Principles of database and knowledge-base systems, Vol. I
Principles of database and knowledge-base systems, Vol. I
Bottom-up beats top-down for datalog
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Automatic recognition of tractability in inference relations
Journal of the ACM (JACM)
REDLOG: computer algebra meets computer logic
ACM SIGSAM Bulletin
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Automated complexity analysis based on ordered resolution
Journal of the ACM (JACM)
Polynomial-time computation via local inference relations
ACM Transactions on Computational Logic (TOCL)
Unions of non-disjoint theories and combinations of satisfiability procedures
Theoretical Computer Science
Complexity Analysis Based on Ordered Resolution
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
A rewriting approach to satisfiability procedures
Information and Computation - RTA 2001
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Model-Theoretic Methods in Combined Constraint Satisfiability
Journal of Automated Reasoning
An interpolating theorem prover
Theoretical Computer Science - Tools and algorithms for the construction and analysis of systems (TACAS 2004)
Combining Nonstably Infinite Theories
Journal of Automated Reasoning
Modular proof systems for partial functions with Evans equality
Information and Computation - Special issue: Combining logical systems
Automated Reasoning in Some Local Extensions of Ordered Structures
ISMVL '07 Proceedings of the 37th International Symposium on Multiple-Valued Logic
Applications of Hierarchical Reasoning in the Verification of Complex Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
Combination Methods for Satisfiability and Model-Checking of Infinite-State Systems
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Constraint solving for interpolation
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Interpolation in local theory extensions
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
What's decidable about arrays?
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Data structure specifications via local equality axioms
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Hierarchic reasoning in local theory extensions
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Automatic Verification of Combined Specifications: An Overview
Electronic Notes in Theoretical Computer Science (ENTCS)
Locality Results for Certain Extensions of Theories with Bridging Functions
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Ordered sets in the calculus of data structures
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
On hierarchical reasoning in combinations of theories
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
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We present an overview of results on hierarchical and modular reasoning in complex theories. We show that for a special type of extensions of a base theory, which we call local, hierarchic reasoning is possible (i.e. proof tasks in the extension can be hierarchically reduced to proof tasks w.r.t. the base theory). Many theories important for computer science or mathematics fall into this class (typical examples are theories of data structures, theories of free or monotone functions, but also functions occurring in mathematical analysis). In fact, it is often necessary to consider complex extensions, in which various types of functions or data structures need to be taken into account at the same time. We show how such local theory extensions can be identified and under which conditions locality is preserved when combining theories, and we investigate possibilities of efficient modular reasoning in such theory combinations.We present several examples of application domains where local theories and local theory extensions occur in a natural way. We show, in particular, that various phenomena analyzed in the verification literature can be explained in a unified way using the notion of locality.