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10
Tractable Databases: How to Make Propositional Unit Resolution Complete through Compilation
, 1994
"... We present procedures to compile any propositional clausal database \Sigma into a logically equivalent "compiled" database \Sigma ? such that, for any clause C, \Sigma j= C if and only if there is a unit refutation of \Sigma ? [ :C. It follows that once the compilation process is complete any qu ..."
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Cited by 38 (5 self)
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We present procedures to compile any propositional clausal database \Sigma into a logically equivalent "compiled" database \Sigma ? such that, for any clause C, \Sigma j= C if and only if there is a unit refutation of \Sigma ? [ :C. It follows that once the compilation process is complete any query about the logical consequences of \Sigma can be correctly answered in time linear in the sum of the sizes of \Sigma ? and the query. The compiled database \Sigma ? is for all but one of the procedures a subset of the set P I (\Sigma) of prime implicates of \Sigma, but \Sigma ? can be exponentially smaller than P I (\Sigma). Of independent interest, we prove the equivalence of unitrefutability with two restrictions of resolution, and provide a new sufficient condition for unit refutation completeness, thus identifying a new class of tractable theories, one which is of interest to abduction problems as well. Finally, we apply the results to the design of a complete LTMS. 1 INTRODUCT...
Resolution strategies as decision procedures
 J. ACM
, 1976
"... ABSTRACT. The resolution principle, an automatic inference technique, is studied as a possible decision procedure for certain classes of firstorder formulas It is shown that most previous resolution strategies do not decide satlsfiabihty even for "simple " solvable classes Two new resolut ..."
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Cited by 30 (0 self)
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ABSTRACT. The resolution principle, an automatic inference technique, is studied as a possible decision procedure for certain classes of firstorder formulas It is shown that most previous resolution strategies do not decide satlsfiabihty even for "simple " solvable classes Two new resolution procedures are described and are shown to be complete (1 e semidecislon procedures) In the general case and, m addition, to be decision procedures for successively wider classes of firstorder formulas These include many previously studied solvable classes The proofs that a complete resolutmn procedure will always halt (without producing the empty clause) when apphed to satisfiable formulas in certain classes provide new, and in some cases more enlightening, demonstrations of the solvablhty of these classes A technique for constructing a model for a formula shown satisfiable in this way is also described
Deduction Systems Based on Resolution
, 1991
"... A general theory of deduction systems is presented. The theory is illustrated with deduction systems based on the resolution calculus, in particular with clause graphs. This theory distinguishes four constituents of a deduction system: ffl the logic, which establishes a notion of semantic entailmen ..."
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Cited by 19 (0 self)
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A general theory of deduction systems is presented. The theory is illustrated with deduction systems based on the resolution calculus, in particular with clause graphs. This theory distinguishes four constituents of a deduction system: ffl the logic, which establishes a notion of semantic entailment; ffl the calculus, whose rules of inference provide the syntactic counterpart of entailment; ffl the logical state transition system, which determines the representation of formulae or sets of formulae together with their interrelationships, and also may allow additional operations reducing the search space; ffl the control, which comprises the criteria used to choose the most promising from among all applicable inference steps. Much of the standard material on resolution is presented in this framework. For the last two levels many alternatives are discussed. Appropriately adjusted notions of soundness, completeness, confluence, and Noetherianness are introduced in order to characterize...
Clauselearning algorithms with many restarts and boundedwidth resolution
, 2009
"... We offer a new understanding of some aspects of practical SATsolvers that are based on DPLL with unitclause propagation, clauselearning, and restarts. On the theoretical side, we do so by analyzing a concrete algorithm which we claim is faithful to what practical solvers do. In particular, befo ..."
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Cited by 13 (1 self)
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We offer a new understanding of some aspects of practical SATsolvers that are based on DPLL with unitclause propagation, clauselearning, and restarts. On the theoretical side, we do so by analyzing a concrete algorithm which we claim is faithful to what practical solvers do. In particular, before making any new decision or restart, the solver repeatedly applies the unitresolution rule until saturation, and leaves no component to the mercy of nondeterminism except for some internal randomness. We prove the perhaps surprising fact that, although the solver is not explicitely designed for it, it ends up behaving as widthk resolution after no more than n 2k+1 conflicts and restarts, where n is the number of variables. In other words, widthk resolution can be thought as n 2k+1 restarts of the unitresolution rule with learning. On the experimental side, we give evidence for the claim that this theoretical result describes real world solvers. We do so by running some of the most prominent solvers on some CNF formulas that we designed to have resolution refutations of width k. It turns out that the upper bound of the theoretical result holds for these solvers and that the true performance appears to be not very far from it.
