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Otter: The CADE13 Competition Incarnations
 JOURNAL OF AUTOMATED REASONING
, 1997
"... This article discusses the two incarnations of Otter entered in the CADE13 Automated Theorem Proving Competition. Also presented are some historical background, a summary of applications that have led to new results in mathematics and logic, and a general discussion of Otter. ..."
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Cited by 43 (3 self)
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This article discusses the two incarnations of Otter entered in the CADE13 Automated Theorem Proving Competition. Also presented are some historical background, a summary of applications that have led to new results in mathematics and logic, and a general discussion of Otter.
A Method for Building Models Automatically. Experiments with an extension of OTTER
 In Proceedings of CADE12
, 1994
"... . A previous work on Herbrand model construction is extended in two ways. The first extension increases the capabilities of the method, by extending one of its key rules. The second, more important one, defines a new method for simultaneous search of refutations and models for set of equational clau ..."
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Cited by 28 (14 self)
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. A previous work on Herbrand model construction is extended in two ways. The first extension increases the capabilities of the method, by extending one of its key rules. The second, more important one, defines a new method for simultaneous search of refutations and models for set of equational clauses. The essential properties of the new method are given. The main theoretical result of the paper is the characterization of conditions assuring that models can be built. Both methods (for equational and non equational clauses) have been implemented as an extension of OTTER. Several running examples are given, in particular a new automatic solution of the ternary algebra problem first solved by Winker. The examples emphasize the unified approach to model building allowed by the ideas underlying our method and the usefulness of using constrained clauses. Several problems open by the present work are the main lines of future work. 1 Introduction It is trivial to say that the use of models o...
Decision Procedures and Model Building in Equational Clause Logic
 JOURNAL OF THE IGPL
, 1998
"... It is shown that a combination of semantic resolution and ordered paramodulation provides a decision procedure for a large class PVD g of clause sets with equality. It is also demonstrated how the inference system can be transformed into an algorithm that extracts finite descriptions of Herbrand ..."
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Cited by 15 (2 self)
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It is shown that a combination of semantic resolution and ordered paramodulation provides a decision procedure for a large class PVD g of clause sets with equality. It is also demonstrated how the inference system can be transformed into an algorithm that extracts finite descriptions of Herbrand models from sets of clauses. This algorithm always terminates on clause sets in PVD g and yields an appropriate model representation. Moreover, an algorithm for evaluating arbitrary clauses over the represented models is defined. Finally, it is proved that PVD g enjoys the finite model property and shown how finite models can be algorithmically extracted from model representations of this type.
Tree Automata and Automated Model Building
, 1997
"... . The use of regular tree grammars to represent and build models of formulae of firstorder logic without equality is investigated. The combination of regular tree grammars with equational constraints provides a powerful and general way of representing Herbrand models. We show that the evaluation pr ..."
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Cited by 9 (4 self)
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. The use of regular tree grammars to represent and build models of formulae of firstorder logic without equality is investigated. The combination of regular tree grammars with equational constraints provides a powerful and general way of representing Herbrand models. We show that the evaluation problem (i.e. the problem of finding the truth value of a formula in a given model) is decidable when models are represented in the way we propose. We also define a method to build such representations of models for firstorder formulae. These results are a powerful extension of our former method for simultaneous search for refutations and models. Keywords: Automated Deduction, Model Building, Tree Automata, Regular Tree Grammars. 1. Introduction The problem of building models or counterexamples of firstorder formulae is a very important one, particularly in the field of automated deduction. Besides their intrinsic interest for disproving conjectures, counterexamples (models) have numerous...
Automated Reasoning and Bledsoe's Dream for the Field
"... In one sense, this article is a personal tribute to Woody Bledsoe. As such, the style will in general be that of private correspondence. However, since this article is also a compendium of experiments with an automated reasoning program, researchers interested in automated reasoning, mathematics, an ..."
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Cited by 7 (6 self)
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In one sense, this article is a personal tribute to Woody Bledsoe. As such, the style will in general be that of private correspondence. However, since this article is also a compendium of experiments with an automated reasoning program, researchers interested in automated reasoning, mathematics, and logic will find pertinent material here. The results of those experiments strongly suggest that research frequently benefits greatly from the use of an automated reasoning program. As evidence, I select from those results some proofs that are better than one can find in the literature, and focus on some theorems that, until now, had never been proved with an automated reasoning program, theorems that Hilbert, Church, and various logicians thought significant. To add spice to the article, I present challenges for reasoning programs, including questions that are still open. 1 This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Depa...
