P. Baumgartner. Refinements of Theory Model Elimination and a Variant without Contrapositives. In A.G. Cohn, editor, 11th European Conference on Artificial Intelligence, ECAI 94. Wiley, 1994. (Long version in: Research Report 8/93, University of Koblenz, Institute for Computer Science, Koblenz, Germany).  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... 9] and STATIC semantics [16, 10] We already have an experimental Prolog program to handle D WFS semantics based on both bottom up partial evaluation and a confluent calculus presented in [9] Another line of development of DisLoP will be to exploit the constraint solving [7] and theory reasoning [2] capabilities of PROTEIN in the context of disjunctive logic programming. Acknowledgements We thank all members of the Artificial Intelligence Research Group at the University of Koblenz, Germany, for useful discussions and comments on this paper. Special thanks are due to Peter Baumgartner and ....

Baumgartner, P.: Refinements of theory model elimination and a variant without contrapositives. In: A.G. Cohn (ed.), Proc. of ECAI '94, Wiley, 1994.

.... Model Elimination The calculus of CME [BS95] can be viewed as a combination of model elimination [Lov68] and CLP [JM94] adapting the work of [Bur91] In addition, it is related to theory resolution [Sti85] and there is also an instantiation of model elimination with respect to theory reasoning [Bau94] But we will not give an exhaustive overview on the field here. So the interested reader is referred to the cited papers. In this paper we will just state the necessary definitions and proofs plus an illustrating example. The definitions stated here slightly differ from those in [BS95] because ....

Peter Baumgartner. Refinements of theory model elimination and a variant without contrapositives. In Anthony G. Cohn, editor, Proceedings of the 11th European Conference on Artificial Intelligence, Amsterdam, The Netherlands, 1994, pages 90--94. John Wiley & Sons, New York, NY, 1994.

....which avoids all contrapositives, and which was used for the example in Section 4. PROTEIN includes theory reasoning which relieves a calculus from explicit reasoning in some domain (e.g. strings, numbers, equality) by separating the domain knowledge and treating it by special inference rules [1]. Several refinements of theory reasoning have been implemented. Theory reasoning allows us to treat strings and arithmetic by theories instead of axiomatizing them. It is possible to declare some literals to be proven by calls given to Prolog procedures. This allows us to incorporate Prolog ....

Peter Baumgartner. Refinements of theory model elimination and a variant without contrapositives. In A.G. Cohn, editor, 11th European Conference on Artificial Intelligence, ECAI'94, pages 90--94. Wiley, 1994.

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P. Baumgartner. Refinements of Theory Model Elimination and a Variant without Contrapositives. In A.G. Cohn, editor, 11th European Conference on Artificial Intelligence, ECAI 94. Wiley, 1994. (Long version in: Research Report 8/93, University of Koblenz, Institute for Computer Science, Koblenz, Germany).

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P. Baumgartner. Refinements of Theory Model Elimination and a Variant without Contrapositives. In A.G. Cohn, editor, 11th European Conference on Artificial Intelligence, ECAI 94. Wiley, 1994. (Long version in: Research Report 8/93, University of Koblenz, Institute for Computer Science, Koblenz, Germany).

....in order to conveniently express another calculus variant defined below. Note that the restart ME calculus does not assume a special selection function which determines which path is to be extended or reduced next. Correctness and completeness of this calculus follows immediately from a result in [1]. From the definition of the inference rule extension, it follows immediately, that this calculus only needs those contrapositives of clauses which contain a positive literal in their heads. The following result is due to [3, 5] Theorem 1.3 (Ground completeness of Strict Restart Model ....

P. Baumgartner. Refinements of Theory Model Elimination and a Variant without Contrapositives. In A. Cohn, editor, 11th European Conference on Artificial Intelligence, ECAI 94. Wiley, 1994.

....(possibly with selection function) loop checking by regularity and also factorization (which is introduced in [20] are parts of the system. Another distinguished feature of PROTEIN is its theory interface (PROTEIN = PROver with a Theory Extension IN terface) PROTEIN includes theory reasoning [32,1,2] in a very general way. Theory reasoning allows a calculus to relieve from explicit reasoning in some domain (e.g. equality, partial orders, taxonomic reasoning) by taking apart the domain knowledge and treating it by special inference rules. In an implementation, this results in a universal ....

P. Baumgartner. Refinements of Theory Model Elimination and a Variant without Contrapositives. In A.G. Cohn, editor, 11th European Conference on Artificial Intelligence, ECAI 94. Wiley, 1994. (Long version in: Research Report 8/93, University of Koblenz, Institute for Computer Science, Koblenz, Germany).

....[Sti88] for model elimination [Lov69] PROTEIN offers alternative inference rules for case analysis [Lov87, BF93] In this setting no contrapositives are needed, and hence the system is well suited as an interpreter for disjunctive logic programming. PROTEIN includes theory reasoning [Sti85, Bau92, Bau94] in a very general way. An auxiliary program can be used to derive a suitable background reasoner from a given Horn theory in a fully automatic way. PROTEIN includes several calculus refinements and flags. The idea of the PTTP implementation technique ( Prolog Technology Theorem Prover ) ....

