C. Schwind. A tableaux-based theorem prover for a decidable subset of default logic. In M. Stickel, editor, Proceedings of the Conference on Automated Deduction, pages 528--542. Springer Verlag, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....credulous one, in which a query is said to be derivable if it belongs to a single extension, and a skeptical one, in which one stipulates that a query lies in all extensions. So far, computational approaches to nonmonotonic logics have mainly focused on the computation of entire extensions, like [4, 22, 9, 25, 14], or credulous queryanswering, like [17, 21] 10] compute intersections of extensions in Autoepistemic Logic. Skeptical query answering has up to now been primarily studied in restricted nonmonotonic reasoning frameworks, like Theorist [15] corresponding to so called prerequisitefree default ....

C. Schwind. A tableaux--based theorem prover for a decidable subset of default logic. In M. Stickel, editor, Proceedings of the Conference on Automated Deduction. Springer Verlag, 1990.

....on restricted subclasses of default theories. These results are directly applicable to autoepistemic logic because the subclasses can be seen as subclasses of autoepistemic premises under the translation (7. 11) Several decision methods for (decidable fragments of) default logic have been proposed [122, 26, 50, 132, 150, 4, 5]. By Theorem 7.6 we obtain an alternative view of default reasoning as a sequence of introspection steps. As in the case of autoepistemic reasoning, two 100 independent sources of complexity in default reasoning can be identified: required classical reasoning and determining a suitable ....

C. Schwind. A tableaux-based theorem prover for a decidable subset of default logic. In Proceedings of the 10th International Conference on Automated Deduction, pages 528--542, Kaiserslautern, FRG, July 1990. Springer-Verlag.

....of a default theory (W; D) its Generating Default Set is GD(W;D;E) 2 D E and E 6 : i ; 8i = 1; n Furthermore, given a default theory (W; D) computing its extension E is equivalent to nding its Generating Default Set since E = Th(W [ cons( 15] De nition 2. [16] Given a default theory (W; D) a set of defaults D is grounded if can be ordered as a sequence ( 1 ; n ) satisfying : 8i = 1; n; W [ cons(f 1 ; i 1 g) pre( i ) Lemma 1. 16] Every generating default set is grounded. The problem we address in this paper ....

....to nding its Generating Default Set since E = Th(W [ cons( 15] De nition 2. 16] Given a default theory (W; D) a set of defaults D is grounded if can be ordered as a sequence ( 1 ; n ) satisfying : 8i = 1; n; W [ cons(f 1 ; i 1 g) pre( i ) Lemma 1. [16] Every generating default set is grounded. The problem we address in this paper consists in an Extension Computation Problem (ECP) that can be de ned w.r.t. our heuristic approach by the following components. If is a default rule, pre( jus( and cons( respectively denotes the prerequisite, ....

C. Schwind. A tableaux-based theorem prover for a decidable subset of default logic. In M. Stickel, editor, Proceedings of the Conference on Automated Deduction. Springer Verlag, 1990.

....Prolog and compiles clauses into Prolog. Input: first order predicate logic in clausal form Implementation: sequential, Prolog and Lisp (Common Lisp) Availability: source code available Contact Address: M. Stickel email: stickel ai.sri.com 20 [C. Schwind] This tableaux based theorem prover [44, 43, 26] contains a kernel for classical logic and extensions to several systems of propositional, modal and temporal logic. One 9 extension of this prover is for default logic, one for action logic. Input: see above Implementation: C (for propositional logic) Prolog II Availability: binaries and ....

C. B. Schwind. A Tableaux-based Theorem Prover for a Decidable Subset of Default Logic. In M.E. Stickel, editor, Proc. CADE 10, 10th International Conference on Automated Deduction, Kaiserslautern, Germany, volume 449 of LNAI, pages 528--542. Springer Verlag, July 1990.

....A credulous one, in which a query is said to be derivable if it belongs to a single extension, and a skeptical one, in which one stipulates that a query lies in all extensions. So far, computational approaches to nonmonotonic logics have mainly focused on the computation of entire extensions, like [4, 19, 7, 22, 11], or credulous query answering, like [14, 18] 8] compute intersections of extensions in Autoepistemic Logic. Skeptical query answering has up to now been primarily studied in restricted nonmonotonic reasoning frameworks, like Theorist [12] corresponding to so called prerequisite free default ....

C. Schwind. A tableaux--based theorem prover for a decidable subset of default logic. In M. Stickel, editor, Proceedings of the Conference on Automated Deduction. Springer, 1990.

