I. Niemela and P. Simons. Ecient implementation of the well-founded and stable model semantics. In Proceedings of JICSLP-96. MIT Press, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... set semantics [14] can be understood as a special case of disjunctive default logic, as established in [17] this translation also yields a correspondence between UCL and logic programming, which makes possible automated reasoning using fast improving, publicly available systems such as smodels [44], dlv [9] and DeReS [7] In fact, DeReS can even work directly with default theories. 15 6.1 Disjunctive Default Logic Here we recall de nitions from [17] A disjunctive default rule is an expression of the form (25) where all of ; 1 ; m ; 1 ; n are (nonmodal) ....

Ilkka Niemela and Patrik Simons. Ecient implementation of the well-founded and stable model semantics. In Proc. Joint Int'l Conf. and Symp. on Logic Programming, pages 289-303, 1996.

....Before providing an outline of these two modules, it is worth noting that the smodels tool box seems to be the current state of art in stable model semantics. A comparison with the SLG system (which is another implementation of stable model semantics for logic programs [7] is provided in [20]. This comparison, reveals that smodels outperforms the SLG system. 3.3.1 The lparse Module According to the Theorem 3.13, the problem of determining whether a logic program has stable models is NP complete. Usually problems in this particular class are dicult to compute with. The reason for ....

I. Niemela and P. Simons. Ecient implementation of well-founded and stable model semantics. In Proceedings of the

....with the stable models evaluator SMODELS. Its main goal is to work as a tool for fast and interactive exploration of knowledge bases. 1 General Information The XNMR package is an attempt of integration between the well founded semantics system XSB[2, 3] and the stable models evaluator SMODELS[1]. It works in UNIX platforms (e.g. Linux, Solaris) and work is being done to port it to Windows NT. The package consists of three layers. The bottom layer is a low level interface between XSB and SMODELS. This interface is written in C, and consists of 177 lines of code. The second layer is a ....

I. Niemela and P. Simons. Ecient implementation of the well-founded and stable model semantics. In Joint International Conference and Symposium on Logic Programming, pages 289-303, 1996.

.... Fages theorem and showed that results of this type can be applied to computing answer sets for a logic program: whenever the two semantics are equivalent, answer sets can be computed by propositional solvers, such as sato [16] or relsat [3] instead of answer set solvers, such as smodels [13] and dlv [6] This possibility is important from the perspective of answer set programming. The idea of this programming method is to reduce a given computational problem to computing an answer set for a logic program. Examples and references can be found in [11] Lloyd and Topor [12] ....

Ilkka Niemela and Patrik Simons. Ecient implementation of the well-founded and stable model semantics. In Proc. Joint Int'l Conf. and Symp. on Logic Programming, pages 289-303,

....and adm expand are complete then for each stable extension E such that 2 Th(T [E) there exist appropriate selections such that CSM( returns E. Proof The theorem follows directly from theorem 5.2. The CSM procedure is based on backward chaining in contrast to the procedure of Niemel a et al. [17, 18] that is based on forward chaining. We explain the di erence between the two procedures in the following example. Example 5.1 p not q q not r r not q Assume that the given query is p. The CSM procedure would compute fnot qg as a support for p. The procedure adm expand(fnot qg) will produce ....

....set of assumptions. Moreover, theorem 16 in [24] replaces the condition in part 2 of theorem 7.1 0 attacks 0 by the (equivalent) condition corresponding to 0 [ 0 attacks itself . For a formal correspondence between the two approaches see [25] Niemel a [17] and Niemel a and Simons [18] give proof procedures for computing credulous and sceptical consequences under stable extensions, for default logic and logic programming, respectively. As discussed in section 5, their proof procedures for computing credulous consequences under stable extensions rely upon forward chaining, ....

I. Niemela, P. Simons, Ecient implementation of the well-founded and stable model semantics. Proc. JICSLP'96, MIT Press, pages 289-303.

