A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
Isar - A Generic Interpretative Approach to Readable Formal Proof Documents
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
On the Mechanization of the Proof of Hessenberg's Theorem in Coherent Logic
Journal of Automated Reasoning
The model evolution calculus as a first-order DPLL method
Artificial Intelligence
Architecting Solvers for SAT Modulo Theories: Nelson-Oppen with DPLL
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
Formalization and Implementation of Modern SAT Solvers
Journal of Automated Reasoning
Instance-Based Selection of Policies for SAT Solvers
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Deciding Effectively Propositional Logic Using DPLL and Substitution Sets
Journal of Automated Reasoning
Skolem machines and geometric logic
ICTAC'07 Proceedings of the 4th international conference on Theoretical aspects of computing
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Geometric resolution: a proof procedure based on finite model search
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
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We present a new, CDCL-based approach for automated theorem proving in coherent logic -- an expressive semi-decidable fragment of first-order logic that provides potential for obtaining human readable and machine verifiable proofs. The approach is described by means of an abstract state transition system, inspired by existing transition systems for SAT and represents its faithful lifting to coherent logic. The presented transition system includes techniques from which CDCL SAT solvers benefited the most (backjumping and lemma learning), but also allows generation of human readable proofs. In contrast to other approaches to theorem proving in coherent logic, reasoning involved need not to be ground. We prove key properties of the system, primarily that the system yields a semidecision procedure for coherent logic. As a consequence, the semidecidability of another fragment of first order logic which is a proper superset of coherent logic is also proven.