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63
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 110 (19 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.
Hyper Tableaux
, 1996
"... This paper introduces a variant of clausal normal form tableaux that we call "hyper tableaux". Hyper tableaux keep many desirable features of analytic tableaux while taking advantage of the central idea from (positive) hyper resolution, namely to resolve away all negative literals of a cla ..."
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Cited by 84 (20 self)
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This paper introduces a variant of clausal normal form tableaux that we call "hyper tableaux". Hyper tableaux keep many desirable features of analytic tableaux while taking advantage of the central idea from (positive) hyper resolution, namely to resolve away all negative literals of a clause in a single inference step. Another feature of the proposed calculus is the extensive use of universally quantified variables. This enables new efficient forwardchaining proof procedures for full first order theories as variants of tableaux calculi.
Minimal Model Generation with Positive Unit HyperResolution Tableaux
, 1996
"... Herbrand models for clausal theories are useful in several areas of computer science. In most cases, however, the conventional model generation algorithms are inappropriate because they generate nonminimal Herbrand models and can be inefficient. This article describes a novel approach for generating ..."
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Cited by 41 (14 self)
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Herbrand models for clausal theories are useful in several areas of computer science. In most cases, however, the conventional model generation algorithms are inappropriate because they generate nonminimal Herbrand models and can be inefficient. This article describes a novel approach for generating minimal Herbrand models of clausal theories. The approach builds upon positive unit hyperresolution (PUHR) tableaux, that are in general smaller than conventional tableaux. To generate only minimal Herbrand models, a complement splitting expansion rule and a specific search strategy are applied. The proposed procedure is optimal in the sense that each minimal model is generated only once, and nonminimal models are rejected before their complete construction. First measurements on an implementation point to the efficiency of the procedure.
Optimizing proof search in model elimination
 13th International Conference on Automated Deduction, volume 1104 of Lecture Notes in Computer Science
, 1996
"... Many implementations of model elimination perform proof search by iteratively increasing a bound on the total size of the proof. We propose an optimized version of this search mode using a simple divideandconquer refinement. Optimized and unoptimized modes are compared, together with depthbounded ..."
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Cited by 37 (2 self)
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Many implementations of model elimination perform proof search by iteratively increasing a bound on the total size of the proof. We propose an optimized version of this search mode using a simple divideandconquer refinement. Optimized and unoptimized modes are compared, together with depthbounded and bestfirst search, over the entire TPTP problem library. The optimized sizebounded mode seems to be the overall winner, but for each strategy there are problems on which it performs best. Some attempt is made to analyze why. We emphasize that our optimization, and other implementation techniques like caching, are rather general: they are not dependent on the details of model elimination, or even that the search is concerned with theorem proving. As such, we believe that this study is a useful complement to research on extending the model elimination calculus.
leanCoP: Lean ConnectionBased Theorem Proving
 UNIVERSITY OF KOBLENZ
, 2000
"... The Prolog program "prove(M,I) : append(Q,[CR],M), "+member(,C), append(Q,R,S), prove([!],[[!C]S],[],I). prove([],,,). prove([LC],M,P,I) : (N=L; L=N) ? (member(N,P); append(Q,[DR],M), copyterm(D,E), append(A,[NB],E), append(A,B,F), (D==E ? append(R,Q,S); len ..."
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Cited by 29 (9 self)
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The Prolog program "prove(M,I) : append(Q,[CR],M), "+member(,C), append(Q,R,S), prove([!],[[!C]S],[],I). prove([],,,). prove([LC],M,P,I) : (N=L; L=N) ? (member(N,P); append(Q,[DR],M), copyterm(D,E), append(A,[NB],E), append(A,B,F), (D==E ? append(R,Q,S); length(P,K), K!I, append(R,[DQ],S)), prove(F,S,[LP],I)), prove(C,M,P,I)." implements a theorem prover for classical firstorder (clausal) logic which is based on the connection calculus. It is sound, complete (if one more line is added), and demonstrates a comparatively strong performance.
