Ulrich Junker and Kurt Konolige. Computing the extensions of autoepistemic and default logics with a TMS. In AAAI-90: Proceedings of the 8th national conference on artificial intelligence, pages 278--283, Boston, MA, 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 ....

U. Junker and K. Konolige. Computing the extensions of autoepistemic and default logic with a TMS. In Proceedings of the AAAI National Conference on Artificial Intelligence, 1990.

..... The novel decision method for autoepistemic reasoning needs only a theorem prover for the underlying monotonic consequence relation j= ae as a subroutine. The approach differs from techniques where nonmonotonic reasoning is reduced to another related problem such as a truth maintenance problem [50, 51], a theorem proving problem [88] or a constraint satisfaction problem [4, 5] These reductions provide valuable insights to the relationships between the In this chapter we use the term full somewhat loosely. Often a set Upsilon Sf ( Sigma) Sf satisfying the two conditions in ....

.... 128 corresponding problems and enable new techniques to be used for solving nonmonotonic reasoning problems. However, while there are interesting subclasses of nonmonotonic reasoning problems where the problem size increases only polynomially as a result of the reduction mapping (see, e.g. [51, 88, 4]) in the general case the reductions can lead to an exponential increase in the problem size. Hence the reductions turn also the worst case space complexity exponential. Furthermore, the reductions appear computationally quite complex even for restricted classes of nonmonotonic reasoning ....

[Article contains additional citation context not shown here]

U. Junker and K. Konolige. Computing the extensions of autoepistemic and default logics with a truth maintenance system. TASSO-Report 16, Gesellschaft fur Mathematik und Datenverarbeitung, St. Augustin, Germany, December 1990.

.... independently by several researchers [83, 87, 101, 103] The author has shown that first order autoepistemic logic where quantifying in is not allowed is decidable if and only if the underlying first order consequence relation is decidable [107] Moore [101] as well as Junker and Konolige [50] report a similar result. Marek and Truszczy nski [83, 87] show that the problem of existence of a Moore style expansion is NP complete for a restricted subclass of propositional autoepistemic logic. In a later paper [88] they establish further com 12 plexity results on restricted classes ....

....reasoning. The author has presented an analytic tableau based decision procedure for propositional Moore style autoepistemic logic [103] Marek and Truszczy nski [83, 87] devise a decision method for Moore style autoepistemic logic which is based on normal form transformations. Junker and Konolige [50] present a decision method for first order default logic and autoepistemic logic where quantifying in is not allowed. The method employs a truth maintenance system and is based on the finitary characterization of stable expansions using LOE subformulae of the premises. The premises are required to ....

[Article contains additional citation context not shown here]

U. Junker and K. Konolige. Computing the extensions of autoepistemic and default logics with a truth maintenance system. In Proceedings of the 8th National Conference on Artificial Intelligence, pages 278--283, Boston, MA, USA, July 1990. The MIT Press.

....literature, yielding different classes of modal nonmonotonic logics. Although modal nonmonotonic logics have been extensively studied from a theoretical point of view (for a recent work discussing proof theoretical issues, cf. e.g. 1] besides some early attempts about implementational issues [4, 2, 21, 3], most of these approaches lack generally available solvers thus far. This despite the fact that recent years witnessed an increasing amount of successful implementations for various nonmonotonic formalisms, mostly for the answer set programming paradigm, as realised, This work was partially ....

U. Junker and K. Konolige. Computing the Extensions of Autoepistemic and Default Logic with a TMS. In Proc. AAAI-90, pages 278--283, 1990.

....implies Lp 1 2 and so on. Several decision methods have been proposed for autoepistemic reasoning. Some of these [85, 115, 66] are straightforward applications of a particular nitary characterization of autoepistemic reasoning, some [86] use extensively a specic underlying proof method and some [73, 44, 74] are based on the idea of mapping a decision problem in autoepistemic logic into another problem. The advanced methods include techniques where nonmonotonic reasoning is reduced to another problem such as a truth maintenance problem [44] a theorem proving problem [74] or a constraint ....

