Sufficient completeness, term rewriting systems and “anti-unification”
Proc. of the 8th international conference on Automated deduction
Explicit representation of terms defined by counter examples
Journal of Automated Reasoning
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
An Efficient Unification Algorithm
ACM Transactions on Programming Languages and Systems (TOPLAS)
Proving termination with multiset orderings
Communications of the ACM
An Effective Method for Handling Initial Algebras
Proceedings of the International Workshop on Algebraic and Logic Programming
A New Quasi-Reducibility Testing Algorithm and its Application to Proofs by Induction
Proceedings of the International Workshop on Algebraic and Logic Programming
Solving Disequations in Equational Theories
Proceedings of the 9th International Conference on Automated Deduction
Stop losing sleep over incomplete data type specifications
POPL '84 Proceedings of the 11th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Constrained equational reasoning
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Equations, disequations and unsolvable subsets (abstract)
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
On solving equations and disequations
Journal of the ACM (JACM)
Extending constraint logic programming with open functions
Proceedings of the 2nd ACM SIGPLAN international conference on Principles and practice of declarative programming
A decision procedure for term algebras with queues
ACM Transactions on Computational Logic (TOCL)
Constraints in computational logics
A Methodological View of Constraint Solving
Constraints
A New Technique for Verifying and Correcting Logic Programs
Journal of Automated Reasoning
Semantic Generalizations for Proving and Disproving Conjectures by Analogy
Journal of Automated Reasoning
Explicit versus implicit representations of subsets of the Herbrand universe
Theoretical Computer Science
Solving Mixed Quantified Constraints over a Domain Based on Real Numbers and Herbrand Terms
FLOPS '02 Proceedings of the 6th International Symposium on Functional and Logic Programming
Negation Elimination from Simple Equational Formulae
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Algorithms on Atomic Representations of Herbrand Models
JELIA '98 Proceedings of the European Workshop on Logics in Artificial Intelligence
PSI '99 Proceedings of the Third International Andrei Ershov Memorial Conference on Perspectives of System Informatics
Extending Decidable Clause Classes via Constraints
Selected Papers from Automated Deduction in Classical and Non-Classical Logics
Completeness and Redundancy in Constrained Clause Logic
Selected Papers from Automated Deduction in Classical and Non-Classical Logics
Extracting models from clause sets saturated under semantic refinements of the resolution rule
Information and Computation
Model elimination and connection tableau procedures
Handbook of automated reasoning
A Decision Procedure for Term Algebras with Queues
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
A Decision Procedure for the Existential Theory of Term Algebras with the Knuth-Bendix Ordering
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Model building with ordered resolution: extracting models from saturated clause sets
Journal of Symbolic Computation - Special issue: First order theorem proving
On the complexity of equational problems in CNF
Journal of Symbolic Computation - Special issue: First order theorem proving
On Deciding Subsumption Problems
Annals of Mathematics and Artificial Intelligence
The first order theory of primal grammars is decidable
Theoretical Computer Science
Knuth--bendix constraint solving is NP-complete
ACM Transactions on Computational Logic (TOCL)
Proceedings of the 2006 ACM symposium on Applied computing
A constraint-based approach to guarded algebraic data types
ACM Transactions on Programming Languages and Systems (TOPLAS)
Decision procedures for term algebras with integer constraints
Information and Computation - Special issue: Combining logical systems
Generalizing DPLL and satisfiability for equalities
Information and Computation
Theory and Practice of Logic Programming
A New Proposal Of Quasi-Solved Form For Equality Constraint Solving
Electronic Notes in Theoretical Computer Science (ENTCS)
Theory of finite or infinite trees revisited
Theory and Practice of Logic Programming
Superposition for Fixed Domains
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Decidability Results for Saturation-Based Model Building
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Analogy and abduction in automated deduction
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
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
A generalization of the folding rule for the Clark-Kunen semantics
FLOPS'08 Proceedings of the 9th international conference on Functional and logic programming
Superposition for fixed domains
ACM Transactions on Computational Logic (TOCL)
Deciding the inductive validity of ∀∃* queries
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Disunification for ultimately periodic interpretations
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Predicate completion for non-Horn clause sets
CADE'11 Proceedings of the 23rd international conference on Automated deduction
CADE'11 Proceedings of the 23rd international conference on Automated deduction
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
The decidability of the first-order theory of knuth-bendix order
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
A complete axiomatization of strict equality
FLOPS'10 Proceedings of the 10th international conference on Functional and Logic Programming
TOSCA'11 Proceedings of the 2011 international conference on Theory of Security and Applications
Tree Automata and Automated Model Building
Fundamenta Informaticae
Completeness and decidability results for first-order clauses with indices
CADE'13 Proceedings of the 24th international conference on Automated Deduction
A Resolution Calculus for First-order Schemata
Fundamenta Informaticae
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Roughly speaking, an equational problem is a first order formula whose only predicatesymbol is =. We propose some rules for the transformation of equational problems and study their correctness in various models. Then, we give completeness results with respect to some ''simple'' problems called solved forms. Such completeness results still hold when adding some control which moreover ensures termination. The termination proofs are given for a ''weak'' control and thus hold for the (large) class of algorithms obtained by restricting the scope of the rules. Finally, it must be noted that a by-product of our method is a decision procedure for the validity in the Herbrand Universe of any first order formula with the only predicate symbol=.