Properties of substitutions and unifications
Journal of Symbolic Computation
First-order logic and automated theorem proving
First-order logic and automated theorem proving
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
Automating first-order relational logic
SIGSOFT '00/FSE-8 Proceedings of the 8th ACM SIGSOFT international symposium on Foundations of software engineering: twenty-first century applications
A machine program for theorem-proving
Communications of the ACM
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
Journal of Automated Reasoning
Ordered Semantic Hyper-Linking
Journal of Automated Reasoning
Partial Instantiation Methods for Inference in First-Order Logic
Journal of Automated Reasoning
Ordered Semantic Hyper Tableaux
Journal of Automated Reasoning
Automated Theorem Proving Proof and Model Generation with Disconnection Tableaux
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
JELIA '96 Proceedings of the European Workshop on Logics in Artificial Intelligence
A DPLL-Based Calculus for Ground Satisfiability Modulo Theories
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
The Disconnection Method - A Confluent Integration of Unification in the Analytic Framework
TABLEAUX '96 Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
Hyper Tableau - The Next Generation
TABLEAUX '98 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Integration of Equality Reasoning into the Disconnection Calculus
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
A Model Generation Style Completeness Proof for Constraint Tableaux with Superposition
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Deciding Separation Formulas with SAT
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
CSL '92 Selected Papers from the Workshop on Computer Science Logic
SATCHMO: A Theorem Prover Implemented in Prolog
Proceedings of the 9th International Conference on Automated Deduction
Soft Typing for Ordered Resolution
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
FDPLL - A First Order Davis-Putnam-Longeman-Loveland Procedure
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Incremental Closure of Free Variable Tableaux
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
New Directions in Instantiation-Based Theorem Proving
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Lifted search engines for satisfiability
Lifted search engines for satisfiability
Depth-first proof search without backtracking for free-variable clausal tableaux
Journal of Symbolic Computation - Special issue: First order theorem proving
Journal of Artificial Intelligence Research
Ordered semantic hyper linking
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Lemma learning in the model evolution calculus
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
The model evolution calculus with equality
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Model representation via contexts and implicit generalizations
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Deciding Effectively Propositional Logic Using DPLL and Substitution Sets
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
SMELS: Satisfiability Modulo Equality with Lazy Superposition
ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
Journal of Automated Reasoning
Designing Visual Languages for Description Logics
Journal of Logic, Language and Information
Annals of Mathematics and Artificial Intelligence
Solving quantified verification conditions using satisfiability modulo theories
Annals of Mathematics and Artificial Intelligence
Deciding Effectively Propositional Logic Using DPLL and Substitution Sets
Journal of Automated Reasoning
Combining instance generation and resolution
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Theoretical Computer Science
Encoding industrial hardware verification problems into effectively propositional logic
Proceedings of the 2010 Conference on Formal Methods in Computer-Aided Design
A slice-based decision procedure for type-based partial orders
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Model Evolution with equality - Revised and implemented
Journal of Symbolic Computation
CDCL-based abstract state transition system for coherent logic
CICM'12 Proceedings of the 11th international conference on Intelligent Computer Mathematics
A bisimulation between DPLL(T) and a proof-search strategy for the focused sequent calculus
Proceedings of the Eighth ACM SIGPLAN international workshop on Logical frameworks & meta-languages: theory & practice
Quantifier instantiation techniques for finite model finding in SMT
CADE'13 Proceedings of the 24th international conference on Automated Deduction
SMELS: Satisfiability Modulo Equality with Lazy Superposition
Journal of Automated Reasoning
Hi-index | 0.00 |
The DPLL procedure is the basis of some of the most successful propositional satisfiability solvers to date. Although originally devised as a proof-procedure for first-order logic, it has been used almost exclusively for propositional logic so far because of its highly inefficient treatment of quantifiers, based on instantiation into ground formulas. The FDPLL calculus by Baumgartner was the first successful attempt to lift the procedure to the first-order level without resorting to ground instantiations. FDPLL lifts to the first-order case the core of the DPLL procedure, the splitting rule, but ignores other aspects of the procedure that, although not necessary for completeness, are crucial for its effectiveness in practice. In this paper, we present a new calculus loosely based on FDPLL that lifts these aspects as well. In addition to being a more faithful lifting of the DPLL procedure, the new calculus contains a more systematic treatment of universal literals, which are crucial to achieve efficiency in practice. The new calculus has been implemented successfully in the Darwin system, described elsewhere. The main results of this paper are theoretical, showing the soundness and completeness of the new calculus. In addition, the paper provides a high-level description of a proof procedure for the calculus, as well as a comparison with other calculi.