Internal Guidance for Satallax

Färber, Michael; Brown, Chad E.

doi:10.1007/978-3-319-40229-1_24

Cited by 24 publications

(17 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The literature evaluates various procedures and techniques [21,36], literal and term order selection functions [20], and clause evaluation functions [19,39], among others. Our work joins the select club of papers devoted to practical aspects of higher-order reasoning [8,16,41,53].…”

Section: Discussionmentioning

confidence: 99%

Making Higher-Order Superposition Work

et al. 2022

View full text Add to dashboard Cite

Superposition is among the most successful calculi for firstorder logic. Its extension to higher-order logic introduces new challenges such as infinitely branching inference rules, new possibilities such as reasoning about formulas, and the need to curb the explosion of specific higher-order rules. We describe techniques that address these issues and extensively evaluate their implementation in the Zipperposition theorem prover. Largely thanks to their use, Zipperposition won the higher-order division of the CASC-J10 competition.

show abstract

Section: Discussionmentioning

confidence: 99%

Making Higher-Order Superposition Work

et al. 2022

View full text Add to dashboard Cite

show abstract

“…We use the state-of-the-art HO provers Leo-III [43], Satallax [17,25] and Ehoh [42,48] as baselines in our evaluation. The first two have refutationally complete calculi for extensional HOL with Henkin semantics, while the third only supports λ-free HOL without first-class Booleans.…”

Section: Discussionmentioning

confidence: 99%

Extending SMT Solvers to Higher-Order Logic

Barbosa

Reynolds

Ouraoui

et al. 2019

Lecture Notes in Computer Science

View full text Add to dashboard Cite

SMT solvers have throughout the years been able to cope with increasingly expressive formulas, from ground logics to full first-order logic (FOL). In contrast, the extension of SMT solvers to higher-order logic (HOL) is mostly unexplored. We propose a pragmatic extension for SMT solvers to support HOL reasoning natively without compromising performance on FOL reasoning, thus leveraging the extensive research and implementation efforts dedicated to efficient SMT solving. We show how to generalize data structures and the ground decision procedure to support partial applications and extensionality, as well as how to reconcile quantifier instantiation techniques with higher-order variables. We also discuss a separate approach for redesigning an HOL SMT solver from the ground up via new data structures and algorithms. We apply our pragmatic extension to the CVC4 SMT solver and discuss a redesign of the veriT SMT solver. Our evaluation shows they are competitive with state-of-the-art HOL provers and often outperform the traditional encoding into FOL.

show abstract

“…Using machine learning for internal guidance is historically motivated by the success of the external guidance methods used mainly for premise selection outside of the core ATP systems [14,37,84]. Guiding the actual proof search of ATPs using machine learning has been considered in the integration of a Naive Bayesian classifier to select next proof actions in Satallax [21], as well as in Enigma [35] where the clause selection in E uses a tree-based n-gram approach to approximate similarity to the learned proofs using a support vector machine classifier. Holophrasm [87] introduces a theorem prover architecture using GRU neural networks to guide the proof search of a tableaux style proof process of MetaMath.…”

Section: Related Workmentioning

confidence: 99%

Machine Learning Guidance for Connection Tableaux

2020

Self Cite

View full text Add to dashboard Cite

Connection calculi allow for very compact implementations of goal-directed proof search. We give an overview of our work related to connection tableaux calculi: first, we show optimised functional implementations of connection tableaux proof search, including a consistent Skolemisation procedure for machine learning. Then, we show two guidance methods based on machine learning, namely reordering of proof steps with Naive Bayesian probabilities, and expansion of a proof search tree with Monte Carlo Tree Search.

show abstract

Internal Guidance for Satallax

Cited by 24 publications

References 14 publications

Making Higher-Order Superposition Work

Making Higher-Order Superposition Work

Extending SMT Solvers to Higher-Order Logic

Machine Learning Guidance for Connection Tableaux

Contact Info

Product

Resources

About