....the XSB logic programming system [15] XMC s underlying logic programming engine. XSB computes the well founded semantics of normal logic programs. Since, in general, P is nonstrati ed, this results in a certain residual program r(P ) of P . Now, feed r(P ) into the stable models generator of [9] with its search procedure suitably modi ed to compute r(P ) s preferred stable model. The answer to the original model checking question can be directly obtained from this model. Experimental results have shown that the residual programs so derived are typically quite small and the preferred ....

I. Niemela and P. Simons. Ecient implementation of the well-founded and stable model semantics. In Joint International Conference and Symposium on Logic Programming, pages 289-303, 1996.

.... results of this type can be applied to computing answer sets for a logic program: whenever the two semantics are equivalent, answer sets can be computed by propositional solvers, such as sato [ Zhang, 1997 ] or relsat [ Bayardo and Schrag, 1997 ] instead of answer set solvers, such as smodels [ Niemel a and Simons, 1996 ] and dlv [ Eiter et al. 1997 ] This possibility is important from the perspective of answer set programming. The idea of this programming method is to reduce a given computational problem to computing an answer set for a logic program. Examples and references can be found in [ Lifschitz, 1999 ....

Ilkka Niemela and Patrik Simons. Ecient implementation of the well-founded and stable model semantics. In Proc. Joint Int'l Conf. and Symp. on Logic Programming, pages 289-303, 1996.

....lparse 1 . The rst part, smodels, is the actual logic programming engine doing all the hard work and lparse just adds a layer of syntactic sugar on top of it. The smodels has been developed in the Laboratory for Theoretical Computer Science in Helsinki University of Technology by Patrik Simons [13, 9, 12, 14, 7, 15, 10, 11] and the lparse has 1 Actually, in Section 1.4 we see that there are also other front ends in addition to lparse. 4 been developed by Tommi Syrj anen [19] The newest versions of smodels, lparse, and this document are available at http: www.tcs.hut.fi Software smodels. 1.1 Short Primer on ....

I. Niemela and P. Simons. Ecient implementation of the well-founded and stable model semantics. In M. Maher, editor, Proceedings of the Joint 89 International Conference and Symposium on Logic Programming, pages 289-303, Bonn, Germany, September 1996. The MIT Press.

....Answer Set Programming. As described in [13] the methodology of these approaches is to encode a computational problem by a logic program such that its stable models represent the solutions. A number of ecient systems for computing stable models have been developed. Of these, Niemel a s smodels [15, 14] is considered one of the most performant systems. Abduction [8] uses a similar predicate representation for the relation between the identi ers of CSP variables and their value. This predicate is declared to be open or abducible. Constraining this relation to be a solution, an abductive system ....

....paradigm. The underlying idea is to represent a problem as a set of rules, each rule being the declarative expression of a piece of knowledge about the problem domain and such that the stable models of the whole program are constrained to be solutions of the problem. The smodels system [15] is an ecient implementation of the stable model semantics. It works with propositional rules and a special pre processing program is used for grounding strongly range restricted logic programs. The implementation combines bottom up inference with backtracking search and employs powerful pruning ....

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I. Niemela and P. Simons. Ecient implementation of the well-founded and stable model semantics. In M. Maher, editor, Logic Programming, Proceedings of the 1996 Joint International Conference and Syposium, pages 289-303, Bonn, Germany, Sept. 1996. MIT Press.

....the stable models to the solutions. Lifschitz [25, 26] introduces the closely related notion of Answer Set Programming and explores its use in satis ability planning [24] Also Niemel a [28] makes a similar point, proposing stable models as a paradigm for constraint programming. The smodels system [29] is one of the most advanced implementations supporting this programming paradigm. A more smooth extension of the basic logic programming paradigm is abductive logic programming [19] Besides the program P , it distinguishes a set of abducibles A (names of predicates not de ned in the program) ....

