Combining unification algorithms for confined regular equational theories
Proc. of the first international conference on Rewriting techniques and applications
Programming with sets; an introduction to SETL
Programming with sets; an introduction to SETL
Unification in combinations of collapse-free theories with disjoint sets of function symbols
Proc. of the 8th international conference on Automated deduction
Combination of unification algorithms
Proc. of the 8th international conference on Automated deduction
Unification in the data structure sets
Proc. of the 8th international conference on Automated deduction
NP-completeness of the set unification and matching problems
Proc. of the 8th international conference on Automated deduction
Associative-commutative unification
Journal of Symbolic Computation
Embedding boolean expressions into logic programming
Journal of Symbolic Computation
Unification in commutative idempotent monoids
Theoretical Computer Science
Journal of Automated Reasoning
A logical language for data and knowledge bases
A logical language for data and knowledge bases
Journal of Symbolic Computation
Boolean unification - The story so far
Journal of Symbolic Computation
F-logic: a higher-order language for reasoning about objects, inheritance, and scheme
SIGMOD '89 Proceedings of the 1989 ACM SIGMOD international conference on Management of data
Unification in a combination of arbitrary disjoint equational theories
Journal of Symbolic Computation
Adventures in associative-commutative unification
Journal of Symbolic Computation
Journal of Computer and System Sciences
A rule-based language with functions and sets
ACM Transactions on Database Systems (TODS)
Set constructors in a logic database language
Journal of Logic Programming
The Z notation: a reference manual
The Z notation: a reference manual
Compilation of set terms in the logic data language (LDL)
Journal of Logic Programming
Implementation of subset-equational programs
Journal of Logic Programming
Complexity of unification problems with associative-commutative operators
Journal of Automated Reasoning
The Go¨del programming language
The Go¨del programming language
Embedding extensional finite sets in CLP
ILPS '93 Proceedings of the 1993 international symposium on Logic programming
Journal of Symbolic Computation
Unification in the union of disjoint equational theories: combining decision procedures
Journal of Symbolic Computation
Optimal unification of bound simple set-terms
CIKM '96 Proceedings of the fifth international conference on Information and knowledge management
Vicious circles: on the mathematics of non-wellfounded phenomena
Vicious circles: on the mathematics of non-wellfounded phenomena
Set constraints and logic programming
Information and Computation
On the complexity of Boolean unification
Information Processing Letters
A uniform axiomatic view of lists, multisets, and sets, and the relevant unification algorithms
Fundamenta Informaticae
Type dependencies for logic programs using ACI-unification
Theoretical Computer Science
An Efficient Unification Algorithm
ACM Transactions on Programming Languages and Systems (TOPLAS)
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
Concrete Math
An Algorithm for General Set Unification and Its Complexity
Journal of Automated Reasoning
Set-Term Matching in Logic Programming
ICDT '92 Proceedings of the 4th International Conference on Database Theory
Set Constraints: Results, Applications, and Future Directions
PPCP '94 Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming
Design and Analysis of Parallel Set-Term Unification
COCOON '97 Proceedings of the Third Annual International Conference on Computing and Combinatorics
Comparing Expressiveness of Set Constructor Symbols
FroCoS '00 Proceedings of the Third International Workshop on Frontiers of Combining Systems
IWWERT '90 Proceedings of the First International Workshop on Word Equations and Related Topics
Proceedings of the 7th International Conference on Automated Deduction
An efficient algorithm for computing bisimulation equivalence
Theoretical Computer Science
An attributive logic of set descriptions and set operations
ACL '94 Proceedings of the 32nd annual meeting on Association for Computational Linguistics
A general framework for lazy functional logic programming with algebraic polymorphic types
Theory and Practice of Logic Programming
A logic-based framework for attribute based access control
Proceedings of the 2004 ACM workshop on Formal methods in security engineering
Decidability results for sets with atoms
ACM Transactions on Computational Logic (TOCL)
JSetL: a Java library for supporting declarative programming in Java
Software—Practice & Experience
External sources of knowledge and value invention in logic programming
Annals of Mathematics and Artificial Intelligence
A uniform approach to constraint-solving for lists, multisets, compact lists, and sets
ACM Transactions on Computational Logic (TOCL)
Integrating Finite Domain and Set Constraints into a Set-based Constraint Language
Fundamenta Informaticae - Advances in Computational Logic (CIL C08)
Theory-specific automated reasoning
A 25-year perspective on logic programming
Programming with partially specified aggregates in Java
Computer Languages, Systems and Structures
Decidable fragments of logic programming with value invention
JELIA'06 Proceedings of the 10th European conference on Logics in Artificial Intelligence
Integrating Finite Domain and Set Constraints into a Set-based Constraint Language
Fundamenta Informaticae - Advances in Computational Logic (CIL C08)
Fundamenta Informaticae
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The unification problem in algebras capable of describing sets has been tackled, directly or indirectly, by many researchers and it finds important applications in various research areas, e.g. deductive databases, theorem proving, static analysis, rapid software prototyping. The various solutions proposed are spread across a large literature. In this paper we provide a uniform presentation of unification of sets, formalizing it at the level of set theory. We address the problem of deciding existence of solutions at an abstract level. This provides also the ability to classify different types of set unification problems. Unification algorithms are uniformly proposed to solve the unification problem in each of such classes. The algorithms presented are partly drawn from the literature – and properly revisited and analyzed – and partly novel proposals. In particular, we present a new goal-driven algorithm for general $ACI1$ unification and a new simpler algorithm for general $(Ab)(C\ell)$ unification.