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Finite Model Building: Improvements and Comparisons
 In: Model Computation – Principles, Algorithms, Applications, CADE19 Workshop W4
, 2003
"... The paper ivestigates nite model building for rst order logic. We consider two main categories of methods: Macetype and Falcontype methods. The paper has two goals: rst, presenting several improvements and strategies for the basic Macetype and Falcontype algorithms, second, comparing the e ..."
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The paper ivestigates nite model building for rst order logic. We consider two main categories of methods: Macetype and Falcontype methods. The paper has two goals: rst, presenting several improvements and strategies for the basic Macetype and Falcontype algorithms, second, comparing the eciency of dierent methods. The improvements to the Macetype algorithms are focused on decreasing the size of the propositional subtasks. A new cell selection heuristics is introduced for the Falcontype algorithms. The methods are implemented in the Gandalf theorem prover. We present both the eect of the introduced improvements and the comparison of method categories for several problem classes, based on their syntactical characteristics. Finally, several suggestions for further investigations are given.
Definites and the Proper Treatment of Rabbits
 in Proceedings of Inference in Computational Semantics, eds., Christof Monz and Maarten de Rijke
, 1999
"... We argue that model generation programs, i.e., deduction systems that automatically compute the interpretations satisfying a given formula, can provide a procedural interpretation for semantic theories of natural language. We illustrate this claim by describing how the higherorder model generat ..."
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We argue that model generation programs, i.e., deduction systems that automatically compute the interpretations satisfying a given formula, can provide a procedural interpretation for semantic theories of natural language. We illustrate this claim by describing how the higherorder model generator Kimba interprets definite descriptions. 1 Introduction The concept of a Discourse Model has repeatedly been advocated as an essential component of natural language understanding. In cognitive psychology, discourse models have been used to explain inferences that people draw in understanding text [3]. In artificial intelligence, Webber proposes them as describing the situation/state which the speaker is talking about [21]. The understanding task then consists in an attempt by the listener to synthesize the appropriate discourse model. In the dynamic/DRT (Discourse Representation Theory [10]) trend of natural language semantics, it represents the context created by previous discourse and ...
The Flowering of Automated Reasoning
, 2001
"... This article celebrates with obvious joy the role automated reasoning now plays for mathematics and logic. Simultaneously, this article evidences the realization of a dream thought impossible just four decades ago by almost all. But there were believers, including Joerg Siekmann to whom this article ..."
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This article celebrates with obvious joy the role automated reasoning now plays for mathematics and logic. Simultaneously, this article evidences the realization of a dream thought impossible just four decades ago by almost all. But there were believers, including Joerg Siekmann to whom this article is dedicated in honor of his sixtieth birthday. Indeed, today (in the year 2001)...
Model Generation without Normal Forms and Applications in NaturalLanguage Semantics
, 1998
"... . I present a new tableauxbased model generation method for firstorder formulas without function symbols. Unlike comparable approaches, the Relational Models (RM) tableaux calculus does not require clausal input theories. I propose some applications of the RM calculus in naturallanguage semantics ..."
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. I present a new tableauxbased model generation method for firstorder formulas without function symbols. Unlike comparable approaches, the Relational Models (RM) tableaux calculus does not require clausal input theories. I propose some applications of the RM calculus in naturallanguage semantics and discuss its usefulness as an inference procedure in naturallanguage processing. 1 Introduction Refutational methods in automated deduction prove the unsatisfiability of logical theories. For many applications, the interpretations of a theory that show its satisfiability are at least as interesting as proofs. Model generation refers to the automatic construction of such interpretations from firstorder theories. In the recent years, there has been a growing interest in the automated deduction community in developing model generation methods for various application areas such as finite mathematics [25, 22], deductive databases [7], diagnosis [13, 1], and planning [19]. As a result, mode...
Application of model search to lattice theory
 AAA Newsletter
, 2001
"... We have used the firstorder modelsearching programs MACE and SEM to study various problems in lattice theory. First, we present a case study in which the two programs are used to examine the differences between the stages along the way from lattice theory to Boolean algebra. Second, we answer seve ..."
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We have used the firstorder modelsearching programs MACE and SEM to study various problems in lattice theory. First, we present a case study in which the two programs are used to examine the differences between the stages along the way from lattice theory to Boolean algebra. Second, we answer several questions posed by Norman Megill and Mladen Pavičić on
Reducing Symmetries to Generate Easier SAT Instances
, 2005
"... Finding countermodels is an effective way of disproving false conjectures. In firstorder predicate logic, model finding is an undecidable problem. But if a finite model exists, it can be found by exhaustive search. The finite model generation problem in the firstorder logic can also be translated ..."
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Finding countermodels is an effective way of disproving false conjectures. In firstorder predicate logic, model finding is an undecidable problem. But if a finite model exists, it can be found by exhaustive search. The finite model generation problem in the firstorder logic can also be translated to the satisfiability problem in the propositional logic. But a direct translation may not be very efficient. This paper discusses how to take the symmetries into account so as to make the resulting problem easier. A static method for adding constraints is presented, which can be thought of as an approximation of the least number heuristic (LNH). Also described is a dynamic method, which asks a model searcher like SEM to generate a set of partial models, and then gives each partial model to a propositional prover. The two methods are analyzed, and compared with each other.
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"... 1 Is there a place for logic in recognizing textual ..."
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