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11
On Unification Problems in Restricted SecondOrder Languages
 In Annual Conf. of the European Ass. of Computer Science Logic (CSL98
, 1998
"... We review known results and improve known boundaries between the decidable and the undecidable cases of secondorder unification with various restrictions on secondorder variables. As a key tool we prove an undecidability result that provides a partial solution to an open problem about simultaneous ..."
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Cited by 6 (3 self)
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We review known results and improve known boundaries between the decidable and the undecidable cases of secondorder unification with various restrictions on secondorder variables. As a key tool we prove an undecidability result that provides a partial solution to an open problem about simultaneous rigid Eunification.
Simultaneous rigid EUnification and other decision problems related to the Herbrand theorem
, 1998
"... Recently, a number of results have been published related to simultaneous rigid Eunification and Herbrand's theorem for logic with equality. The aim of this article is to overview these results, fill in some proofs that have only been sketched before, and present some new results. ..."
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Cited by 3 (2 self)
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Recently, a number of results have been published related to simultaneous rigid Eunification and Herbrand's theorem for logic with equality. The aim of this article is to overview these results, fill in some proofs that have only been sketched before, and present some new results.
Comparing Computational Representations of Herbrand Models
 Computational Logic and Proof Theory, 5th Kurt Godel Colloquium, KGC'97, volume 1289 of LNCS
, 1997
"... . Finding computationally valuable representations of models of predicate logic formulas is an important issue in the field of automated theorem proving, e.g. for automated model building or semantic resolution. In this article we treat the problem of representing single models independently of buil ..."
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Cited by 3 (2 self)
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. Finding computationally valuable representations of models of predicate logic formulas is an important issue in the field of automated theorem proving, e.g. for automated model building or semantic resolution. In this article we treat the problem of representing single models independently of building them and discuss the power of different mechanisms for this purpose. We start with investigating contextfree languages for representing single Herbrand models. We show their computational feasibility and prove their expressive power to be exactly the finite models. We show an equivalence with "ground atoms and ground equations" concluding equal expressive power. Finally we indicate how various other well known techniques could be used for representing essentially infinite models (i.e. models of not finitely controllable formulas), thus motivating our interest in relating model properties with syntactical properties of corresponding Herbrand models and in investigating connections betwe...
Using Grammars for Finite Domain Evaluation
 INT. WORKSHOP ON FIRSTORDER THEOREM PROVING (FTP'97), RISCLINZ REPORT SERIES NO. 9750
, 1997
"... In [8] we investigated representing Herbrand models via contextfree grammars and found the representation power of this method to be exactly the finite models. Based on these observations we now present a clause set evaluation algorithm that operates directly on grammars, avoiding the exponential ..."
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Cited by 2 (2 self)
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In [8] we investigated representing Herbrand models via contextfree grammars and found the representation power of this method to be exactly the finite models. Based on these observations we now present a clause set evaluation algorithm that operates directly on grammars, avoiding the exponential blowup from the number of nonterminals in the grammar to the number of elements in the finite domain of the corresponding model, ending up with a notsoobvious evaluation procedure for arbitrary clause sets over finite interpretations (specified via grammars).
Rigid Variables Considered Harmful
, 1997
"... We study complexity of methods using rigid variables, like the method of matings or the tableau method, on a decidable class of predicate calculus with equality. We show some intrinsic complications introduced by rigid variables. We also consider strategies for increasing multiplicity in rigidvaria ..."
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We study complexity of methods using rigid variables, like the method of matings or the tableau method, on a decidable class of predicate calculus with equality. We show some intrinsic complications introduced by rigid variables. We also consider strategies for increasing multiplicity in rigidvariable methods, and formally show that the use of intelligent strategies can result in an essential gain in efficiency. 1 Section 1. Introduction Section 1 Introduction Automated reasoning methods for firstorder classical logic can generally be divided in two classes. Methods of the first class use universal variables (resolution [34], the inverse method [27]). Variables in these methods are local to a clause (formula, sequent) and can be considered as universally quantified in this clause (respectively formula or sequent). [29, 28] characterized these methods as local methods (see also [30]). Methods of the second class use rigid variables (the tableau method [4], the mating or the connecti...
CHAPTER 1 EQUALITY AND OTHER THEORIES
"... Theory reasoning is an important technique for increasing the efficiency of automated deduction systems. The knowledge from a given domain (or theory) is made use of by applying efficient methods for reasoning in that domain. The general purpose foreground reasoner calls a special purpose background ..."
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Theory reasoning is an important technique for increasing the efficiency of automated deduction systems. The knowledge from a given domain (or theory) is made use of by applying efficient methods for reasoning in that domain. The general purpose foreground reasoner calls a special purpose background reasoner to
Strategies in RigidVariable Methods
"... We study complexity of methods using rigid variables, like the method of matings or the tableau method, on a decidable class of predicate calculus with equality. We show some intrinsic complications introduced by rigid variables. We also consider strategies for increasing multiplicity in rigidvaria ..."
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We study complexity of methods using rigid variables, like the method of matings or the tableau method, on a decidable class of predicate calculus with equality. We show some intrinsic complications introduced by rigid variables. We also consider strategies for increasing multiplicity in rigidvariable methods, and formally show that the use of intelligent strategies can result in an essential gain in efficiency. 1