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25
The Model Evolution Calculus
, 2003
"... The DPLL procedure is the basis of some of the most successful propositional satisfiability solvers to date. Although originally devised as a proofprocedure for firstorder logic, it has been used almost exclusively for propositional logic so far because of its highly inefficient treatment of quanti ..."
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Cited by 86 (14 self)
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The DPLL procedure is the basis of some of the most successful propositional satisfiability solvers to date. Although originally devised as a proofprocedure for firstorder logic, it has been used almost exclusively for propositional logic so far because of its highly inefficient treatment of quantifiers, based on instantiation into ground formulas. The recent FDPLL calculus by Baumgartner was the first successful attempt to lift the procedure to the firstorder level without resorting to ground instantiations. FDPLL lifts to the firstorder case the core of the DPLL procedure, the splitting rule, but ignores other aspects of the procedure that, although not necessary for completeness, are crucial for its effectiveness in practice. In this paper, we present a new calculus loosely based on FDPLL that lifts these aspects as well. In addition to being a more faithful litfing of the DPLL procedure, the new calculus contains a more systematic treatment of universal literals, one of FDPLL's optimizations, and so has the potential of leading to much faster implementations.
Automated Deduction Techniques for the Management Of Personalized Documents
"... This work is about a "realworld" application of automated deduction. The application is the management of documents (such as mathematical textbooks) as they occur in a readily available tool. In this "Slicing Information Technology tool", documents are decomposed ("sliced") into small units. A part ..."
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Cited by 47 (10 self)
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This work is about a "realworld" application of automated deduction. The application is the management of documents (such as mathematical textbooks) as they occur in a readily available tool. In this "Slicing Information Technology tool", documents are decomposed ("sliced") into small units. A particular application task is to assemble a new document from such units in a selective way, based on the user's current interest and knowledge. It is
Inference methods for a pseudoBoolean satisfiability solver
, 2002
"... We describe two methods of doing inference during search for a pseudoBoolean version of the RELSAT method. One inference method is the pseudoBoolean equivalent of learning. ..."
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Cited by 42 (2 self)
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We describe two methods of doing inference during search for a pseudoBoolean version of the RELSAT method. One inference method is the pseudoBoolean equivalent of learning.
A FirstOrder Logic DavisPutnamLogemannLoveland Procedure
"... The DavisPutnamLogemannLoveland procedure (DPLL) was introduced in the early ..."
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Cited by 38 (6 self)
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The DavisPutnamLogemannLoveland procedure (DPLL) was introduced in the early
New Directions in InstantiationBased Theorem Proving
"... We consider instantiationbased theorem proving whereby instances of clauses are generated by certain inferences, and where inconsistency is detected by propositional tests. We give a model construction proof of completeness by which restrictive inference systems as well as admissible simplification ..."
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Cited by 31 (3 self)
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We consider instantiationbased theorem proving whereby instances of clauses are generated by certain inferences, and where inconsistency is detected by propositional tests. We give a model construction proof of completeness by which restrictive inference systems as well as admissible simplification techniques can be justified. Another contribution of the paper are novel inference systems that allow one to also employ decision procedures for firstorder fragments more complex than propositional logic. The decision procedure provides for an approximative consistency test, and the instance generation inference system is a means of successively refining the approximation.
Generalizing Boolean satisfiability I: Background and survey of existing work
 Journal of Artificial Intelligence Research
, 2004
"... This is the first of three planned papers describing zap, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern highperformance solvers. The fundamental idea underlying zap is that many problems passed to such engines contain ..."
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Cited by 18 (3 self)
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This is the first of three planned papers describing zap, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern highperformance solvers. The fundamental idea underlying zap is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal is to define a representation in which this structure is apparent and can easily be exploited to improve computational performance. This paper is a survey of the work underlying zap, and discusses previous attempts to improve the performance of the DavisPutnamLogemannLoveland algorithm by exploiting the structure of the problem being solved. We examine existing ideas including extensions of the Boolean language to allow cardinality constraints, pseudoBoolean representations, symmetry, and a limited form of quantification. While this paper is intended as a survey, our research results are contained in the two subsequent articles, with the theoretical structure of zap described in the second paper in this series, and zap’s implementation described in the third. 1.
