Special relations in automated deduction
Journal of the ACM (JACM) - The MIT Press scientific computation series
Completeness results for inequality provers
Artificial Intelligence
Journal of Symbolic Computation
On restrictions of ordered paramodulation with simplification
CADE-10 Proceedings of the tenth international conference on Automated deduction
A completion procedure for conditional equationst
Journal of Symbolic Computation
Completeness of a prover for dense linear orders
Journal of Automated Reasoning
Automatic Theorem Proving with Built-in Theories Including Equality, Partial Ordering, and Sets
Journal of the ACM (JACM)
Journal of Automated Reasoning
Selected papers from the 10th Workshop on Specification of Abstract Data Types Joint with the 5th COMPASS Workshop on Recent Trends in Data Type Specification
Bi-rewriting, a Term Rewriting Technique for Monotonic Order Relations
RTA '93 Proceedings of the 5th International Conference on Rewriting Techniques and Applications
Some reordering properties for inequality proof trees
Proceedings of the Symposium "Rekursive Kombinatorik" on Logic and Machines: Decision Problems and Complexity
The Special-Relation Rules are Incomplete
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
PVS: A Prototype Verification System
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Superposition for Divisible Torsion-Free Abelian Groups
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
A Maximal-Literal Unit Strategy for Horn Clauses
Proceedings of the 2nd International CTRS Workshop on Conditional and Typed Rewriting Systems
Efficient deductive methods for program analysis
POPL '01 Proceedings of the 28th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Herbrand's Theorem for Prenex Gödel Logic and its Consequences for Theorem Proving
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
Deriving Focused Calculi for Transitive Relations
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
Issues of Decidability for Description Logics in the Framework of Resolution
Selected Papers from Automated Deduction in Classical and Non-Classical Logics
Superposition and Chaining for Totally Ordered Divisible Abelian Groups
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
Journal of Symbolic Computation
Modular proof systems for partial functions with Evans equality
Information and Computation - Special issue: Combining logical systems
Automated theorem proving by resolution in non-classical logics
Annals of Mathematics and Artificial Intelligence
Electronic Notes in Theoretical Computer Science (ENTCS)
Deciding expressive description logics in the framework of resolution
Information and Computation
On Automating the Calculus of Relations
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
On the refutational completeness of signed binary resolution and hyperresolution
Fuzzy Sets and Systems
Automated verification of refinement laws
Annals of Mathematics and Artificial Intelligence
A resolution mechanism for Prenex Gödel logic
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Automated engineering of relational and algebraic methods in isabelle/hol
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
An extension of complex role inclusion axioms in the description logic SROIQ
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Proof theory for locally finite many-valued logics: Semi-projective logics
Theoretical Computer Science
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We propose inference systems for binary relations that satisfy composition laws such as transitivity. Our inference mechanisms are based on standard techniques from term rewriting and represent a refinement of chaining methods as they are used in the context of resolution-type theorem proving. We establish the refutational completeness of these calculi and prove that our methods are compatible with the usual simplification techniques employed in refutational theorem provers, such as subsumption or tautology deletion. Various optimizations of the basic chaining calculus will be discussed for theories with equality and for total orderings. A key to the practicality of chaining methods is the extent to which so-called variable chaining can be avoided. We demonstrate that rewrite techniques considerably restrict variable chaining and that further restrictions are possible if the transitive relation under consideration satisfies additional properties, such as symmetry. But we also show that variable chaining cannot be completely avoided in general.