P. Baumgartner. Linear and Unit-Resulting Refutations for Horn Theories. Journal of Automated Reasoning, 1995 (?). (To appear, also in: Research Report 9/93, Institute for Computer Science, University of Koblenz, Germany) .  Home/Search   Document Details and Download   Summary   Related Articles   Check

....or less general implementation techniques like those described in [BP96] for which our cooperation approach is feasible. Focusing on the specialized results from Section 5, one potentially interesting application could come in conjunction with Baumgartner s results on linearizing completion [Bau96] a technique for producing background reasoners automatically for certain universal Horn theories. Linearizing completion takes a finite set of Horn clauses and either diverges or produces a finite set I(T ) of unit resulting inference rules. This set constitutes an inference system that in ....

.... interestingly for us though, R can be used as a rather e#cient background reasoner for partial theory reasoning calculi: one that preserves the completeness of the overall calculus while only needing key sets up to a certain cardinality, and producing few residues, all of them unit (see [Bau96] for more details) The major limitation of linearizing completion is that it often diverges on the input set of clauses. In some cases, however, it is possible to partition into two sets 2 such that linearizing completion on each of them separately succeeds [Bau01] Until now this ....

Peter Baumgartner. Linear and unit-resulting refutations for Horn theories. Journal of Automated Reasoning, 16(3):241--319, June 1996.

....set Unsatisfiable Satisfiable Found a proof for A j= T No more A 6j= T Figure 3.7: The Hyper Linking Procedure [Chu94] Ast92] Ast94] The relevant works mentioned above are to be reviewed in the near future. We are also to investigate an extension to the approach presented in [BF94a] and [BF94b] 3.5 Semantics in Automated Theorem proving As we have investigated in chapter 2, semantics in the form of models is the meaning of a formula set. It plays an important role in automated theorem proving because it provides us with an implication of what the theorem is like and how ....

Peter Baumgartner and Ulrich Furbach. Linear and unit-resulting refutations for horn theories. Journal of Automated Reasoning, 13:339--359, 1994.

....more or less general implementation techniques like those described in [BP96] for which our cooperation approach is feasible. Focusing on the specialized results from Section 5, one potentially interesting application could come in conjunction with Baumgartner s results on linearizing completion [Bau96] a technique for producing background reasoners automatically for certain universal Horn theories. Linearizing completion takes a nite set T of Horn clauses and either diverges or produces a nite set I(T ) of unit resulting inference rules. This set denotes an inference system that in turn can ....

.... More interestingly for us though, R T can be used as a rather ecient background reasoner for partial theory reasoning calculi: one that preserves the completeness of the overall calculus while only needing key sets up to a certain cardinality and producing few T residues, all of them unit (see [Bau96] for more details) The major limitation of linearizing completion is that it often diverges on the input set T of clauses. In some cases, however, it is possible to partition T into two sets T 1 and T 2 such that linearizing completion on each of them separately succeeds [Bau01] Until now this ....

Peter Baumgartner. Linear and unit-resulting refutations for Horn theories. Journal of Automated Reasoning, 16(3):241-319, June 1996.

....bases have the obvious and well known property that no inferences between their members are needed in refutational proofs [3] since all those inferences are redundant. This has also been used by Baumgartner for obtaining linear resolution proofs between precompiled theories and unit queries [4], but by unordered resolution. There, however, the resolution basis has not been for a synthesis of inference rules, as in the following section. 4 Derivation of the Inference Rules This section contains the second synthesis step. We now use the clauses of the resolution basis of proposition 1 ....

P. Baumgartner. Linear and unit-resulting refutations for horn theories. J. Automated Reasoning, 16(3):241--319, 1996.

....important example are background reasoners based on resolution: if a resolvent can be derived from a key Phi, then it is valid for all extensions Phi [ Psi of Phi; resolvents may be invalid for an instance Phioe of the key, but to check this is much easier than to recompute all resolvents. In [3] a uniform translation from Horn theories to partial background reasoners based on unit resulting positive hyper resolution with input restriction is described. This procedure can be used to generate incremental background reasoners for a huge class of theories. 4.4 Semantic Tableaux and ....

P. Baumgartner. Linear and unit-resulting refutations for Horn theories. Journal of Automated Reasoning, 1996. To appear.

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P. Baumgartner. Linear and Unit-Resulting Refutations for Horn Theories. Journal of Automated Reasoning, 1995 (?). (To appear, also in: Research Report 9/93, Institute for Computer Science, University of Koblenz, Germany) .

....how to obtain for a given theory a background calculus. To this end, one of the authors has designed a compilation technique which allows to transform a Horn theory into inference rules which are suitable to be used in conjunction with model elimination. This method, called linearizing completion [Baumgartner, 1995 ] is used throughout all our experiments. Fortunately, theory reasoning can be applied to ordinary model elimination, as well as restart model elimination in a complete way. Together with various sub variants of restart model elimination we have now a considerable spectrum of different calculi ....

.... In partial theory reasoning semantical complementary sets are computed stepwise by means of intermediate goals (called residues ) The partial variant is of particular interest for us because we have a technique to automatically construct background reasoners for partial theory model elimination [Baumgartner, 1995 ] This technique, called linearizing completion is briefly described below in Section 3.1. Definition 3.1 (Theory model elimination (TME) The inference rule theory extension step which transforms a branch set and some clauses in a new branch set is defined as follows: fK 1 Delta Delta ....

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P. Baumgartner. Linear and Unit-Resulting Refutations for Horn Theories. Journal of Automated Reasoning, 1995 (?). (To appear, also in: Research Report 9/93, Institute for Computer Science, University of Koblenz, Germany).

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