# A Survey of the Proof-Theoretic Foundations of Logic Programming

@article{Miller2021ASO,
title={A Survey of the Proof-Theoretic Foundations of Logic Programming},
author={Dale Miller},
journal={ArXiv},
year={2021},
volume={abs/2109.01483}
}
• Dale Miller
• Published 3 September 2021
• Computer Science
• ArXiv
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this article, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using this foundation for the past 35 years to elevate logic programming from its roots in first-order classical logic into higher-order versions of intuitionistic and linear logic. These more expressive logic programming languages allow for capturing stateful…

## References

SHOWING 1-10 OF 267 REFERENCES
Uniform Proofs as a Foundation for Logic Programming
• Computer Science
Ann. Pure Appl. Log.
• 1991
A Two-Level Logic Approach to Reasoning About Computations
• Computer Science, Philosophy
Journal of Automated Reasoning
• 2011
It is shown how provability in the specification logic can be transparently encoded in ${\cal G}$, and an interactive theorem prover called Abella is described that implements this two-level logic approach and is presented to demonstrate the efficacy of Abella in reasoning about computations.
The foundation of a generic theorem prover
Higher-order logic has several practical advantages over other meta-logics, such as Huet's higher-order unification procedure, and Isabelle is now based on higher- order logic-a precise and well-understood foundation.
Investigations into logical deduction
• The Collected Papers of Gerhard Gentzen, M. E. Szabo, Ed. North-Holland, Amsterdam, 68–131. Translation of articles that appeared in 1934-35. Collected papers appeared in 1969.
• 1935
Answer set programming at a glance
• Computer Science
Commun. ACM
• 2011
The motivation and key concepts behind answer set programming---a promising approach to declarative problem solving.
After a formal definition of ASP, this chapter surveys the main contribution given by the Italian community to the ASP field in the last 25 years.
• Computer Science
LPAR
• 2015
A new interpreter for Prolog is presented that runs consistently faster than the byte code compiled by Teyjus, and is considered the best available implementation of the language.
• Computer Science
• 2015
We present a new interpreter for λProlog that runs consistently faster than the byte code compiled by Teyjus, that is believed to be the best available implementation of λProlog. The key insight is
A multiple-conclusion meta-logic
• Dale A. Miller
• Computer Science
Proceedings Ninth Annual IEEE Symposium on Logic in Computer Science
• 1994
Forum is presented, a logic programming presentation of all of linear logic that modularly extends the languages /spl lambda/Prolog, Lolli, and LO, and greatly extends the expressiveness of these other logic programming languages.
System Description: Twelf - A Meta-Logical Framework for Deductive Systems
• Computer Science