....a specic underlying proof method and some [73, 44, 74] are based on the idea of mapping a decision problem in autoepistemic logic into another problem. The advanced methods include techniques where nonmonotonic reasoning is reduced to another problem such as a truth maintenance problem [44], a theorem proving problem [74] or a constraint satisfaction problem [4] These reductions provide valuable insights to the relationships between the corresponding problems and enable new techniques to be used for solving nonmonotonic reasoning problems. However, while there are interesting ....

[Article contains additional citation context not shown here]

U. Junker and K. Konolige. Computing the extensions of autoepistemic and default logics with a truth maintenance system. In Proceedings of the 8th National Conference on Articial Intelligence, pages 278283, Boston, MA, USA, July 1990. The MIT Press.

....of decision methods for default reasoning. Methods based on the characterization of extensions in terms of generating defaults (Theorem 4. 1) can be found, e.g. in [MT93, BH95, RS94] There are approaches where default reasoning is reduced into another problem like a truth maintenance problem [JK90] or a constraint satisfaction problem [BED91] An interesting approach to provide proof theory for default reasoning based on sequent calculus is proposed by [Bon96, BO97] A novelty in this approach is that it includes an explicit proof theoretic treatment of non validity needed in default ....

U. Junker and K. Konolige. Computing the extensions of autoepistemic and default logics with a truth maintenance system. In Proceedings of the 8th National Conference on Articial Intelligence, pages 278-283, Boston, MA, USA, July 1990. MIT Press.

....unstratied case, and its eoeectiveness in achieving tractability can be traced to this very property. The tools applied in developing automated theorem proving methods for nonmonotonic logics have been very dioeerent from the ones in developing theorem provers for classical logics. For example, Junker and Konolige [ 1990 ] base their theorem prover for default logic on truth maintenance systems, and Ben Eliyahu and Dechter [ 1992a; 1992b ] on techniques developed for solving constraint networks. For our algorithm we present techniques that directly lead to implementations that use theorem provers for classical ....

U. Junker and K. Konolige. Computing the extensions of autoepistemic and default logics with a truth maintenance system. In Proceedings of the 9th National Conference on Articial Intelligence, pages 278283, Boston, 1990. Morgan Kaufmann Publishers.

....that has already been explored extensively. Moreover, our method introduces a deterministic algorithm for computing extensions of any finite propositional default theory, 1 In this paper, when we mention default logic we mean Reiter s default logic . 3 while previous algorithms 2 (e.g. [KS91, Sti90, JK90, Eth87a]) produce an extension only for certain subsets of all default theories. Our translation is exponential in general. However, there is a significant sublanguage which we call 2 default theories (2 DT) for which our translation is tractable. The class 2 DT includes the so called network default ....

.... in this paper and what is called Clark s predicate completion [Cla78] A preliminary version of this work appears in [BED91] There have been attempts in the past to relate default logic to other forms of nonmonotonic reasoning systems, such as autoepistemic logic, circumscription, and TMS [Kon88, MT89, Eth87b, JK90]. We believe that embedding default logic in classical logic is just as valuable since classical logic is a well understood formalism supported by a large body of computational knowledge. A Proofs A.1 Useful theorems and definitions Definition A.1 ( Lee67] If S is any set of clauses, then the ....

Ulrich Junker and Kurt Konolige. Computing the extensions of autoepistemic and default logics with a TMS. In AAAI-90: Proceedings of the 8th national conference on artificial intelligence, pages 278--283, Boston, MA, 1990.

.... in [WB93] GM90] PC89] RM89] and [FH89] The last two papers use autoepistemic logic instead of logic programs) They led to a better understanding of the semantics of nonmonotonic truth maintenance systems, to their use for computing stable models [Esg90] and autoepistemic extensions [JK91], for doing abductive reasoning [IS91] RP91] and to the development of variants of TMSs based on other semantics of logic programs. A good description of one such system, based on the well founded semantics, together with the proof of its tractability can be found in [Wit91] 67 10 ....

U. Junker and K. Konolige. Computing the extensions of autoepistemic and default logics with a truth maintenance systems. In Proc. of AAAI 90, pages 278--283, 1991.

