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12
Model Elimination without Contrapositives and its Application to PTTP
 PROCEEDINGS OF CADE12, SPRINGER LNAI 814
, 1994
"... We give modifications of model elimination which do not necessitate the use of contrapositives. These restart model elimination calculi are proven sound and complete and their implementation by PTTP is depicted. The corresponding proof procedures are evaluated by a number of runtime experiments and ..."
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Cited by 22 (8 self)
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We give modifications of model elimination which do not necessitate the use of contrapositives. These restart model elimination calculi are proven sound and complete and their implementation by PTTP is depicted. The corresponding proof procedures are evaluated by a number of runtime experiments and they are compared to other well known provers. Finally we relate our results to other calculi, namely the connection method, modified problem reduction format and NearHorn Prolog.
A Model Elimination Calculus with Builtin Theories
 Proceedings of the 16th German AIConference (GWAI92
, 1992
"... this paper, we will show how to extend model elimination with theory reasoning. Technically, theory reasoning means to relieve a calculus from explicit reasoning in some domain (e.g. equality, partial orders) by taking apart the domain knowledge and treating it by special inference rules. In an impl ..."
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Cited by 17 (10 self)
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this paper, we will show how to extend model elimination with theory reasoning. Technically, theory reasoning means to relieve a calculus from explicit reasoning in some domain (e.g. equality, partial orders) by taking apart the domain knowledge and treating it by special inference rules. In an implementation, this results in a universal "foreground" reasoner that calls a specialized "background" reasoner for theory reasoning. Theory reasoning comes in two variants (Sti85) : total and
Model Elimination without Contrapositives
, 1994
"... We present modifications of model elimination which do not necessitate the use of contrapositives. These restart model elimination calculi are proven sound and complete. The corresponding proof procedures are evaluated by a number of runtime experiments and they are compared to other well known pro ..."
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Cited by 16 (6 self)
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We present modifications of model elimination which do not necessitate the use of contrapositives. These restart model elimination calculi are proven sound and complete. The corresponding proof procedures are evaluated by a number of runtime experiments and they are compared to other well known provers. Finally we relate our results to other calculi, namely the connection method, modified problem reduction format and NearHorn Prolog.
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
Model Elimination, Logic Programming and Computing Answers
 University of Koblenz
, 1995
"... We demonstrate that theorem provers using model elimination (ME) can be used as answer complete interpreters for disjunctive logic programming. More specifically, we introduce a mechanism for computing answers into the restart variant of ME. Building on this, we develop a new calculus called ancestr ..."
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Cited by 10 (5 self)
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We demonstrate that theorem provers using model elimination (ME) can be used as answer complete interpreters for disjunctive logic programming. More specifically, we introduce a mechanism for computing answers into the restart variant of ME. Building on this, we develop a new calculus called ancestry restart ME. This variant admits a more restrictive regularity restriction than restart ME, and, as a side effect, it is in particular attractive for computing definite answers. The presented calculi can also be used successfully in the context of automated theorem proving. We demonstrate experimentally that it is more difficult to compute (nontrivial) answers to goals, instead of only proving the existence of answers.
Computing Answers with Model Elimination
, 1997
"... We demonstrate that theorem provers using model elimination (ME) can be used as answercomplete interpreters for disjunctive logic programming. More specifically, we introduce a mechanism for computing answers into the restart variant of ME. Building on this we develop a new calculus called ancestry ..."
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Cited by 9 (2 self)
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We demonstrate that theorem provers using model elimination (ME) can be used as answercomplete interpreters for disjunctive logic programming. More specifically, we introduce a mechanism for computing answers into the restart variant of ME. Building on this we develop a new calculus called ancestry restart ME. This variant admits a more restrictive regularity restriction than restart ME, and, as a side effect, it is in particular attractive for computing definite answers. The presented calculi can also be used successfully in the context of automated theorem proving. We demonstrate experimentally that it is more difficult to compute (nontrivial) answers to goals, instead of only proving the existence of answers. Keywords. Automated reasoning; theorem proving; model elimination; logic programming; computing answers. In first order automatic theorem proving one is interested in the question whether a given formula follows logically from a set of axioms. This is a rather artificial t...
Refinements of Theory Model Elimination and a Variant without Contrapositives
 University of Koblenz, Institute for Computer Science
, 1994
"... Theory Reasoning means to buildin certain knowledge about a problem domain into a deduction system or calculus, which is in our case model elimination. Several versions of theory model elimination (TME) calculi are presented and proven complete: on the one hand we have highly restricted versions of ..."
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Cited by 8 (6 self)
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Theory Reasoning means to buildin certain knowledge about a problem domain into a deduction system or calculus, which is in our case model elimination. Several versions of theory model elimination (TME) calculi are presented and proven complete: on the one hand we have highly restricted versions of total and partial TME. These restrictions allow (1) to keep fewer path literals in extension steps than in related calculi, and (2) discard proof attempts with multiple occurrences of literals along a path (i.e. regularity holds). On the other hand, we obtain by small modifications to TME versions which do not need contrapositives (a la NearHorn Prolog). We show that regularity can be adapted for these versions. The independence of the goal computation rule holds for all variants. Comparative runtime results for our PTTPimplementations are supplied. 1 Introduction The model elimination calculus (ME calculus) has been developed already in the early days of automated theorem proving [Lovel...
A Unified Approach to Theory Reasoning
, 1992
"... Theory reasoning is a kind of twolevel reasoning in automated theorem proving, where the knowledge of a given domain or theory is separated and treated by special purpose inference rules. We define a classification for the various approaches for theory reasoning which is based on the syntactic con ..."
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Cited by 6 (1 self)
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Theory reasoning is a kind of twolevel reasoning in automated theorem proving, where the knowledge of a given domain or theory is separated and treated by special purpose inference rules. We define a classification for the various approaches for theory reasoning which is based on the syntactic concepts of literal level  term level  variable level. The main part is a review of theory extensions of common calculi (resolution, model elimination and a connection method). In order to see the relationships among these calculi, we define a supercalculus called theory consolution. Completeness of the various theory calculi is proven. Finally, due to its relevance in automated reasoning, we describe current ways of equality handling.
A Disjunctive Positive Refinement of Model Elimination and its Application to Subsumption Deletion
 Journal of Automated Reasoning
, 1995
"... The Model Elimination (ME) calculus is a refutational complete, goaloriented calculus for firstorder clause logic. In this paper, we introduce a new variant called disjunctive positive ME (DPME); it improves on Plaisted's positive refinement of ME in that reduction steps are allowed only with p ..."
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Cited by 5 (0 self)
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The Model Elimination (ME) calculus is a refutational complete, goaloriented calculus for firstorder clause logic. In this paper, we introduce a new variant called disjunctive positive ME (DPME); it improves on Plaisted's positive refinement of ME in that reduction steps are allowed only with positive literals stemming from disjunctive clauses.