K. A. Berman, J. S. Schlipf, and J. V. Franco. Computing the well-founded semantics faster. In A. Nerode, W. Marek, and M. Truszczynski, editors, Logic Programming and Non-Monotonic Reasoning, Proceedings of the Third International Conference, LNCS 928, pages 113--126, Berlin, Germany, Springer, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....in logic programs. This area has been recently studied formally for semantics of (disjunctive) logic programs (well founded as well as stable) in [9, 10, 11] The use of Tarjan s algorithm for computing the well founded semantics in almost linear time has been explicitly addressed e.g. in [7, 15]. 47 To date, we are not aware of any existing work on the semantics of agent programs that is polynomial and that has been implemented. In this paper, we have described a wide variety of parameters (e.g. conflict freedom tests, finiteness tables, etc. that go into the design and development of ....

K. A. Berman, J. S. Schlipf, and J. V. Franco. Computing the well-founded semantics faster. In A. Nerode, W. Marek, and M. Truszczynski, editors, Logic Programming and Non-Monotonic Reasoning, Proceedings of the Third International Conference, LNCS 928, pages 113--126, Berlin, Germany, Springer, 1995.

....F 2 P # 1 g: Notice that on stratified programs, WFS and stratified semantics coincide. Theorem 4.4 (implicit in [124, 125] LP under WFS is P complete. Datalog under WFS is data complete in P and program complete in DEXPTIME. Whether deciding P j= wfs A can be done in linear time is open [19]. For full LP, the following is known. Theorem 4.5 ( 119] Full LP under WFS is Pi 1 1 complete. 4.3. LP under the stable model semantics An interpretation I of a normal logic program P is a stable model of P [64] if I = T 1 P I , i.e. I is the least Herbrand model of P I . In ....

K. Berman, J. Schlipf, and J. Franco. Computing WellFounded Semantics Faster. In W. Marek, A. Nerode, and M. Truszczynski, editors, Proc. LPNMR-95, LNCS/LNAI 982, pp. 113--126. Springer, 1995.

....from rule bodies, and rules containing false input literals are removed completely. The resulting propositional program is of polynomial size and can therefore be evaluated in polynomial time by EvalHORN. This procedure can be extended to stratified programs by evaluating the strata one by one [Berman et al. 1995]. Algorithm EvalLIT. For Datalog LIT, the algorithm proceeds in two phases: 1) Monadic rules are transformed in such a way that every rule contains at most one variable. This can be easily achieved by introducing new rules with variable free heads. If there is a e.g. a rule Fx Gx; My, it will ....

....only by a constant factor, and can be done in linear time by a subprogram Normalize. Normalize guarantees that the number of ground instances of monadic rules is bounded by jAj. 2) The Datalog program is evaluated stratum by stratum as a propositional Horn program similarly as sketched in [Berman et al. 1995]. Since the ground instances of a guarded rule are determined by the ground substitutions of the variables in the guard, the number of ground instantiations of a guarded rule is bounded by the number of tuples in the guard relation, and thus by jAj. We conclude that for every rule, the number of ....

Berman, K. A., Schlipf, J. S., and Franco, J. V. (1995). Computing wellfounded semantics faster. In LPNMR'95, LNCS, pages 113--126. Springer.

....of Technology. 1 At(P ) is the set of atoms occurring in a logic program P , jAt(P )j denotes the cardinality of At(P ) and size(P ) is the size of P (the total number of atom occurrences in P ) Improving on this algorithm turned out to be difficult. The first progress was obtained in [2]. The algorithm described there, when restricted to programs whose rules contain at most two positive occurrences of atoms in their bodies, runs in time O(jAt(P )j 4=3 jP j 2=3 ) where jAt(P )j stands for the number of atoms in At(P ) and jP j for the number of rules in P . For programs ....

.... Thus, for programs with size(P ) jAt(P )j 2 , our algorithm 2 runs in linear time and is asymptotically optimal It is also easy to see that when jP j jAt(P )j, the asymptotic estimate of the running time of our algorithm is better than that of algorithms by Van Gelder [16] and Berman et al. [2]. As mentioned above, our approach is restricted to the class LP 1 . Applicability of our method can, however, be slightly extended. Let us denote by LP 1 the class of these logic programs that, after simplifying by means of PSNF transformations (or, equivalently, with respect to the ....

