The undecidability of the second-order unification problem
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It is shown that there is no effective procedure for determining whether or not two terms of the language of second-order logic have a common instance.About:
This article is published in Theoretical Computer Science.The article was published on 1981-01-01 and is currently open access. It has received 334 citations till now. The article focuses on the topics: Unification & Order (business).read more
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CHAPTER 6 – Rewrite Systems
TL;DR: In this paper, the authors focus on rewrite systems, which are directed equations used to compute by repeatedly replacing sub-terms of a given formula with equal terms until the simplest form possible is obtained.
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Lambda Calculus with Types
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Equations and rewrite rules: a survey
Gérard Huet,Derek C. Oppen +1 more
TL;DR: The problem of "solving" equations, the problem of proving termination of sets of rewrite rules, and the decidability and complexity of word problems and of combinations of equational theories are discussed.
Journal ArticleDOI
A Logic Programming Language with Lambda-Abstraction, Function Variables, and Simple Unification
TL;DR: This paper presents a logic programming language, called L, that also contains both function variables and A-abstractions, but certain restriction are placed on occurrences of function variables, so an implementation of LA does not need to implement full higher-order unification.
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Automated Theorem Proving
TL;DR: A comparison study of the connection method in propositional logic and its applications in first-order logic and in natural and formal logic.
References
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Journal ArticleDOI
A Machine-Oriented Logic Based on the Resolution Principle
TL;DR: The paper concludes with a discussion of several principles which are applicable to the design of efficient proof-procedures employing resolution as the basle logical process.
Proceedings ArticleDOI
Linear unification
Mike Paterson,M. N. Wegman +1 more
TL;DR: A unification algorithm is described which tests a set of expressions for unifiability and which requires time and space which are only linear in the size of the input.
Journal ArticleDOI
The undecidability of unification in third order logic
TL;DR: The problem of the existence of a unifying substitution between two terms is shown to be undecidable, even if the objects of the language are restricted to third order.
Journal ArticleDOI
Some results on the length of proofs
TL;DR: This paper shall consider questions regarding the length of proofs of theories formalised in some language of thelower predicate calculus by means of a finite number of axioms, axiomschemata and schematic rules of inference, including Hilbert type and Gentzen type formalisations of classical and in-tuitionistic arithmetic.