M. Denecker and D. De Schreye. On the Duality of Abduction and Model Generation in a Framework for Model Generation with Equality. Journal of Theoretical Computer Science, 122(1&2):225--262, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....(resp. body) literal. Clearly, a range restricted clause in implication form is ground if its body is ground, e.g. if it is . Note that clauses considered in many applications of minimal model generation e.g. database view updates [6, 2] database schema design [7] abductive reasoning [6, 16, 17], diagnosis [54, 61, 53] are range restricted. Also, clauses obtained from many sorted formulas through the standard representation in first order logic [18] are range restricted. A transformation is first defined, which associates a set RR(S) of range restricted clauses in implication form ....

....observed e.g. in [43] 11 3.2 Comparison of PUHR Tableaux With Related Refutation Methods The PUHR tableaux are a formalization of the principle of the SATCHMO programs, one of them is recalled in the next section. Other formalizations of the SATCHMO approach to theorem proving can be found in [16, 33, 17, 12, 3, 37, 11, 71]. A further more or less implicit formalization is subjacent to [43] In [71, 11] EP Tableaux are proposed that generalize PUHR Tableaux to nonclausal formulas with restricted quantification . PUHR and hyper tableaux [3, 37] are more in the tableaux style (cf. 66, 25, 73, 74] than the ....

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M. Denecker and D. Schreye. On the Duality of Abduction and Model Generation in a Framework for Model Generation With Equality. Theoretical Computer Science, 122, 225--262, 1994.

....entire PUHR tableau explicitly in memory. 5.2. Future Plans There are many possible directions for further developments. From a theorem proving perspective, extensions to be investigated and implemented include a more efficient treatment of non range restricted clauses and reasoning with equality [3]. In addition, bidirectional search as in SATCHMORE [9] can accelerate proofs of Satchmo. From a logic programming perspective, we would like to support nonmonotonic features such as aggregation and negation as failure, as well as access to predicates defined outside the clausal theory. We would ....

M. Denecker and D. De Schreye. On the duality of abduction and model generation in a framework for model generation with equality. Theoretical Computer Science, 122(1--2):225--262, 1994.

....Model generation lies somewhere in between deduction and abduction, the inference to the best explanation. Minimal models are, in the sense of Occam s Razor, often the best explanations for the truth of a theory. The duality of model generation and abduction has been investigated in detail in [17, 10]. Inference systems that are related to abductive logic programming have been proposed earlier for inference to the best explanation in natural language interpretation [15] The approach of Hobbs requires sophisticated control mechanisms for maintaining the equivalence of abductive proofs and ....

M. Denecker and D. De Schreye. On the duality of abduction and model generation in a framework for model generation with equality. Theoretical Computer Science, 122(1--2):225--262, 3 Jan. 1994.

....efficiently many realistic problems that cannot be handled by model generators for clausal theories like PUHR tableaux. Other approaches for model generation involving constraints in the literature work with equational constraints: Satchmo has been extended to handle equations in rule heads [6]. Equations are added to an equational theory for the current branch at runtime. Caferra et al. 5,4] use equality and disequality constraints for model generation. Both their calculus and their use of constraints is quite different to ours: It attaches constraints to universally rather than ....

....This does never lead to branching or impose new constraints on the existential variables. Furthermore, the mechanism that avoids repeated application of a rule to the same electrons is not comparable to the one used in CPUHR tableaux. 5 Similar techniques have been used in extensions of Satchmo [6]. 6 In our terminology: Unification succeeds only if G 0 is already satisfied. CHR can be used for the implementation of CPUHR tableaux. In fact the idea of combining features of CHR and Satchmo have led to the work presented in this paper. 6 Conclusion and Future Work In this paper, we ....

M. Denecker and D. De Schreye. On the duality of abduction and model generation in a framework for model generation with equality. Journal of Theoretical Computer Science, 1994.

