Journal of Symbolic Computation
RTA-91 Proceedings of the 4th international conference on Rewriting techniques and applications
Any ground associative-commutative theory has a finite canonical system
RTA-91 Proceedings of the 4th international conference on Rewriting techniques and applications
Handbook of theoretical computer science (vol. B)
Syntacticness, cycle-syntacticness, and shallow theories
Information and Computation
Theorem proving with ordering and equality constrained clauses
Journal of Symbolic Computation
Information and Computation
Ordered Paramodulation and Resolution as Decision Procedure
LPAR '93 Proceedings of the 4th International Conference on Logic Programming and Automated Reasoning
On Narrowing, Refutation Proofs and Constraints
RTA '95 Proceedings of the 6th International Conference on Rewriting Techniques and Applications
Superposition with Simplification as a Desision Procedure for the Monadic Class with Equality
KGC '93 Proceedings of the Third Kurt Gödel Colloquium on Computational Logic and Proof Theory
Some Termination Criteria for Narrowing and E-Narrowing
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Journal of Automated Reasoning
Complexity of Linear Standard Theories
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
On the Confluence of Linear Shallow Term Rewrite Systems
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
On the Confluence of Linear Shallow Term Rewrite Systems
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
The Unification Problem for Confluent Right-Ground Term Rewriting Systems
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
Combining superposition, sorts and splitting
Handbook of automated reasoning
Paramodulation with Built-In Abelian Groups
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
The unification problem for confluent right-ground term rewriting systems
Information and Computation - RTA 2001
Superposition with completely built-in Abelian groups
Journal of Symbolic Computation
Modular proof systems for partial functions with Evans equality
Information and Computation - Special issue: Combining logical systems
Narrowing and Rewriting Logic: from Foundations to Applications
Electronic Notes in Theoretical Computer Science (ENTCS)
Superposition for Fixed Domains
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Unique Normalization for Shallow TRS
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
Termination of narrowing revisited
Theoretical Computer Science
LPAR'00 Proceedings of the 7th international conference on Logic for programming and automated reasoning
Superposition for fixed domains
ACM Transactions on Computational Logic (TOCL)
Natural narrowing for general term rewriting systems
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Confluence of shallow right-linear rewrite systems
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
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We prove that for sets of Horn clauses saturated under basic paramodulation, the word and unifiability problems are in NP, and the number of minimal unifiers is simply exponential (i). For Horn sets saturated wrt.\ a special ordering under the more restrictive inference rule of basic superposition, the word and unifiability problems are still decidable and unification is finitary (ii). We define standard theories, which include and significantly extend shallow theories. Standard presentations can be finitely closed under superposition and result (ii) applies. Generalizing shallow theories to the Horn case, we obtain (two versions of) a language we call Catalog, a natural extension of Datalog to include functions and equality. The closure under paramodulation is finite for Catalog sets, hence (i) applies. Since for shallow sets this closure is even polynomial, shallow unifiability is in NP, which is optimal: unifiability in ground theories is already NP-hard. We even go beyond: the shallow word problem is tractable and for Catalog sets we prove decidability of the full first-order theory of the corresponding quotient term algebra.