124 research outputs found
A Posthumous Contribution by {Larry Wos}: {E}xcerpts from an Unpublished Column
International audienceShortly before Larry Wos passed away, he sent a manuscript for discussion to Sophie Tourret, the editor of the AAR newsletter. We present excerpts from this final manuscript, put it in its historic context and explain its relevance for today’s research in automated reasoning
Extensional Higher-Order Paramodulation in Leo-III
Leo-III is an automated theorem prover for extensional type theory with
Henkin semantics and choice. Reasoning with primitive equality is enabled by
adapting paramodulation-based proof search to higher-order logic. The prover
may cooperate with multiple external specialist reasoning systems such as
first-order provers and SMT solvers. Leo-III is compatible with the TPTP/TSTP
framework for input formats, reporting results and proofs, and standardized
communication between reasoning systems, enabling e.g. proof reconstruction
from within proof assistants such as Isabelle/HOL. Leo-III supports reasoning
in polymorphic first-order and higher-order logic, in all normal quantified
modal logics, as well as in different deontic logics. Its development had
initiated the ongoing extension of the TPTP infrastructure to reasoning within
non-classical logics.Comment: 34 pages, 7 Figures, 1 Table; submitted articl
SPASS-SATT: A CDCL(LA) Solver
International audienceSPASS-SATT is a CDCL(LA) solver for linear rational and linear mixed/integer arithmetic. This system description explains its specific features: fast cube tests for integer solvability, bounding transformations for unbounded problems, close interaction between the SAT solver and the theory solver, efficient data structures, and small-clause-normal-form generation. SPASS-SATT is currently one of the strongest systems on the respective SMT-LIB benchmarks
Template-Based Conjecturing for Automated Induction in Isabelle/HOL
Proof by induction plays a central role in formal verification. However, its
automation remains as a formidable challenge in Computer Science. To solve
inductive problems, human engineers often have to provide auxiliary lemmas
manually. We automate this laborious process with template-based conjecturing,
a novel approach to generate auxiliary lemmas and use them to prove final
goals. Our evaluation shows that our working prototype, TBC, achieved 40
percentage point improvement of success rates for problems at intermediate
difficulty level.Comment: To appear at Fundamentals of Software engineering 2023
(http://fsen.ir/2023/
MizAR 60 for Mizar 50
As a present to Mizar on its 50th anniversary, we develop an AI/TP system that automatically proves about 60% of the Mizar theorems in the hammer setting. We also automatically prove 75% of the Mizar theorems when the automated provers are helped by using only the premises used in the human-written Mizar proofs. We describe the methods and large-scale experiments leading to these results. This includes in particular the E and Vampire provers, their ENIGMA and Deepire learning modifications, a number of learning-based premise selection methods, and the incremental loop that interleaves growing a corpus of millions of ATP proofs with training increasingly strong AI/TP systems on them. We also present a selection of Mizar problems that were proved automatically
The Tactician (extended version): A Seamless, Interactive Tactic Learner and Prover for Coq
We present Tactician, a tactic learner and prover for the Coq Proof
Assistant. Tactician helps users make tactical proof decisions while they
retain control over the general proof strategy. To this end, Tactician learns
from previously written tactic scripts and gives users either suggestions about
the next tactic to be executed or altogether takes over the burden of proof
synthesis. Tactician's goal is to provide users with a seamless, interactive,
and intuitive experience together with robust and adaptive proof automation. In
this paper, we give an overview of Tactician from the user's point of view,
regarding both day-to-day usage and issues of package dependency management
while learning in the large. Finally, we give a peek into Tactician's
implementation as a Coq plugin and machine learning platform.Comment: 19 pages, 2 figures. This is an extended version of a paper published
in CICM-2020. For the project website, see https://coq-tactician.github.i
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