....PRQ(F) is obtained by a renaming of the elements of the universe of M. 5 Extended Positive Tableaux Extended Positive tableaux, short EP tableaux, are a refinement of the PUHR tableaux defined in [11] as a formalization of the SATCHMO theorem prover [25] Other related formalizations are given in [13, 3]. The refinement of EP tableaux consists of the processing of PRQ formulas instead of (Skolemized) clauses, and in a tableaux expansion rule for existentially quantified subformulas which, as opposed to the standard ffi rule [32, 16] performs no run time Skolemization . Example 2. Consider S = ....

M. Denecker and D. de Schreye. On the Duality of Abduction and Model Generation in a Framework of Model Generation with Equality. Theoretical Computer Science, 122, 1994.

....in the right the computed formula is called the explanation formula. Though such a procedure can be used to solve abductive problems, it is much weaker than an abductive procedure like SLDNFA because naive unfolding cannot guarantee the consistency of the right hand of the explanation formula. In [5, 9], we show that SLDNFA can be interpreted also as a kind of an unfolding procedure, but SLDNFA is equipped with a mechanism for checking the consistency of each of the disjuncts at the right hands of the generated explanation formula. In our opinion, this is absolutely necessary because even for ....

M. Denecker and D. De Schreye. On the Duality of Abduction and Model Generation in a Framework for Model Generation with Equality. Journal of Theoretical Computer Science, 122(1&2):225--262, 1994.

....it turns out that SLDNFA verifies the original integrity constraint in a bottom up way: an instance of the body of the rule is found and this fires the abduction of the head of the rule. A subject for future research is to compare with special purpose procedures (such as the one in [38] In [9, 11], we have formalised a procedural duality between abduction and an extension of Satchmo [28] for model generation under FEQ with equality atoms in the head of the rules. Interestingly, the duality framework indicates a close relation between Eshghi s approach of abducing equality facts [13] and ....

....approach of abducing equality facts [13] and the approach of Shanahan [41] Missiaen [32] and of section 5.2 of extending unification for dealing with skolem constants. Eshghi s problem of keeping a set of ground equality facts consistent wrt FEQ also occurs during model generation under FEQ. In [9, 11], we developed efficient techniques to do this, inspired by Term Rewriting. New equality atoms which are derived during model generation, are processed in a special way. In the first step, called dynamic completion, the derived equality atoms are transformed to a complete term rewriting system. In ....

M. Denecker and D. De Schreye. On the Duality of Abduction and Model Generation in a Framework for Model Generation with Equality. Journal of Theoretical Computer Science, 122(1&2), 1994.

....a rich functionality to a knowledge base with uncertainty. It has been used in AI diagnosis, for natural language interpretation, for temporal reasoning such as scheduling and planning, etc. We have shown that in the context of OLP FOL, abductive procedures can be used for model generation [29, 33], deduction and satisfiability proving [34] Others have shown the use of abduction for belief revision and assimilation and default reasoning [45] We are currently integrating SLDNFA with constraint solvers for real number arithmetic and finite domain solvers [2] and a constraint solver for the ....

M. Denecker and D. De Schreye. On the Duality of Abduction and Model Generation in a Framework for Model Generation with Equality. Journal of Theoretical Computer Science, 122(1&2):225--262, 1994.

....in the right the computed formula is called the explanation formula. Though such a procedure can be used to solve abductive problems, it is much weaker than an abductive procedure like SLDNFA because naive unfolding cannot guarantee the consistency of the righ hand of the explanation formula. In [5, 9], we show that SLDNFA can be interpreted also as a kind of an unfolding procedure, but SLDNFA is equiped with a mechanism for checking the consistency of each of the disjuncts at the right hands of the generated explanation formula. In our opinion, this is absolutely necessary because even for ....

M. Denecker and D. De Schreye. On the Duality of Abduction and Model Generation in a Framework for Model Generation with Equality. Journal of Theoretical Computer Science, 122(1&2), 1994.

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