Uniform Proofs as a Foundation for Logic Programming

@article{Miller1991UniformPA,
  title={Uniform Proofs as a Foundation for Logic Programming},
  author={Dale A. Miller and Gopalan Nadathur and Frank Pfenning and Andre Scedrov},
  journal={Ann. Pure Appl. Log.},
  year={1991},
  volume={51},
  pages={125-157}
}
Abstract Miller, D., G. Nadathur, F. Pfenning and A. Scedrov, Uniform proofs as a foundation for logic programming, Annals of Pure and Applied Logic 51 (1991) 125–157. A proof-theoretic characterization of logical languages that form suitable bases for Prolog-like programming languages is provided. This characterization is based on the principle that the declarative meaning of a logic program, provided by provability in a logical system, should coincide with its operational meaning, provided by… Expand
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References

SHOWING 1-10 OF 59 REFERENCES
A higher-order logic as the basis for logic programming
The objective of this thesis is to provide a formal basis for higher-order features in the paradigm of logic programming. Towards this end, a non-extensional form of higher-order logic that is basedExpand
A Logical Analysis of Modules in Logic Programming
TLDR
A logical language which extends the syntax of positive Horn clauses by permitting implications in goals and in the bodies of clauses is presented and it is shown how to build a Kripke-like model for programs by a fixed-point construction and shown that the operational meaning of implication is sound and complete for intuitionistic logic. Expand
Specifying Theorem Provers in a Higher-Order Logic Programming Language
TLDR
An extended logic programming language where first-order terms are replaced with simply-typed λ-terms, higher-order unification replaces first- order unification, and implication and universal quantification are allowed in queries and the bodies of clauses is presented. Expand
AN OVERVIEW OF PROLOG
λProlog is a logic programming language that extends Prolog by incorporating notions of higher-order functions, λ-terms, higher-order unification, polymorphic types, and mechanisms for buildingExpand
A Logic Programming Approach to Manipulating Formulas and Programs
TLDR
This paper shows how a simple natural deduction theorem prover may be implemented in $\lambda$Prolog, and how some simple program transformers for a functional programming language may be written in this language. Expand
Contributions to the Theory of Logic Programming
TLDR
It is shown that nondeterministic flowchart schemata of bounded nondeterminacy are modeled by this special case of Hom clauses, and the connection between finite failure and greatest fixpoint is used to give a semantic characterization of termination, blocking, and nontermination of such flowchart Schemata. Expand
A Kripke-Kleene Semantics for Logic Programs
  • M. Fitting
  • Computer Science, Mathematics
  • J. Log. Program.
  • 1985
The use of conventional classical logic is misleading for characterizing the behavior of logic programs because a logic program, when queried, will do one of three things: succeed with the query,Expand
Hornlog: A Graph-Based Interpreter for General Horn Clauses
Abstract This paper presents hornlog , a general Horn-clause proof procedure that can be used to interpret logic programs. The system is based on a form of graph rewriting, and on the linear-timeExpand
Some Uses of Higher-Order Logic in Computational Linguistics
TLDR
A higher-order logic programming language is described, called λProlog, which represents programs as higher- order definite clauses and interprets them using a depth-first interpreter and claims that its use makes the task of providing formal justifications for the computations specified much more direct. Expand
Natural Deduction as Higher-Order Resolution
TLDR
An interactive theorem prover, Isabelle, is under development, which has been used to prove theorems in Martin-Lof's constructive type theory and may have potential for logic programming. Expand
...
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...