....as an implementation of a language enriched with open functions. In fact, one could go further, using the known relationship between abduction an stable models [20] it looks feasible to further translate programs (at least if all other functors are constants) into input for the smodels system [29, 28]. However we believe a more promising path towards a high performance implementation is by a direct implementation which extends the solver of a CLP language with the machinery to handle open functions. 8. CONCLUSION Constraint logic programming is a very powerful paradigm but has several ....

I. Niemela and P. Simons. Ecient implementation of the well-founded and stable model semantics. In M. Maher, editor, Logic Programming, Proc. 1996 Joint Int. Conf. and Symp. on Logic Programming (JICLP'96), pages 289-303. MIT Press, 1996.

....and the proof procedure gives a positive answer for innocent(father(Mary) generating only the one relevant assumption needed in the example. Chen and Warren discuss possible adaptations for the stable model semantics, but do not present any concrete proof procedure. Niemel a and Simmons [29] de ne proof procedures computing both credulous and sceptical stable semantics consequences for range restricted, function free logic programs. Because of these restrictions, these proof procedures cannot be applied to examples 3.1 and 3.2. Satoh [38] adapts the (credulous) proof procedure in ....

....adm e 27 P rog defends e P rog LP lean attacks P rog a sld P rog set j= all pref(X) then X 2 Th(T [ for all maximal admissible sets of assumptions . The proof of soundness can be found in appendix E. Many of the procedures for computing stable semantics in the literature (e.g. [36, 29, 28]) can be obtained by appropriately instantiating and executing (more ecient versions of) the following procedure: stable( fullcover( not attacks( stable( 0 ; expand( 0 ; 1 ) nocover( 1 ; stable( 1 [ f g; where attacks( stands for attacks and the ....

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I. Niemela, P. Simons, Ecient implementation of the well-founded and stable model semantics. Proc. JICSLP'96, MIT Press, pages 289-303.

....are satis ed by the objects of the domain. Such incompleteness causes Prolog like engines to go into in nite loops or to return the answer unknown to too many queries. The situation changed recently with the coming of age of a new class of inference engines for A Prolog, such as smodels ([25]) dlv ( 8] DeReS ( 5] These engines are limited to programs which have a nite number of answer sets. Given a program they compute one or all of such models. In this sense, the engines can be better viewed as satis ability checkers than as theorem provers. Their development substantially ....

I. Niemela and P. Simons. Ecient implementation of the well-founded and stable model semantics. In Proc. of Joint Int'l Conf. and Symposium on Logic Programming, pp. 289-303. MIT Press, 1996.

....to default logic. In Section 7 we show how the decision method developed for default logic in Section 5 can be further optimized to provide the basis for one of the most ecient current implementations of the stable model semantics for normal (non disjunctive) logic programs, the smodels system [NS96, NS97] 2 Default Logic Default logic introduced by Reiter [Rei80] is one of the most well known nonmonotonic logics. Default logic assumes knowledge to be represented in terms of a default theory. A default theory is a pair (D; W ) where W is a set of rst order formulae representing the facts ....

....[MT91] For many practical purposes this subclass of default theories is sucient. Our aim is to employ the techniques devised for default logic and show how they can be further developed to exploit the more limited structure of logic programs. This is the approach used in a system called smodels [NS96] which provides an implementation of the stable model semantics in C . The system is publicly available (see http: www.tcs.hut. Software smodels) and seems to outperform clearly other current approaches to computing stable models. We discuss rst the propositional case, i.e. ground programs. ....

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Ilkka Niemela and Patrik Simons. Ecient Implementation of the Well-founded and Stable Model Semantics. In M. Maher, editor, Proceedings of the Joint International Conference and Symposium on Logic Programming, pages 289-303, Bonn, Germany, September 1996. The MIT Press.