Simplification  A general constraint propagation technique for propositional and modal tableaux
, 1998
"... . Tableau and sequent calculi are the basis for most popular interactive theorem provers for formal verification. Yet, when it comes to automatic proof search, tableaux are often slower than DavisPutnam, SAT procedures or other techniques. This is partly due to the absence of a bivalence principle ..."
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Cited by 25 (2 self)
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. Tableau and sequent calculi are the basis for most popular interactive theorem provers for formal verification. Yet, when it comes to automatic proof search, tableaux are often slower than DavisPutnam, SAT procedures or other techniques. This is partly due to the absence of a bivalence principle (viz. the cutrule) but there is another source of inefficiency: the lack of constraint propagation mechanisms. This paper proposes an innovation in this direction: the rule of simplification, which plays for tableaux the role of subsumption for resolution and of unit for the DavisPutnam procedure. The simplicity and generality of simplification make possible its extension in a uniform way from propositional logic to a wide range of modal logics. This technique gives an unifying view of a number of tableauxlike calculi such as DPLL, KE, HARP, hypertableaux, BCP, KSAT. We show its practical impact with experimental results for random 3SAT and the industrial IFIP benchmarks for hardware ve...
DELTA  A Bottomup Preprocessor for TopDown Theorem Provers  System Abstract
 In Proceedings of CADE12
, 1994
"... ? Johann M. Ph. Schumann Institut fur Informatik, Technische Universitat Munchen D80290 Munchen email: schumann@informatik.tumuenchen.de Topdown theorem provers with depthfirst search (e.g., PTTP [Sti88], METEOR [AL91], SETHEO [LSBB92]) have the general disadvantage that during the search ..."
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Cited by 15 (3 self)
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? Johann M. Ph. Schumann Institut fur Informatik, Technische Universitat Munchen D80290 Munchen email: schumann@informatik.tumuenchen.de Topdown theorem provers with depthfirst search (e.g., PTTP [Sti88], METEOR [AL91], SETHEO [LSBB92]) have the general disadvantage that during the search the same goals have to be proven over and over again, thus causing a large amount of redundancy. Resolutionbased bottomup theorem provers (e.g., OTTER [McC90]), on the other hand, avoid this problem by performing backward and forward subsumption and by using elaborate storage and indexing techniques. Those provers, however, often lack the goalorientedness of topdown provers. In order to combine the advantages of topdown and bottomup theorem proving, we have developed the preprocessor DELTA. DELTA processes one part of the search space (the "bottom" part) in a preprocessing phase, using bottomup techniques (see also [?]). It generates unitclauses (e.g., by applying URresolution) whi...
Positive Unit Hyperresolution Tableaux and Their Application to Minimal Model Generation
 Journal of Automated Reasoning
, 2000
"... . Minimal Herbrand models of sets of firstorder clauses are useful in several areas of computer science, e.g. automated theorem proving, program verification, logic programming, databases, and artificial intelligence. In most cases, the conventional model generation algorithms are inappropriate bec ..."
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Cited by 15 (0 self)
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. Minimal Herbrand models of sets of firstorder clauses are useful in several areas of computer science, e.g. automated theorem proving, program verification, logic programming, databases, and artificial intelligence. In most cases, the conventional model generation algorithms are inappropriate because they generate nonminimal Herbrand models and can be inefficient. This article describes an approach for generating the minimal Herbrand models of sets of firstorder clauses. The approach builds upon positive unit hyperresolution (PUHR) tableaux, that are in general smaller than conventional tableaux. PUHR tableaux formalize the approach initially introduced with the theorem prover SATCHMO. Two minimal model generation procedures are described. The first one expands PUHR tableaux depthfirst relying on a complement splitting expansion rule and on a form of backtracking involving constraints. A Prolog implementation, named MMSATCHMO, of this procedure is given and its performance on ben...