....in performance of satisfiability algorithms [SLM92, SKC96, DABC96, CA96] demonstrate the value of experimental studies. The progress in understanding default logic resulted in several algorithms for computing extensions and led to first implementation projects [Nie92, MT93, ALS94, BL93, JK90, BED91] In the last few years, implementing nonmonotonic reasoning systems became one of the most actively pursued directions in the area of nonmonotonic logics. Several working systems were presented recently at the Fourth Conference on Logic Programming and Nonmonotonic Reasoning [DFN97] Our ....

U. Junker and K. Konolige. Computing the extensions of autoepistemic and default logics with a truth maintenance system. In Proceedings of the Eighth National Conference on Artificial Intelligence (AAAI-90). Morgan Kaufmann, 1990.

....the relationship between WFSX semantics and ATMS structure. We have shown that we can use ATMS to remove contradictions but we haven t said how to use ATMS to compute WFSX. There have been some work [15, 7] on relationships between stable models [9] of logic programs and ATMS , and some other work [8, 17, 11] on relationships between autoepistemic logic (or default logic) and Doyle s TMS [6] There is also some work on computing 3 valed stable models by using ATMS [12] and AMTS implementation of logic programming [4] However, It has not been clear to us how to compute WFSX by using ATMS or TMS, ....

Junker, U., Konolige, K., Computing the extensions of autoepistemic and default theories with a truth maintenance system, AAAI 90, 1990, 279 -- 283

....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 ....

U. Junker and K. Konolige. Computing the extensions of autoepistemic and default logic with a TMS. In Proceedings of the National Conference on Artificial Intelligence, 1990.

....size of input (see [5] Systematic experimentation may be the most direct way and, perhaps, the only way to answer the above questions. In addition to complexity results mentioned earlier, several algorithms for reasoning from default theories and logic programs with negation were presented in [19, 13, 28, 26]. In view of the large body of these results, it seems that the main problem hindering the research on these algorithms and the efforts to develop reasoning systems based on nonmonotonic logics is the lack of adequate experimentation testbed. In this paper we address this issue. To experiment with ....

U. Junker and K. Konolige. Computing the extensions of autoepistemic and default logics with a truth maintenance system. In Proceedings of AAAI-90, Los Altos, CA., 1990. American Association for Artificial Intelligence, Morgan Kaufmann.

.... in [WB93] GM90] PC89] RM89] and [FH89] The last two papers use autoepistemic logic instead of logic programs) They led to a better understanding of the semantics of nonmonotonic truth maintenance systems, to their use for computing stable models [Esg90] and autoepistemic extensions [JK91], for doing abductive reasoning [IS91] RP91] and to the development of variants of TMSs based on other semantics of logic programs. A good description of one such system, based on the well founded semantics, together with the proof of its tractability can be found in [Wit91] 10 ....

U. Junker and K. Konolige. Computing the extensions of autoepistemic and default logics with a truth maintenance systems. In Proc. of AAAI 90, pages 278--283, 1991.

.... query answering has so far only been addressed indirectly: On the one hand, we find approaches that are primarily interested in the construction of extensions; queries are then either answerable by simple membership tests or by directing the construction towards extensions containing the query [7, 14, 9, 3]. On the other hand, we find approaches based on variants of default logic that guarantee the existence of extensions and that allow for local proof procedures [12] Unfortunately, these variants do not offer the same expressiveness as the original approach [1] In the general case, there is thus ....

....and an on line process: We start with a compilation phase which results in the block graph Gamma Delta of a default theory Delta. Gamma Delta contains the essential information about the blocking relations between the default rules in Delta and is quadratic in the number of defaults. Unlike [7, 14], our approach does thus not suffer from exponential space complexity. The subsequent query answering phase aims at finding a default proof P such that Delta Psi P possesses an extension. This gives us a default proof which contains only the ultimately necessary defaults. To be more precise, a ....

[Article contains additional citation context not shown here]

U. Junker and K. Konolige. Computing the extensions of autoepistemic and default logic with a TMS. In Proc. AAAI National Conf. on Artificial Intelligence, 1990.