The Complexity of Automated Reasoning
, 1989
"... This thesis explores the relative complexity of proofs produced by the automatic theorem proving procedures of analytic tableaux, linear resolution, the connection method, tree resolution and the DavisPutnam procedure. It is shown that tree resolution simulates the improved tableau procedure and th ..."
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Cited by 9 (0 self)
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This thesis explores the relative complexity of proofs produced by the automatic theorem proving procedures of analytic tableaux, linear resolution, the connection method, tree resolution and the DavisPutnam procedure. It is shown that tree resolution simulates the improved tableau procedure and that SLresolution and the connection method are equivalent to restrictions of the improved tableau method. The theorem by Tseitin that the DavisPutnam Procedure cannot be simulated by tree resolution is given an explicit and simplified proof. The hard examples for tree resolution are contradictions constructed from simple Tseitin graphs.
ACTP: A Configurable TheoremProver
 Data & Knowledge Engineering
, 1994
"... There has been a considerable amount of research into the provision of explicit representation of control regimes for resolutionbased theorem provers. ..."
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Cited by 2 (2 self)
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There has been a considerable amount of research into the provision of explicit representation of control regimes for resolutionbased theorem provers.
On Modern ClauseLearning Satisfiability Solvers
, 2010
"... In this paper, we present a perspective on modern clauselearning SAT solvers that highlights the roles of, and the interactions between, decision making and clause learning in these solvers. We discuss two limitations of these solvers from this perspective and discuss techniques for dealing with t ..."
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Cited by 1 (0 self)
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In this paper, we present a perspective on modern clauselearning SAT solvers that highlights the roles of, and the interactions between, decision making and clause learning in these solvers. We discuss two limitations of these solvers from this perspective and discuss techniques for dealing with them. We show empirically that the proposed techniques significantly improve stateoftheart solvers.
Paramodulation Decision Procedures
, 2003
"... The aim of this thesis is to present Paramodulation Operators deciding the (i) Ackermann class with Equality [FS93] and (ii) the monadic class with equality [BGW93]. Ad (i) a refinement of the Ordered Paramodulation calculus [HR91] is used to define the appropriate inference operator; ad (ii) a vari ..."
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The aim of this thesis is to present Paramodulation Operators deciding the (i) Ackermann class with Equality [FS93] and (ii) the monadic class with equality [BGW93]. Ad (i) a refinement of the Ordered Paramodulation calculus [HR91] is used to define the appropriate inference operator; ad (ii) a variant of the Superposition calculus [BG94] is employed for this purpose. It seemed natural to give a uniform presentation of these underlying equational calculi. Hence, the first part of this thesis is designed to be a uniform treatment of these calculi. In the definition of the paramodulation operator that decides the monadic class with equality ordering constraints are used. Therefor we choose to present all the inference rules that Ordered Paramodulation and Superposition define with respect to ordering constraints. These constraints are used to express the restrictions normally given with the description of an inference rule as part of the object language.
Logic; I Theorem Proving and A SEMANTICALLY GUIDED DEDUCTIVE SYSTEM FOR AUTOMATIC THEOREMPROVING
"... This paper presents a semantic and deductive formal system for automatic theoremproving. The system has, as its deductive component, a form of natural deduction. Its semantic component relies on an underlying representation of a model. This model is invoked to prune subgoals generated by the deduct ..."
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This paper presents a semantic and deductive formal system for automatic theoremproving. The system has, as its deductive component, a form of natural deduction. Its semantic component relies on an underlying representation of a model. This model is invoked to prune subgoals generated by the deductive component, whenever such subgoals test false in the model. In addition, the model is used to suggest inferences to be made at the deductive level. Conversely, the current state of the proof suggests changes to be made to the model, e.g. when a construction is required as in geometry. The system is seen to possess a very smooth and transparent interface between its semantics and deductive syntax. These semantic and syntactic subsystems interact continuously during the search for a proof, each suggesting to the other how next to proceed. Particularly appealing is the naturalness of the system from a human point of view. 1.
Proceedings of the TwentyThird AAAI Conference on Artificial Intelligence (2008) A New Clause Learning Scheme for Efficient Unsatisfiability Proofs
"... We formalize in this paper a key property of asserting clauses (the most common type of clauses learned by SAT solvers). We show that the formalized property, which is called empowerment, is not exclusive to asserting clauses, and introduce a new class of learned clauses which can also be empowering ..."
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We formalize in this paper a key property of asserting clauses (the most common type of clauses learned by SAT solvers). We show that the formalized property, which is called empowerment, is not exclusive to asserting clauses, and introduce a new class of learned clauses which can also be empowering. We show empirically that (1) the new class of clauses tends to be much shorter and induce further backtracks than asserting clauses and (2) an empowering subset of this new class of clauses significantly improves the performance of the Rsat solver on unsatisfiable problems.