A New Method for Automated Finite Model Building Exploiting Failures and Symmetries
, 1998
"... . A method for building finite models is proposed. It combines enumeration of the set of interpretations on a finite domain with strategies in order to prune significantly the search space. The main new ideas underlying our method are to benefit from symmetries and from the information extracted fro ..."
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Cited by 6 (2 self)
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. A method for building finite models is proposed. It combines enumeration of the set of interpretations on a finite domain with strategies in order to prune significantly the search space. The main new ideas underlying our method are to benefit from symmetries and from the information extracted from the structure of the problem and from failures of model verification tests. The algorithms formalizing the approach are given and the standard properties (termination, completeness, and soundness) are proven. The method can deal with firstorder logic with equality. In contrast to existing ones, it does not require to transform the initial problem into a normal form and can be easily extended to other logics. Experimental results and comparisons with related works are reported. 1. Introduction The capital importance of the notion of "model" in Logic was naturally inherited by Automated Deduction, where, since the very beginning, the use of models has been recognized as an useful technique...
Building Models By Using Tableaux Extended By Equational Problems
, 1993
"... The problem of model construction is known to be a very important one. An extension of semantic tableaux (that can also be applied to the matings and to the connection method) allowing the building of models in a systematic way is presented. This approach is different from the usual one in semantic ..."
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Cited by 5 (2 self)
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The problem of model construction is known to be a very important one. An extension of semantic tableaux (that can also be applied to the matings and to the connection method) allowing the building of models in a systematic way is presented. This approach is different from the usual one in semantic tableaux, in which model construction is a byproduct of refutation failures (and this only in very particular cases). In fact, we incorporate in the object level, reasoning usually done in an ad hoc manner in the metalevel. Some of the rules introduced by this extension are essentially new. The impossibility of simulating them by the standard tableaux rules and their necessity in extending the class of captured models is shown. These rules and the modified classical ones are based on the use of equational problems. Equational problems are formulae containing only equalities and inequalities, connected by "and", "or" and quantified in a particular way. The method preserves the refutational...
Simplifying and generalizing formulae in tableaux. Pruning the search space and building models (long version)
, 1997
"... . A powerful extension of the tableau method is described. It consists in a new simplification rule allowing to prune the search space and a new way of extracting a model from a given (possibly infinite) branch. These features are combined with a former method for simultaneous search for refutations ..."
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Cited by 5 (0 self)
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. A powerful extension of the tableau method is described. It consists in a new simplification rule allowing to prune the search space and a new way of extracting a model from a given (possibly infinite) branch. These features are combined with a former method for simultaneous search for refutations and models. The possibilities of the new method w.r.t. the original one are clearly stated. In particular it is shown that the method is able to build model for each formula having a model expressible by equational constraints. 1. Introduction The construction and the use of models or counterexamples are crucial techniques widely used in all aspects of human reasoning. In mathematics, models allow the rejection of false conjectures or help to prove theorems. Incorporating such abilities into automated theorem provers is therefore a very natural idea, which has been considered since the beginning [15, 25]. Nevertheless, it is not until the nineties that feasible methods have been proposed ...
Combining inference and disinference rules with enumeration for model building (Extended Abstract)
, 1997
"... ) Ricardo Caferra and Nicolas Peltier Laboratory LEIBNIZIMAG 46, Avenue F'elix Viallet 38031 Grenoble Cedex FRANCE Ricardo.Caferra@imag.fr, Nicolas.Peltier@imag.fr Phone: (33) (0)4 76 57 46 59 1 Introduction The possibility of systematic model building in firstorder logic exists at least since t ..."
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Cited by 1 (1 self)
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) Ricardo Caferra and Nicolas Peltier Laboratory LEIBNIZIMAG 46, Avenue F'elix Viallet 38031 Grenoble Cedex FRANCE Ricardo.Caferra@imag.fr, Nicolas.Peltier@imag.fr Phone: (33) (0)4 76 57 46 59 1 Introduction The possibility of systematic model building in firstorder logic exists at least since the introduction of the tableaux method (Hintikka, Beth, Smullyan,: : : ), approximately 40 years ago. Some striking results in interactive model building have been obtained less than 20 years ago [21]. But it is only since less than 10 years that results on model building are regularly published [15, 7, 8, 5, 12, 13, 20, 22]. One important difference must be underlined between proof calculi and model building methods. Different calculi for firstorder logic (resolution, tableaux, connection method (matings), : : : ) are potentially able to prove the same class of theorems. In papers on model building methods what is emphasized in general is the class of models that the methods can (or cannot...