Marc Denecker and Danny De Schreye. A family of abductive procedures for normal abductive programs, their soundness and completeness. Technical Report 136, Department of Computer Science, K.U.Leuven, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the intuitions behind SLDNFA and de ne the basic inference operators. In section 3 we formalise SLDNFA and its soundness and completeness. In section 4, we present variants of SLDNFA, which yield other completeness results. Finally, we end with a discussion. Due to space restrictions, we refer to [5] for all proofs. 2 Basic computation steps in SLDNFA The SLDNFA procedure is an abductive procedure for normal abductive programs. An abductive logic program is a normal logic program (with negation as failure) except that a set of abductive predicates occurs which are unde ned. For a given ....

....it is possible to construct an SLDNF refutation with the same goals, resolution steps and substitutions. Vice versa, for every SLDNF refutation an equivalent SLDNFA can be constructed. We have proved the following soundness result for the SLDNFA procedure with respect to completion semantics (see [5]) Below, comp(L Sk( P ) denotes the Clark completion ( 3] of the non abductive program consisting of the clauses of P and . Q 0 ) denotes the open conjunction of literals of Q. Theorem 3.1 (soundness) If ( is the result of an SLDNFA refutation for a goal Q 0 then comp(L Sk( P ....

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Marc Denecker and Danny De Schreye. A family of abductive procedures for normal abductive programs, their soundness and completeness. Technical Report 136, Department of Computer Science, K.U.Leuven, 1992.

....resolution, flipping ground negative literals in a goal to the converse type of goal are the primitive inference operators on which SLDNFA is built. We have formalised the procedure, and have proven the soundness of SLDNFA with respect to the completion semantics: completion(P Delta) j= Q ([2]) As a completeness result, we have proved that if the computation terminates, then SLDNFA generates at least all minimal solutions ( 2] This means that for every abductive solution Delta, SLDNFA generates a solution Delta such that there exists a substitution of the skolem constants of ....

....SLDNFA is built. We have formalised the procedure, and have proven the soundness of SLDNFA with respect to the completion semantics: completion(P Delta) j= Q ( 2] As a completeness result, we have proved that if the computation terminates, then SLDNFA generates at least all minimal solutions ([2]) This means that for every abductive solution Delta, SLDNFA generates a solution Delta such that there exists a substitution of the skolem constants of Delta which is a bijection between Delta and a subset of Delta. This minimality reflects well the nonmonotonic character of abduction: ....

M. Denecker and D. De Schreye. A family of abductive procedures for normal abductive programs, their soundness and completeness. Technical Report 136, Department of Computer Science, K.U.Leuven, 1992.

....is used which distinguishes two types of variables: those universally quantified in front of 8(Q 0 Psi) and those universally quantified inside Psi. The possibility of getting rid of skolem constants was somehow already clear in the proofs of the correctness of the old version of SLDNFA [12]. The proof of the completeness of SLNDFA in [12] already relied on an explicit substitution of skolem constants by variables. There is a well known theorem in classical logic which states a strong relationship between skolem constants and universally quantified variables: for a given theory T , ....

....those universally quantified in front of 8(Q 0 Psi) and those universally quantified inside Psi. The possibility of getting rid of skolem constants was somehow already clear in the proofs of the correctness of the old version of SLDNFA [12] The proof of the completeness of SLNDFA in [12] already relied on an explicit substitution of skolem constants by variables. There is a well known theorem in classical logic which states a strong relationship between skolem constants and universally quantified variables: for a given theory T , formula F [X] and constant sk which appears ....

M. Denecker and D. De Schreye. A family of abductive procedures for normal abductive programs, their soundness and completeness. Technical Report 136, Department of Computer Science, K.U.Leuven, 1992.

....constraints. That an abductive procedure can be used for explanation of some observation is well known from [21] It is less known that an abductive procedure can also be used for deduction and for proving consistency of a theory. In section 4, we apply the abductive procedure called SLDNFA [5, 6], to solve distinct computational tasks involving complete and incomplete knowledge. The paper is structured as follows. In section 2, we recall the language A and its semantics. In section 3, the transformation from A to situation calculus programs is presented and the soundness and completeness ....

M. Denecker and D. De Schreye. A family of abductive procedures for normal abductive programs, their soundness and completeness. Technical Report 136, Department of Computer Science, K.U.Leuven, 1992.

....of this method has been implemented. An interesting experiment was its extension to an abductive planner based on the event calculus. Our prototype planner was able to solve some hard problems with context dependent events, problems that are not properly solved by existing systems [23] 22] In [7, 8], we proved the soundness of the procedure with respect to Completion semantics, in the sense that for any query Q and generated solution Delta: P Delta j= Q This implies the soundness of the procedure with respect to the Generalised Stable Model semantics of [14] a generated solution can ....

M. Denecker and D. De Schreye. A family of abductive procedures for normal abductive programs, their soundness and completeness. Technical Report 136, Department of Computer Science, K.U.Leuven, 1992.

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