• Corpus ID: 118273145

On Simultaneous Rigid E-Unification

@inproceedings{Veanes1997OnSR,
  title={On Simultaneous Rigid E-Unification},
  author={Margus Veanes},
  year={1997}
}
Automated theorem proving methods in classical logic with equality that are based on the Herbrand theorem, reduce to a problem called Simultaneous Rigid E-Unification, or SREU for short. Recent dev ... 
On Unification Problems in Restricted Second-Order Languages
We review known results and improve known boundaries between the decidable and the undecidable cases of second-order unification with various restrictions on second-order variables. As a key tool we
The Undecidability of Simultaneous Rigid E-Unification with Two Variables
  • M. Veanes
  • Mathematics
    Kurt Gödel Colloquium
  • 1997
TLDR
It is shown that 4 rigid equations with ground left-hand sides and 2 variables already imply undecidability, which contributes to a complete characterization of decidability of the prenex fragment of intuitionistic logic with equality, in terms of the quantifier prefix.
Equality and Other Theories
TLDR
The general purpose foreground reasoner calls a special purpose background reasoner to handle problems from a certain theory to increase the efficiency of automated deduction systems.
Proof Search in Intuitionistic Logic with Equality, or Back to Simultaneous Rigid E-Unification
  • A. Voronkov
  • Philosophy
    Journal of Automated Reasoning
  • 2004
TLDR
It is shown that the problem of existence of a sequent proof with a given skeleton is polynomial-time equivalent to simultaneous rigid E-unifiability, which gives a proof procedure for intuitionistic logic with equality modulo simultaneous rigidE-unification.
Proof-Search in Intuitionistic Logic with Equality, or Back to Simultaneous Rigid E-Unification
  • A. Voronkov
  • Philosophy
    Journal of Automated Reasoning
  • 2004
TLDR
It is shown that the problem of existence of a sequent proof with a given skeleton is polynomial-time equivalent to simultaneous rigid E-unifiability, which gives a proof procedure for intuitionistic logic with equality modulo simultaneous rigidE-unification.
Constraint Solving on Terms
In this chapter, we focus on constraint solving on terms, also called Herbrand constraints in the introductory chapter, and we follow the main concepts introduced in that chapter.
The relation between second-order unification and simultaneous rigid E-unification
  • M. Veanes
  • Computer Science
    Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226)
  • 1998
TLDR
This work uses finite tree automata techniques to present a very elementary undecidability proof of second-order unification, by reduction from the halting problem for Turing machines, which follows from that proof that second- order unification is undecidable for all nonmonadicsecond-order term languages having at least two second-orders variables with sufficiently high arities.
Kanger’s Choices in Automated Reasoning
TLDR
The contribution of Kanger to automated deduction is well-recognized, and his monograph [1957] introduced a calculus LC, which was one of the first calculi intended for automated proof-search.
Rigid E-unification
By replacing syntactical unification with rigid E-unification, equality handling can be added torigid variable calculi for first-order logic, including free variable tableau (Fitting, 1996), the
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References

SHOWING 1-10 OF 138 REFERENCES
Reduction of Second-Order Unification to Simultaneous Rigid E-Unification
The simultaneous rigid E-uni cation problem is used in automated reasoning with equality. In our previous paper we proved the undecidability of this problem by reduction of monadic semiuni cation.
Simultaneous rigid E-unification and related algorithmic problems
TLDR
It is proved decidability results for fragments of monadic simultaneous rigid E-unification are found and the connections between this notion and some algorithmic problems of logic and computer science are shown.
The Undecidability of the Second-Order Unification Problem
The Undecidability of Simultaneous Rigid E-Unification with Two Variables
  • M. Veanes
  • Mathematics
    Kurt Gödel Colloquium
  • 1997
TLDR
It is shown that 4 rigid equations with ground left-hand sides and 2 variables already imply undecidability, which contributes to a complete characterization of decidability of the prenex fragment of intuitionistic logic with equality, in terms of the quantifier prefix.
The Undecidability of Simultaneous Rigid E-Unification
PROBLEM OF DECIDABILITY FOR SOME CONSTRUCTIVE THEORIES OF EQUALITIES
The question of the existence of a decidable algorithm for the following three deductive theories, constructed on the basis of constructive predicate calculus, is considered herein.
A Complete Connection Calculus with Rigid E-Unification
TLDR
The problem whether for the construction of a complete goal-oriented prover with equality it is sufficient to be able to solve only a restricted version of the simultaneous rigid E-unification problem is posed.
An algorithm for reasoning about equality
A simple technique for reasoning about equalities that is fast and complete for ground formulas with function symbols and equality is presented. A proof of correctness is given as well.
An Intuitionistic Predicate Logic Theorem Prover
A complete theorem prover for intuitionistic predicate logic based on the cut-free calculus is presented. It includes a treatment of "quasi-free" identity based on a delay mechanism and a special
The Decidability of Simultaneous Rigid E-Unification with One Variable
TLDR
This work shows that simultaneous rigid E-unification, or SREU for short, is decidable and in fact EXPTIME-complete in the case of one variable, and obtains a complete classification of decidability of the prenex fragment of intuitionistic logic with equality, in terms of the quantifier prefix.
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