....character of an inference rule and the additional consistency check. While the latter is handled in default logic in the usual manner by testing satisfiability, the former needs a more subtle treatment: The character of an inference rule can be captured by the notion of groundedness defined by [ Schwind,1990 ] We call a set of default rules Delta grounded in a set of facts W iff there exists an enumeration hffi i i i2I of Delta such that W [ Conseq(fffi 0 ; ffi i Gamma1 g) Prereq(ffi i ) 3) for i 2 I : For convenience, we denote the prerequisite of a default rule ffi by Prereq(ffi) and ....

C. Schwind. A tableaux-based theorem prover for a decidable subset of default logic. In M. Stickel, editor, Proceedings of the Conference on Automated Deduction. Springer Verlag, 1990.

....on restricted subclasses of default theories. These results are directly applicable to autoepistemic logic because the subclasses can be seen as subclasses of autoepistemic premises under the translation (7. 11) Several decision methods for (decidable fragments of) default logic have been proposed [122, 26, 50, 132, 150, 4, 5]. By Theorem 7.6 we obtain an alternative view of default reasoning as a sequence of introspection steps. As in the case of autoepistemic reasoning, two 100 independent sources of complexity in default reasoning can be identified: required classical reasoning and determining a suitable ....

C. Schwind. A tableaux-based theorem prover for a decidable subset of default logic. In Proceedings of the 10th International Conference on Automated Deduction, pages 528--542, Kaiserslautern, FRG, July 1990. Springer-Verlag.

.... possible world semantics both in the design of reasoning procedures [6, 8, 11, 16] and in their implementation [3] The design of systematic tableaux calculi for nonmonotonic modal logics (NMMLs for short) has not been considered, although decision procedures for many nonmonotonic logics exist [1, 2, 14, 21, 22, 23, 24, 29]. A major obstacle for the development of a semantic tableaux method has also been the lack of a Kripke style semantics for NMMLs. In fact, NMMLs have been originally proposed in terms of a fix point construction which specifies the introspective capabilities of a reasoning agent. The first ....

....based on the following three steps: i) identification of a candidate model; ii) preference verification (iii) logical entailment. Step (ii) embodies the aspects that are specific to a logic and a preference semantics. Although other tableaux methods for nonmonotonic reasoning have been proposed [1, 2, 21, 29] and decision procedures for some nonmonotonic modal logics were known [14, 23] our proposal has many advantages: uniformly covers a wide range of nonmonotonic formalisms, including autoepistemic logic, default logic, and the logic of minimal knowledge[10] is semantically based and thus ....

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C. B. Schwind. A tableaux-based theorem prover for a decidable subset of default logic. In Proc. of CADE-90, LNAI, pages 528--542. 1990.

....hierarchy. Many successful attempts at finding polynomially tractable subcases have been proposed, and all of them attack both sources of complexity at the same time. Algorithms for performing default reasoning have been presented by Reiter [129] Etherington [50] Zhang and Marek [158] Schwind [141] and Poole et al. 117] Algorithms described in [129, 50, 158] use satisfiability testers as subroutines. 4 Modal Non Monotonic Logics In this section we review complexity results presented in the literature concerning nonmonotonic versions of modal logics, with special attention to the best ....

C. B. Schwind. A tableaux-based theorem prover for a decidable subset of default logic. In Proceedings of the Tenth Conference on Automated Deduction (CADE90) , pages 528--542, 1990.

.... possible world semantics both in the design of reasoning procedures [6, 8, 11, 16] and in their implementation [3] The design of systematic tableaux calculi for nonmonotonic modal logics (NMMLs for short) has not been considered, although decision procedures for many nonmonotonic logics exist [1, 2, 14, 21, 22, 23, 24, 30]. One of the major obstacles towards the development of a semantic tableaux method has been the lack of a true Kripke style semantics for NMMLs. In fact, NMMLs have been originally proposed in terms of a fix point construction which specifies the introspective capabilities of a reasoning agent. ....

....of a candidate model; ii) verification of the preference condition (iii) check of logical entailment. Step (ii) embodies the aspects that are specific to the modal system and to the corresponding preference semantics. Although other tableaux methods for nonmonotonic reasoning have been proposed [1, 2, 21, 30] and decision procedures for many nonmonotonic modal logics are known [14, 23] the advantage of our proposal is that it uniformly covers a wide range of nonmonotonic reasoning formalisms, including autoepistemic logic, default logic, and the logic of minimal knowledge [10] Moreover, it is ....

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C. B. Schwind. A tableaux-based theorem prover for a decidable subset of default logic. In Proc. of CADE-90, LNAI, pages 528--542. 1990.

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C. Schwind. A tableaux-based theorem prover for a decidable subset of default logic. In M. Stickel, editor, Proceedings of the Conference on Automated Deduction, pages 528--542. Springer Verlag, 1990.

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