Hyperresolution for guarded formulae
 J. Symbolic Computat
, 2000
"... Abstract. This paper investigates the use of hyperresolution as a decision procedure and model builder for guarded formulae. In general hyperresolution is not a decision procedure for the entire guarded fragment. However we show that there are natural fragments which can be decided by hyperresolutio ..."
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Cited by 15 (9 self)
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Abstract. This paper investigates the use of hyperresolution as a decision procedure and model builder for guarded formulae. In general hyperresolution is not a decision procedure for the entire guarded fragment. However we show that there are natural fragments which can be decided by hyperresolution. In particular, we prove decidability of hyperresolution with or without splitting for the fragment GF1 − and point out several ways of extending this fragment without loosing decidability. As hyperresolution is closely related to various tableaux methods the present work is also relevant for tableaux methods. We compare our approach to hypertableaux, and mention the relationship to other clausal classes which are decidable by hyperresolution. 1
Darwin: A Theorem Prover for the Model Evolution Calculus
, 2004
"... Darwin is the first implementation of the Model Evolution Calculus by Baumgartner and Tinelli. The Model Evolution Calculus lifts the DPLL procedure to firstorder logic. Darwin is meant to be a fast and clean implementation of the calculus, showing its e#ectiveness and providing a base for further ..."
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Cited by 14 (4 self)
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Darwin is the first implementation of the Model Evolution Calculus by Baumgartner and Tinelli. The Model Evolution Calculus lifts the DPLL procedure to firstorder logic. Darwin is meant to be a fast and clean implementation of the calculus, showing its e#ectiveness and providing a base for further improvements and extensions. Based on a brief summary of the Model Evolution Calculus, we describe in the main part of the paper Darwin's proof procedure and its data structures and algorithms, discussing the main design decisions and features that influence Darwin's performance. We also report on practical experiments carried out with problems from the CADE18 and CADE19 system competitions, as well as on results on parts of the TPTP Problem Library.
Algorithms, datastructures, and other issues in efficient automated deduction
 Automated Reasoning. 1st. International Joint Conference, IJCAR 2001, number 2083 in LNAI
, 2001
"... Abstract. Algorithms and datastructures form the kernel of any efficient theorem prover. In this abstract we discuss research on algorithms and datastructures for efficient theorem proving based on our experience with the theorem prover Vampire. We also briefly overview other works related to algori ..."
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Cited by 11 (0 self)
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Abstract. Algorithms and datastructures form the kernel of any efficient theorem prover. In this abstract we discuss research on algorithms and datastructures for efficient theorem proving based on our experience with the theorem prover Vampire. We also briefly overview other works related to algorithms and datastructures, and to efficient theorem proving in general. 1
Knowledge Representation and Classical Logic
, 2007
"... Mathematical logicians had developed the art of formalizing declarative knowledge long before the advent of the computer age. But they were interested primarily in formalizing mathematics. Because of the important role of nonmathematical knowledge in AI, their emphasis was too narrow from the perspe ..."
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Cited by 11 (4 self)
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Mathematical logicians had developed the art of formalizing declarative knowledge long before the advent of the computer age. But they were interested primarily in formalizing mathematics. Because of the important role of nonmathematical knowledge in AI, their emphasis was too narrow from the perspective of knowledge representation, their formal languages were not sufficiently expressive. On the other hand, most logicians were not concerned about the possibility of automated reasoning; from the perspective of knowledge representation, they were often too generous in the choice of syntactic constructs. In spite of these differences, classical mathematical logic has exerted significant influence on knowledge representation research, and it is appropriate to begin this handbook with a discussion of the relationship between these fields. The language of classical logic that is most widely used in the theory of knowledge representation is the language of firstorder (predicate) formulas. These are the formulas that John McCarthy proposed to use for representing declarative knowledge in his advice taker paper [176], and Alan Robinson proposed to prove automatically using resolution [236]. Propositional logic is, of course, the most important subset of firstorder logic; recent