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On the Undecidability of SecondOrder Unification
 INFORMATION AND COMPUTATION
, 2000
"... ... this paper, and it is the starting point for proving some novel results about the undecidability of secondorder unification presented in the rest of the paper. We prove that secondorder unification is undecidable in the following three cases: (1) each secondorder variable occurs at most t ..."
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Cited by 33 (16 self)
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... this paper, and it is the starting point for proving some novel results about the undecidability of secondorder unification presented in the rest of the paper. We prove that secondorder unification is undecidable in the following three cases: (1) each secondorder variable occurs at most twice and there are only two secondorder variables; (2) there is only one secondorder variable and it is unary; (3) the following conditions (i)#(iv) hold for some fixed integer n: (i) the arguments of all secondorder variables are ground terms of size <n, (ii) the arity of all secondorder variables is <n, (iii) the number of occurrences of secondorder variables is #5, (iv) there is either a single secondorder variable or there are two secondorder variables and no firstorder variables.
On ProofSearch in Intuitionistic Logic with Equality, or Back to Simultaneous Rigid EUnification
 Automated Deduction  CADE13
, 1996
"... We characterize provability in intuitionistic logic with equality in terms of a constraint calculus. This characterization uncovers close connections between provability in intuitionistic logic with equality and solutions to simultaneous rigid Eunification. We show that the problem of existence of ..."
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Cited by 17 (9 self)
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We characterize provability in intuitionistic logic with equality in terms of a constraint calculus. This characterization uncovers close connections between provability in intuitionistic logic with equality and solutions to simultaneous rigid Eunification. We show that the problem of existence of a sequent proof with a given skeleton is polynomialtime equivalent to simultaneous rigid Eunifiability. This gives us a proof procedure for intuitionistic logic with equality modulo simultaneous rigid Eunification. We also show that simultaneous rigid Eunifiability is polynomialtime reducible to intuitionistic logic with equality. Thus, any proof procedure for intuitionistic logic with equality can be considered as a procedure for simultaneous rigid Eunifiability. In turn, any procedure for simultaneous rigid Eunifiability gives a procedure for establishing provability in intuitionistic logic with equality. 2 2 Copyright c fl 1995, 1996 Andrei Voronkov. This technical report and ot...
Monadic simultaneous rigid Eunification and related problems
 AUTOMATA, LANGUAGES AND PROGRAMMING, 24TH INTERNATIONAL COLLOQUIUM, ICALP'97, VOLUME 1256 OF LECTURE NOTES IN COMPUTER SCIENCE
, 1997
"... We study the monadic case of a decision problem know as simultaneous rigid Eunification. We show its equivalence to an extension of word equations. We prove decidability and complexity results for special cases of this problem. ..."
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Cited by 8 (1 self)
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We study the monadic case of a decision problem know as simultaneous rigid Eunification. We show its equivalence to an extension of word equations. We prove decidability and complexity results for special cases of this problem.
The Logic in Computer Science Column
 In Bulletin of the European Association for Theoretical Computer Science
, 1996
"... The famous Herbrand's theorem of mathematical logic plays an important role in automated theorem proving. In the first part of this article, we recall the theorem and formulate a number of natural decision problems related to it. Somewhat surprisingly, these problems happen to be equivalent. One of ..."
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The famous Herbrand's theorem of mathematical logic plays an important role in automated theorem proving. In the first part of this article, we recall the theorem and formulate a number of natural decision problems related to it. Somewhat surprisingly, these problems happen to be equivalent. One of these problems is the socalled simultaneous rigid Eunification problem. In the second part, we survey recent result on the simultaneous rigid Eunification problem.
The Logic in Computer Science Column
 In Bulletin of the European Association for Theoretical Computer Science
, 1988
"... The famous Herbrand's theorem of mathematical logic plays an important role in automated theorem proving. In the first part of this article, we recall the theorem and formulate a number of natural decision problems related to it. Somewhat surprisingly, these problems happen to be equivalent. One of ..."
Abstract
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The famous Herbrand's theorem of mathematical logic plays an important role in automated theorem proving. In the first part of this article, we recall the theorem and formulate a number of natural decision problems related to it. Somewhat surprisingly, these problems happen to be equivalent. One of these problems is the socalled simultaneous rigid Eunification problem. In the second part, we survey recent result on the simultaneous rigid Eunification problem. 1 Problems This simultaneous rigid Eunification : : : It has too procedural a definition. Vaughan Pratt, private communication. We start with some decision problems having nonprocedural definitions. Most of these problems naturally stem from the famous Herbrand theorem. 1.1 Herbrand's theorem and six decision problems The Herbrand theorem [28] asserts that an existential firstorder formula 9¯x'(¯x) is provable (in classical firstorder logic) if and only if a particular disjunction '( ¯ t 1 ) : : : '( ¯ t n ) is provab...
The Logic in Computer Science Column
 In Bulletin of the European Association for Theoretical Computer Science
, 1988
"... The famous Herbrand's theorem of mathematical logic plays an important role in automated theorem proving. In the first part of this article, we recall the theorem and formulate a number of natural decision problems related to it. Somewhat surprisingly, these problems happen to be equivalent. One ..."
Abstract
 Add to MetaCart
The famous Herbrand's theorem of mathematical logic plays an important role in automated theorem proving. In the first part of this article, we recall the theorem and formulate a number of natural decision problems related to it. Somewhat surprisingly, these problems happen to be equivalent. One of these problems is the socalled simultaneous rigid Eunification problem. In the second part, we survey recent result on the simultaneous rigid problem.