Logic for computer science: foundations of automatic theorem proving
Logic for computer science: foundations of automatic theorem proving
An algebraic approach to unification under associativity and commutativity
Proc. of the first international conference on Rewriting techniques and applications
Unification in datastructure multisets
Journal of Automated Reasoning
Complete sets of unifiers and matchers in equational theories
Theoretical Computer Science
Logic program semantics for programming with equations
Proceedings on Third international conference on logic programming
A categorical unification algorithm
Proceedings of a tutorial and workshop on Category theory and computer programming
Sufficient completeness, term rewriting systems and “anti-unification”
Proc. of the 8th international conference on Automated deduction
Combination of unification algorithms
Proc. of the 8th international conference on Automated deduction
Logical foundations of artificial intelligence
Logical foundations of artificial intelligence
Journal of Automated Reasoning
Unification under associativity and idempotence is of type nullary
Journal of Automated Reasoning
The theory of idempotent semigroups is of unification type zero
Journal of Automated Reasoning
POPL '87 Proceedings of the 14th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Generalized subsumption and its applications to induction and redundancy
Artificial Intelligence
Opening the AC-unification race
Journal of Automated Reasoning
Foundations of deductive databases and logic programming
Unification: a multidisciplinary survey
ACM Computing Surveys (CSUR)
Constraint satisfaction in logic programming
Constraint satisfaction in logic programming
Journal of Symbolic Computation
Journal of Symbolic Computation
Equational problems anddisunification
Journal of Symbolic Computation
On equational theories, unification, and (Un)decidability
Journal of Symbolic Computation
Unification in a combination of arbitrary disjoint equational theories
Journal of Symbolic Computation
Matching - A special case of unification?
Journal of Symbolic Computation
Automated reasoning (2nd ed.): introduction and applications
Automated reasoning (2nd ed.): introduction and applications
A resolution principle for constrained logics
Artificial Intelligence
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Complete Sets of Reductions for Some Equational Theories
Journal of the ACM (JACM)
A Unification Algorithm for Associative-Commutative Functions
Journal of the ACM (JACM)
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
Lazy Theory Unification inProlog: An Extension of the warren Abstract machine
GWAI-86 und 2. Österreichische Artificial-Intelligence-Tagung
Proceedings of the 7th International Conference on Automated Deduction
Solving Disequations in Equational Theories
Proceedings of the 9th International Conference on Automated Deduction
Completion of a set of rules modulo a set of equations
POPL '84 Proceedings of the 11th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Constraints in computational logics
A New Proposal Of Quasi-Solved Form For Equality Constraint Solving
Electronic Notes in Theoretical Computer Science (ENTCS)
On the cooperation of the constraint domains ℋ, ℛ, and ℱ in cflp
Theory and Practice of Logic Programming
Sequence disunification and its application in collaborative schema construction
WISE'07 Proceedings of the 2007 international conference on Web information systems engineering
Equational constraint solving via a restricted form of universal quantification
FoIKS'06 Proceedings of the 4th international conference on Foundations of Information and Knowledge Systems
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We are interested in the problem of solving a systemi=ti:1≤i≤n,pj≠qj:1≤j≤m of equations and disequations, also known as disunification. Solutions to disunification problems are substitutions for the variables of the problem that make the two terms of each equation equal, but leave those of the disequations different. We investigate this in both algebraic and logical contexts where equality is defined by an equational theory and more generally by a definitive clause equality theory E. We show how E-disunification can be reduced to E-unification, that is, solving equations only, and give a disunification algorithm for theories given a unification algorithm. In fact, this result shows that for theories in which the solutions of all unification problems can also be represented finitely. We sketch how disunification can be applied to handle negation in logic programming with equality in a similar style to Colmerauer's logic programming with rational trees, and to represent many solutions to AC-unification problems by a few solutions to ACI-disunification problems.