....it always pays o to rst compute the wellfounded semantics (which can be done in polynomial time, as opposed to computing stable models, which 10 is one level higher in the polynomial hierarchy) and to use the results to simplify the program. In fact, this is one of the techniques employed in [NS96] which is currently the fastest method to compute stable models (see also [DFN99] Therefore if we know a semantics is rational, it is also cumulative and satis es in particular the above property. De nition 8 (Partial Distribution) A con uent LP system CS satis es partial distribution if for ....

Ilkka Niemela and Patrik Simons. Ecient Implementation of the Wellfounded and Stable Model Semantics. In M. Maher, editor, Proceedings of the Joint International Conference and Symposium on Logic Programming, pages 289-303, Bonn, Germany, September 1996. The MIT Press.

....if it is ensured that residual clauses are produced for all atoms, using the residual program may bring a performance gain since the search space of algorithms to compute stable models will be correspondingly reduced. In fact, by using XSB in conjunction with a Stable Model generator, Smodels [30], an ecient system has been devised for model checking of concurrent systems that is 10 20 times faster than competing systems [28] 5.4 Tabled Aggregation The following shortest path predicate is a modi cation of the path 2 predicate of Section 5.2: table path 3. path(X,Y,C) ....

I. Niemela and P. Simons. Ecient implementation of the well-founded and stable model semantics. In Joint International Conference and Symposium on Logic Programming, pages 289-303, 1996.

....least xpoint lfp( P ) of Fitting s operator P : lfp( P ) known BASE(P ) f itt(P ) Proof. See Appendix A. 2 Note, that for a given ground program P this normal form f itt(P ) can be computed in time that is linear in the size of P . An ecient algorithm based on [DG84] can be found in [NS96]. The four parts of this implementation, that reduce body literals, correspond directly to the four basic transformations de ned above. Thus, that algorithm can be seen as an ecient implementation of our rewriting system 7 PSNF . For many programs, e.g. for programs without positive loops, the ....

....P1 ; This set has the property required for A in De nition 4.11: Lemma 4.12 (Loop Detection) Let P 1 be a ground program and let P 2 = A B) 2 P 1 A 2 lfp(T P1 ; Then P 1 7 L P 2 (unless P 2 = P 1 ) and P 2 is irreducible w.r.t. 7 L . Proof. See Appendix A. 2 As shown in [NS96], the set lfp(T P1 ; of possible atoms can be computed by the linear time algorithm of [DG84] As a consequence, also the operation of loop detection can be performed in time that is linear in the size of P 1 . We compute lfp(T P1 ; and delete all rules A B with A 62 lfp(T P1 ; Example ....

[Article contains additional citation context not shown here]

Ilka Niemela and Patrik Simons. Ecient implementation of the wellfounded and stable model semantics. Technical Report 7/96, Universitat Koblenz-Landau, 1996.

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I. Niemela and P. Simons. Ecient implementation of the well-founded and stable model semantics. In Proceedings of JICSLP-96. MIT Press, 1996.

....nonmonotonic logics (suitably restricted) as eciently as classical logics and maybe eciently enough to make them interesting for real applications. A serious e ort to demonstrate the applicability of nonmonotonic reasoning techniques started and led to the development of the Smodels system [23, 24, 27] (http: www.tcs. hut.fi Software smodels ) whose rst version was released in summer 1995. It turned out that the nonmonotonic techniques in Smodels are promising in many areas such as constraint satisfaction, combinatorial problems and planning [22] The maturing implementation technology for ....

I. Niemela and P. Simons. Ecient implementation of the well-founded and stable model semantics. In M. Maher, editor, Proceedings of the Joint International Conference and Symposium on Logic Programming, pages 289-303, Bonn, Germany, September 1996. The MIT Press.