....the problem of finding all the stable models of a knowledge base corresponds to the problem of finding all the models of a propositional theory. Satoh and Iwayama (1991) provide a nondeterministic procedure for computing Ben Eliyahu the stable models of logic programs with integrity constraints. Junker and Konolige (1990) present an algorithm for computing TMS labels. Antoniou and Langetepe (1994) introduce a method for representing some classes of default theories as normal logic programs in such a way that SLDNF resolution can be used to compute extensions. Pimentel and Cuadrado (1989) develop a ....

....for autoepistemic logic can also be adopted for computing stable models. The procedures by Marek and Truszczy nski (1993) Antoniou and Langetepe (1994) Pimentel and Cuadrado (1989) BenEliyahu and Dechter (1991) Satoh and Iwayama (1991) Bell et al. 1994) Subrahmanian et al. 1995) and Junker and Konolige (1990) do not take advantage of the structure of the knowledge base as reflected in its dependency graph, and therefore are not efficient for stratified knowledge bases. Sacc a and Zaniolo (1990) present a backtracking fixpoint algorithm for constructing one stable model of a first order knowledge ....

Junker, U., & Konolige, K. (1990). Computing the extensions of autoepistemic and default logics with a TMS. In AAAI-90: Proceedings of the 8th national conference on artificial intelligence, pp. 278--283. AAAI Press.

....compute stable models quite eOEciently for non strati ed (propositional) logic programs consisting of several hundreds of rules. 1 Introduction We study automated theorem proving methods for default logic of Reiter [ 1980 ] Although there are some approaches to automating default reasoning [ Junker and Konolige, 1990; Ben Eliyahu and Dechter, 1991; Baader and Hollunder, 1992; Risch and Schwind, 1994 ] relatively little attention has been paid to eOEciency considerations. Also test cases of realistic size are lacking. In this paper we put forward combinatorial problems as an application domain with rich and ....

U. Junker and K. Konolige. Computing the extensions of autoepistemic and default logics with a truth maintenance system. In Proceedings of the 8th National Conference on Artiøcial Intelligence, pages 278283, Boston, MA, USA, July 1990. The MIT Press.

..... The novel decision method for autoepistemic reasoning needs only a theorem prover for the underlying monotonic consequence relation j= ae as a subroutine. The approach differs from techniques where nonmonotonic reasoning is reduced to another related problem such as a truth maintenance problem [50, 51], a theorem proving problem [88] or a constraint satisfaction problem [4, 5] These reductions provide valuable insights to the relationships between the 1 In this chapter we use the term full somewhat loosely. Often a set Upsilon Sf L ( Sigma) Sf L ( Sigma) satisfying the two ....

.... 128 corresponding problems and enable new techniques to be used for solving nonmonotonic reasoning problems. However, while there are interesting subclasses of nonmonotonic reasoning problems where the problem size increases only polynomially as a result of the reduction mapping (see, e.g. [51, 88, 4]) in the general case the reductions can lead to an exponential increase in the problem size. Hence the reductions turn also the worst case space complexity exponential. Furthermore, the reductions appear computationally quite complex even for restricted classes of nonmonotonic reasoning ....

[Article contains additional citation context not shown here]

U. Junker and K. Konolige. Computing the extensions of autoepistemic and default logics with a truth maintenance system. TASSO-Report 16, Gesellschaft fur Mathematik und Datenverarbeitung, St. Augustin, Germany, December 1990.

.... independently by several researchers [83, 87, 101, 103] The author has shown that first order autoepistemic logic where quantifying in is not allowed is decidable if and only if the underlying first order consequence relation is decidable [107] Moore [101] as well as Junker and Konolige [50] report a similar result. Marek and Truszczy nski [83, 87] show that the problem of existence of a Moore style expansion is NP complete for a restricted subclass of propositional autoepistemic logic. In a later paper [88] they establish further com 12 plexity results on restricted classes ....

....reasoning. The author has presented an analytic tableau based decision procedure for propositional Moore style autoepistemic logic [103] Marek and Truszczy nski [83, 87] devise a decision method for Moore style autoepistemic logic which is based on normal form transformations. Junker and Konolige [50] present a decision method for first order default logic and autoepistemic logic where quantifying in is not allowed. The method employs a truth maintenance system and is based on the finitary characterization of stable expansions using LOE subformulae of the premises. The premises are required to ....

