The Go¨del programming language
The Go¨del programming language
Journal of Automated Reasoning
Journal of Symbolic Computation
Automated reasoning and its applications
A uniform axiomatic view of lists, multisets, and sets, and the relevant unification algorithms
Fundamenta Informaticae
Journal of Computer and System Sciences
Sets and constraint logic programming
ACM Transactions on Programming Languages and Systems (TOPLAS)
Set theory for computing: from decision procedures to declarative programming with sets
Set theory for computing: from decision procedures to declarative programming with sets
Information and Computation
Automated Development of Fundamental Mathematical Theories
Automated Development of Fundamental Mathematical Theories
Specifying Systems: The TLA+ Language and Tools for Hardware and Software Engineers
Specifying Systems: The TLA+ Language and Tools for Hardware and Software Engineers
STMM: A Set Theory for Mechanized Mathematics
Journal of Automated Reasoning
Set Theory, Higher Order Logic or Both?
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
ZUM '97 Proceedings of the 10th International Conference of Z Users on The Z Formal Specification Notation
Instructing Equational Set-Reasoning with Otter
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Ensuring correctness of ruby transformations
DCC'96 Proceedings of the 3rd international conference on Designing Correct Circuits
Theory and Practice of Logic Programming
Theory-specific automated reasoning
A 25-year perspective on logic programming
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Formal set theory is traditionally concerned with pure sets; consequently, the satisfiability problem for fragments of set theory was most often addressed (and in many cases positively solved) in the pure framework. In practical applications, however, it is common to assume the existence of a number of primitive objects (sometimes called atoms) that can be members of sets but behave differently from them. If these entities are assumed to be devoid of members, the standard extensionality axiom must be revised; then decidability results can sometimes be achieved via reduction to the pure case and sometimes can be based on direct goal-driven algorithms. An alternative approach to modeling atoms that allows one to retain the original formulation of extensionality was proposed by Quine: atoms are self-singletons. In this article we adopt this approach in coping with the satisfiability problem: We show the decidability of this problem relativized to ∃*∀-sentences, and develop a goal-driven unification algorithm.