....evidence E , an assignment A for B which maximizes the conditional probability P (AjE) The evidence is a partial assignment for B representing observations. In this paper we investigate the possibility of solving MAP problems using an ecient rule based constraint programming system, smodels [ Niemel a and Simons, 1996 ] based on logic programs with the stable model semantics. The approach has provided encouraging results in many application areas, such as planning [ Dimopoulos et al. 1997 ] veri cation of distributed systems [ Heljanko, 1999 ] and constraint satisfaction [ Niemel a, 1998 ] Hence, it is ....

....model S = fr; pg because the reduct P S of P with respect to S is p r r and S = Cl(P S ) For instance, S 0 = fp; sg is not a stable model of P because the reduct P S 0 is fp rg and Cl(P S 0 ) fg 6= S 0 . In fact, P has one other stable model fs; qg. The smodels system [ Niemel a and Simons, 1996 ] is an implementation supporting this paradigm. Given a program, smodels computes all or a given number of stable models of the program or determines that the program has no stable models. It supports programs that extend normal programs considerably. In this paper we employ a couple of these ....

I. Niemela and P. Simons. Ecient implementation of the well-founded and stable model semantics. In M. Maher, editor, Proc. of the Joint International Conference and Symposium on Logic Programming, pages 289-303, Bonn, Germany, September 1996. The MIT Press.

....computational problems in cut free tableaux [7] In order make the method more ecient we devise simpli cation rules and a search heuristic which attempts to minimize the search space of the algorithm. The heuristic is inspired by the search technique used in a system for computing stable models [15, 18]. Experimental results indicate that the cutbased tableau method combined with suitable deduction and simpli cation rules and the search space minimizing heuristic has promising performance, e.g. in symbolic model checking applications. The rest of the paper is structured as follows. We start by ....

I. Niemela and P. Simons. Ecient implementation of the well-founded and stable model semantics. In M. Maher, editor, Proceedings of the Joint International Conference and Symposium on Logic Programming, pages 289-303. The MIT Press, 1996.

....[40] and it was directly applicable to both default logic [41] and the stable model semantics [43] The algorithm was needlessly complex and I was able to simplify it while at the same time making it prune the search space more. In response to this, Ilkka devised a way to strengthen the algorithm [44, 45] by employing the Fitting semantics [19] I further improved the procedure [58] by making systematic use of backward chaining [7] and lookahead. Di erent types of rules were then introduced [59] and more optimizations were done. 1.4 Contributions The key contributions of this work are: the new ....

I. Niemela and P. Simons. Ecient implementation of the well-founded and stable model semantics. In Proceedings of the 1996 Joint International Conference and Symposium on Logic Programming, pages 289{ 303, Bonn, Germany, September 1996. The MIT Press.

....[40] and it was directly applicable to both default logic [41] and the stable model semantics [43] The algorithm was needlessly complex and I was able to simplify it while at the same time making it prune the search space more. In response to this, Ilkka devised a way to strengthen the algorithm [44, 45] by employing the Fitting semantics [19] I further improved the procedure [58] by making systematic use of backward chaining [7] and lookahead. Di erent types of rules were then introduced [59] and more optimizations were done. 1.4 Contributions The key contributions of this work are: the new ....

I. Niemela and P. Simons. Ecient implementation of the wellfounded and stable model semantics. Forschungsbericht 7-96, Universit at Koblenz-Landau, 1996.

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I. Niemela and P. Simons. Ecient implementation of the well-founded and stable model semantics. In M. Maher, editor, Proceedings of the Joint International Conference and Symposium on Logic Programming, pages 289-303, Bonn, Germany, September 1996. The MIT Press.

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Ilkka Niemela and Patrik Simons. Ecient implementation of the wellfounded and stable model semantics. In Proceedings of the Joint International Conference and Symposium on Logic Programming, Bonn, Germany, 1996. The MITPress.

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I. Niemela and P. Simons. Ecient implementation of the well-founded and stable model semantics. In M. Maher, editor, Proc. of the Joint International Conference and Symposium on Logic Programming, pages 289-303, Bonn, Germany, 1996. MIT Press.

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