K. Berman, J. Schlipf, and J.Franco. Computing the well-founded semantics faster. In Logic Programming and Nonmonotonic Reasoning (Lexington, KY, 1995), volume 928 of Lecture Notes in Computer Science, pages 113--125, Berlin, 1995. Springer.

....WFM ( P 2 ; P ref 2 ] norm ) corresponds to a unique, strongly preferred optimal world for [P 2 ; P ref 2 ] so that [P 2 ; P ref 2 ] is simple. We consider known subclasses of the well founded semantics that can be evaluated more e ciently than the general case of the well founded semantics. In [1], it is shown that programs that have at most two positive literals in any rule body can be evaluated somewhat more eciently than in the general case. Clearly, however, P 2 ; P ref 2 ] norm does not t into this class. 4] identi es two new subclasses of the well founded semantics that can be ....

K. Berman, J. Schlipf, and J. Franco. Computing the well-founded semantics faster. In International Conference on Logic Programming and Non-Monotonic Reasoning, pages 113{ 21 125. Springer-Verlag, 1995.

....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 tting operator computes the well founded model. This positive e ect of the tting operator has also been pointed out in [BSF95, SNV95]. However, positive loops have to be detected and removed separately. Example 4.10. Consider the following program Loop: p: q not p: q r: r q: We can apply negative reduction to delete q not p, since not p is obviously false. But 7 PSNF does not allow to delete q r and r q. To remove ....

Kenneth A. Berman, John S. Schlipf, and John V. Franco. Computing the Well-Founded Semantics Faster. In A. Nerode, W. Marek, and M. Truszczynski, editors, Logic Programming and Non-Monotonic Reasoning, Proceedings of the Third International Conference, LNCS 928, pages 113-126, Berlin, June 1995. Springer.

....over A are removed, and rules containing false input literals are removed completely. The resulting propositional program is of polynomial size and can therefore be evaluated in polynomial time by EvalHORN. This procedure can be extended to stratified programs by evaluating the strata one by one [5]. Theorem 1. The time complexity of model checking (i.e. evaluation) of Datalog LIT is (a) linear in the input size and the program size for programs where all guards are input relations. b) linear in the input size and the program size for bounded arity programs. c) linear in the input ....

....only by a constant factor, and can be done in linear time by a subprogram Normalize. Normalize guarantees that the number of ground instances of monadic rules is bounded by jAj. 2) The Datalog program is evaluated stratum by stratum as a propositional Horn program similarly as sketched in [5]. Since the ground instances of a guarded rule are determined by the ground substitutions of the variables in the guard, the number of ground instantiations of a guarded rule is bounded by the number of tuples in the guard relation, and thus by jAj. We conclude that for every rule, the number of ....

K. A. Berman, J. S. Schlipf, and J. V. Franco, Computing well-founded semantics faster, in LPNMR '95, LNCS, Springer, 1995, pp. 113--126.

....= fnot(a 0 ) a 1 ; not(a 2 ) a 3 ; g. Hence NAnt(P ) is covered (in linear time) and the computation of Dcl(P B ; does not need to be invoked at all to compute the unique stable model (well founded model) of P . This positive effect of the Fitting operator has also been pointed out in [SNV94, BSF95]. The used search heuristic has a major influence on the performance of the algorithm sm in Figure 1. The heuristic can be incorporated in the phase where there are atoms in NAnt(P ) not yet covered by B n and one of them has to be chosen in order to extend the full set under construction. In ....

K.A. Berman, J.S. Schlipf, and J.V. Franco. Computing the well-founded semantics faster. In Proceedings of the 3rd International Workshop on Logic Programming and Non-monotonic Reasoning, pages 113--126, Lexington, KY, June 1995. The MIT Press.

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Kenneth A. Berman, John S. Schlipf, and John V. Franco. Computing the Well-Founded Semantics Faster. In A. Nerode, W. Marek, and M. Truszczy'nski, editors, Logic Programming and Non-Monotonic Reasoning, Proceedings of the Third International Conference, LNCS 928, pages 113--126, Berlin, June 1995. Springer.

No context found.

Kenneth A. Berman, John S. Schlipf, and John V. Franco. Computing the Well-Founded Semantics Faster. In A. Nerode, W. Marek, and M. Truszczy'nski, editors, Logic Programming and Non-Monotonic Reasoning, Proceedings of the Third International Conference, LNCS 928, pages 113--126, Berlin, June 1995. Springer.

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