....an implementation, this results in a universal foreground reasoner that calls a specialized background reasoner for theory reasoning. See [BFP92] for an overview. Fortunately, the calculus features case analysis reasoning and theory reasoning are fairly compatible with model elimination [Bau94]. In [BF93, BF94] we have shown that case analysis in the non theory setting requires only a small change to the calculus. PROTEIN is the respective implementation for theory reasoning. Furthermore PROTEIN includes several calculus refinements and flags such as unitlemmas, factorisation, ....

P. Baumgartner. Refinements of Theory Model Elimination and a Variant without Contrapositives. In Proc. ECAI'94, 1994. (to appear).

....in order to conveniently express another calculus variant defined below. Note that the restart ME calculus does not assume a special selection function for determining which path is to be extended or reduced next. Correctness and completeness of this calculus follows immediately from a result in [Baumgartner, 1994] . From the definition of the inference rule extension, it follows immediately, that this calculus only needs those contrapositives of clauses which contain a positive literal in their heads. The following result is due to [Baumgartner and Furbach, 1994a] THEOREM 1.3 (Ground completeness of ....

P. Baumgartner. Refinements of Theory Model Elimination and a Variant without Contrapositives. In A.G. Cohn, editor, 11th European Conference on Artificial Intelligence, ECAI 94. Wiley, 1994. (Long version in: Research Report 8/93, University of Koblenz, Institute for Computer Science, Koblenz, Germany).

....Stickel, 1989] which rely on model elimination. This paper deals with several variants of model elimination with an emphasis on the implementational issue. These variants are called restart model elimination [Baumgartner and Furbach, 1994a] and theory model elimination [Baumgartner, 1992, Baumgartner, 1994] They will be reviewed in the respective sections below. For a more detailed description the reader is referred to the cited literature. In brief, restart model elimination is a variant which was motivated by taking a logic programming view at theorem proving. In logic programming one typically ....

....precisely such a proof by case analysis. Now let us turn to the other variant, theory model elimination. Theory reasoning was introduced by M. Stickel within the general, non linear resolution calculus [Stickel, 1985] for model elimination it is defined and investigated in [Baumgartner, 1992, Baumgartner, 1994] Theory reasoning means to relieve a calculus from explicit reasoning in some domain (e.g. equality, partial orders, taxonomic reasoning) by taking apart the domain knowledge and treating it by special inference rules. In an implementation, this results in a universal foreground reasoner ....

[Article contains additional citation context not shown here]

P. Baumgartner. Refinements of Theory Model Elimination and a Variant without Contrapositives. In A.G. Cohn, editor, 11th European Conference on Artificial Intelligence, ECAI 94. Wiley, 1994.

....Take e.g. equality: The paramodulation inference rule for equational reasoning is an instance of partial TME, but a paramodulation step does not compute all equational consequences of the given key set. Such restrictions can be formulated within the general framework defined in the full version ([5]) This framework allows to specify a filtering out of T valid implications which are not relevant for a derivation. An important class of theories are definite theories, i.e. theories that are axiomatized by a set of definite clauses 4 . For such theories we find a special structure of ....

P. Baumgartner, `Refinements of Theory Model Elimination and a Variant without Contrapositives', Research Report 8/93, University of Koblenz, (1993).

....g would be satisfiable) Then by ground completeness (which is to be proven below) a refutation on the ground level with top clause G exists. However, this proof does not give us the claimed independence of the computation rule. A respective result (for the ground case) was proven explicitly in (Baumgartner, 1994). This proof works for any set of inference rules which work locally , which means that only one single branch is affected by the inference rules. Since this applies in our case we can take the respective result for our calculus as granted. The lifting to the first order case can be carried out ....

....fA; A B; B :Ag; and select A as top clause. Both existing refutations without reduction steps have to violate the full regularity restriction. Nevertheless, regularity wrt. open branches holds. Proof of Lemma 17. If G is a negative clause we will rely on earlier completeness proofs (e.g. (Baumgartner, 1994)) Thus suppose from now on that G is a definite clause. By the completeness theorem from (Baumgartner, 1994) we know that there exists a ME refutation R of S with top clause G. Now we proceed in two stages: we will show (1) how possibly applied reduction steps in R can be jar final.tex; ....

[Article contains additional citation context not shown here]

P. Baumgartner. Refinements of Theory Model Elimination and a Variant without Contrapositives. In A.G. Cohn, editor, 11th European Conference on Artificial Intelligence, ECAI 94. Wiley, 1994.

....in order to conveniently express another calculus variant defined below. Note that the restart ME calculus does not assume a special selection function which determines which path is to be extended or reduced next. Correctness and completeness of this calculus follows immediately from a result in [Baumgartner, 1994] . From the definition of the inference rule extension, it follows immediately, that this calculus only needs those contrapositives of clauses which contain a positive literal in their heads. 2 Computing Answers In this section we introduce the notion of computed answers and we state an answer ....

P. Baumgartner. Refinements of Theory Model Elimination and a Variant without Contrapositives. In A.G. Cohn, editor, 11th European Conference on Artificial Intelligence, ECAI 94. Wiley, 1994. (Long version in: Research Report 8/93, University of Koblenz, Institute for Computer Science, Koblenz, Germany).

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