[Article contains additional citation context not shown here]

U. Junker and K. Konolige. Computing the extensions of autoepistemic and default logics with a truth maintenance system. In Proceedings of the 8th National Conference on Artificial Intelligence, pages 278--283, Boston, MA, USA, July 1990. The MIT Press.

....an implicit preference for the rule with the precondition helicopter(X) in the context of helicopter holding for a particular rule instance. 2. 3 Inference Engines for Default Logic There are experimental implementations of automated reasoning systems for default logic and related logics [BQQ83, JK90, NR92, Nie94, Nie95a, Nie95b, NS96, SB96, Hop93, Sch95, RS94, LS95, SN97] These include systems that compute extensions and systems that provide credulous and skeptical query answering. An inference engine can be viewed as being composed of classical reasoning and conflict resolution. These two ....

U. Junker and K. Konolige. Computing the extensions of autoepistemic and default logics with a truth maintenance system. In Proceedings of the Eighth National Conference on Artifical Intelligence (AAAI'90), pages 278--283. MIT Press, 1990.

....with what has been derived (either by finding a model, or by finite failure using a complete inference system) and then infer the consequent of the default. This choice may have to be undone if some justifications used are not consistent with some subsequent default. Junker and Konolige [Junker and Konolige, 1990] have developed a proof procedure based on translating default logic into a truth maintenance system. They develop a finite representation for extensions of closed default theories, and develop a correspondence between the fixed point of a TMS and the representation for an extension. 6.2 Backward ....

U. Junker and K. Konolige. Computing the extensions of autoepistemic and default logics with a truth maintenance system. In Proc. 8th National Conference on Artificial Intelligence, pages 278--283, Boston, MA, July 1990.

....the detection of conflicts (or nogoods) Conflict based approaches are common in nonmonotonic reasoning, belief revision, model based diagnosis, configuration, and planning. Some good examples are hitting set trees [Reiter, 1987] conditionals [Geffner and Pearl, 1992] TMS based default provers [Junker and Konolige, 1990] . In recent years, conflictbased reasoning is also gaining interest in the field of constraint satisfaction. Examples are conflict based backjumping [Prosser, 1993] dynamic backtracking [Ginsberg, 1993] distributed CSP s [Yokoo, 1995] over constrained CSP s [R egin et al. 2000] Tabu ....

U. Junker and K. Konolige. Computing the extensions of autoepistemic and default logics with a truth maintenance system. In AAAI-90, pages 278--283, Boston, MA, 1990. MIT press.

....that are correct w.r.t. the formalism, but are not intuitive. A solution to avoid contraposition for prioritized defaults is to select priorities carefully. Also partially ordered defaults can be helpful. In the next time, we will integrate an improved Doyle style TMS into Except II following [Junker and Konolige, 1990], Junker, 1990] and [Junker, 1991] This will improve the computation of further solutions. Currently, the system finds the first solution of a default theory in good time, but spends too much time to do backtracking. TMS exploits the precise dependencies between defaults and thus avoids useless ....

....formalism, but are not intuitive. A solution to avoid contraposition for prioritized defaults is to select priorities carefully. Also partially ordered defaults can be helpful. In the next time, we will integrate an improved Doyle style TMS into Except II following [Junker and Konolige, 1990] [Junker, 1990], and [Junker, 1991] This will improve the computation of further solutions. Currently, the system finds the first solution of a default theory in good time, but spends too much time to do backtracking. TMS exploits the precise dependencies between defaults and thus avoids useless choices. This ....

U. Junker and K. Konolige. Computing the extensions of autoepistemic and default logics with a truth maintenance system. TASSOReport 16, GMD, St. Augustin, FRG, December 1990. 100

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Ulrich Junker and Kurt Konolige. Computing the extensions of autoepistemic and default logics with a TMS. In AAAI-90: Proceedings of the 8th national conference on artificial intelligence, pages 278--283, Boston, MA, 1990.

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U. Junker and K. Konolige. Computing the extensions of autoepistemic and default logic with a TMS. In Proceedings of the National Conference on Artificial Intelligence, pages 278--283. The AAAI Press/The MIT Press, 1990.

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