Automated deduction by theory resolution
Journal of Automated Reasoning
Programming with sets; an introduction to SETL
Programming with sets; an introduction to SETL
Journal of Computer and System Sciences
Mechanical geometry theorem proving
Mechanical geometry theorem proving
Complexity of deciding Tarski algebra
Journal of Symbolic Computation
Journal of Symbolic Computation
The problem of finding and inference rule for set theory
Journal of Automated Reasoning
Computable set theory
Handbook of theoretical computer science (vol. B)
Journal of Automated Reasoning - Special issue on new trends in automated reasoning
A derived algorithm for evaluating ε-expressions over abstract sets
Journal of Symbolic Computation - Special issue on automatic programming
Automated deduction in von Neumann-Bernays-Go¨del set theory
Journal of Automated Reasoning
IMPS: an interactive mathematical proof system
Journal of Automated Reasoning
Journal of Symbolic Computation
ILPS '97 Proceedings of the 1997 international symposium on Logic programming
A Mechanical Proof Procedure and its Realization in an Electronic Computer
Journal of the ACM (JACM)
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
A Practical Decision Procedure for Arithmetic with Function Symbols
Journal of the ACM (JACM)
Fast Decision Procedures Based on Congruence Closure
Journal of the ACM (JACM)
On the complexity of integer programming
Journal of the ACM (JACM)
Deciding Combinations of Theories
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Set theory for computing: from decision procedures to declarative programming with sets
Set theory for computing: from decision procedures to declarative programming with sets
Information and Computation
T-Resolution: Refinements and Model Elimination
Journal of Automated Reasoning
Unions of non-disjoint theories and combinations of satisfiability procedures
Theoretical Computer Science
A 'Theory' Mechanism for a Proof-Verifier Based on First-Order Set Theory
Computational Logic: Logic Programming and Beyond, Essays in Honour of Robert A. Kowalski, Part II
ISAAC '88 Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Combining Equational Theories Sharing Non-Collapse-Free Constructors
FroCoS '00 Proceedings of the Third International Workshop on Frontiers of Combining Systems
FroCoS '02 Proceedings of the 4th International Workshop on Frontiers of Combining Systems
TABLEAUX '99 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
A Tableau Calculus for Combining Non-disjoint Theories
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Embedding Finite Sets in a Logic Programming Language
ELP '92 Proceedings of the Third International Workshop on Extensions of Logic Programming
Decision Problems for Tarski and Presburger Arithmetics Extended With Sets
CSL '90 Proceedings of the 4th Workshop on Computer Science Logic
A New Fast Tableau-Based Decision Procedure for an Unquantified Fragment of Set Theory
Selected Papers from Automated Deduction in Classical and Non-Classical Logics
An Equational Re-engineering of Set Theories
Selected Papers from Automated Deduction in Classical and Non-Classical Logics
Decision Procedures for Some Fragments of Set Theory
Proceedings of the 5th Conference on Automated Deduction
Combining Multisets with Integers
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Instructing Equational Set-Reasoning with Otter
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Journal of Automated Reasoning
Decidability results for sets with atoms
ACM Transactions on Computational Logic (TOCL)
Combining Nonstably Infinite Theories
Journal of Automated Reasoning
Theory and Practice of Logic Programming
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Decision procedures for extensions of the theory of arrays
Annals of Mathematics and Artificial Intelligence
Decision Procedures: An Algorithmic Point of View
Decision Procedures: An Algorithmic Point of View
A faster PSPACE algorithm for deciding the existential theory of the reals
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Satisfiability Procedures for Combination of Theories Sharing Integer Offsets
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
Stable models and difference logic
Annals of Mathematics and Artificial Intelligence
Putting theories together to make specifications
IJCAI'77 Proceedings of the 5th international joint conference on Artificial intelligence - Volume 2
On the decidability of formulae involving continuous and closed functions
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 1
Theorem proving in type theory
IJCAI'77 Proceedings of the 5th international joint conference on Artificial intelligence - Volume 1
Social processes, program verification and all that
Mathematical Structures in Computer Science
Reasoning, Action and Interaction in AI Theories and Systems
Set Graphs. III. Proof Pearl: Claw-Free Graphs Mirrored into Transitive Hereditarily Finite Sets
Journal of Automated Reasoning
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In designing a large-scale computerized proof system, one is often confronted with issues of two kinds: issues regarding an underlying logical calculus, and issues that refer to theories, either specified axiomatically or characterized by indication of either a privileged model or a family of intended models. Proof services related to the theories most often take the form of satisfiability decision or semi-decision procedures (in a sense, polyadic inference rules), while some of the services offered by the calculus (e.g., the Davis-Putnam propositional satisfiability checker) provide low-level mechanisms for integrating services of the former kind. Integration among services can ensure speed-up (i.e., lower number of steps) in the proofs, but it must always be legitimatized by a conservativeness result. Interoperability among proof checkers and autonomous theorem provers is another key point of integration. In discussing these and related issues, this paper refers to Set Theory as the unifying background, and to a specific proof-checker based on a slightly unorthodox formalization of it as an arena for experimentation.