SAT-Based Subsumption Resolution

Subsumption resolution is an expensive but highly effective simplifying inference for first-order saturation theorem provers. We present a new SAT-based reasoning technique for subsumption resolution, without requiring radical changes to the underlying saturation algorithm. We implemented our work in the theorem prover Vampire, and show that it is noticeably faster than the state of the art

SCL(EQ): SCL for First-Order Logic with Equality

We propose a new calculus SCL(EQ) for first-order logic with equality thatonly learns non-redundant clauses. Following the idea of CDCL (Conflict DrivenClause Learning) and SCL (Clause Learning from Simple Models) a ground literalmodel assumption is used to guide inferences that are then guaranteed to benon-redundant. Redundancy is defined with respect to a dynamically changingordering derived from the ground literal model assumption. We prove SCL(EQ)sound and complete and provide examples where our calculus improves onsuperposition.<br

Cyclic Hypersequent System for Transitive Closure Logic

We propose a cut-free cyclic system for transitive closure logic (TCL) based on a form of hypersequents, suitable for automated reasoning via proof search. We show that previously proposed sequent systems are cut-free incomplete for basic validities from Kleene Algebra (KA) and propositional dynamic logic (PDL), over standard translations. On the other hand, our system faithfully simulates known cyclic systems for KA and PDL , thereby inheriting their completeness results. A peculiarity of our system is its richer correctness criterion, exhibiting ‘alternating traces’ and necessitating a more intricate soundness argument than for traditional cyclic proofs.</p

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions