T. Przymusinski. Stationary semantics for normal and disjunctive logic programs. In C. Delobel, M. Kifer, and Y. Masunagar, editors, Proceedings of DOOD'91. Springer-Verlag, 1991.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the composition of general logic programs. Some compositionality results for extended logic programs, including general programs, were established by Brogi et al. in [5] The authors showed that many semantics for general programs (such as stable models, wellfounded models, stationary expansions [18], complete scenaria [8] can be de ned in terms of the Herbrand models of the positive version of a program. The compositionality of Herbrand models w.r.t. the union of programs then induces general compositionality results for the various semantics considered. While these results can be applied ....

T. Przymusinski. Stationary semantics for normal and disjunctive logic programs. In C. Delobel, M. Kifer, and Y. Masunagar, editors, Proc. of DOOD'91. SpringerVerlag, 1991.

....the composition of general logic programs. Some compositionality results for extended logic programs, including general programs, were established by Brogi et al. in [5] The authors showed that many semantics for general programs (such as stable models, well founded models, stationary expansions [27], complete scenaria [14] can be de ned in terms of the Herbrand models of the positive version of a program. The compositionality of Her16 brand models w.r.t. the union of programs then induces general compositionality results for the various semantics considered. While these results can be ....

T. Przymusinski. Stationary semantics for normal and disjunctive logic programs. In C. Delobel, M. Kifer, and Y. Masunagar, editors, Proc. of DOOD'91. SpringerVerlag, 1991.

....comp [Cla78] Nondis. ffl ffl ffl WFS [vGRS91] Nondis. ffl ffl ffl ffl GCWA [Min82] Pos. ffl ffl (trivial) ffl WGCWA [RLM89] 5 Pos. ffl (trivial) Positivism [BH86] Dis. ffl ffl ffl STABLE [GL91, Prz91a] Dis. ffl ffl ffl ffl Strong WFS [Ros89] Dis. ffl STATIONARY [Prz91b] Dis. ffl ffl ffl ffl STATIC [Prz95] Dis. ffl ffl ffl ffl D WFS [BD95c] Dis. ffl ffl ffl ffl REG SEM [YY94] Dis. ffl ffl ffl ffl An important property of our approach is its applicability also to semantics stronger than D WFS. If only our transformation Phi 7 Phi is sound for such a ....

Teodor Przymusinski. Stationary Semantics for Normal and Disjunctive Logic Programs. In C. Delobel, M. Kifer, and Y. Masunaga, editors, DOOD '91, Proceedings of the 2nd International Conference, Berlin, December 1991. Muenchen, Springer. LNCS 566.

....has a straightforward extension to disjunctive programs: not even for WFS does there exist a canonical disjunctive version. We claim that our D WFS is this counterpart of WFS. The novelty of our approach is that it is not exclusively declarative (like Przymusinski s stationary or static approach [34, 35]) nor exclusively procedural (like the approaches of Minker and his group [4, 3, 26] We introduced in [8, 11] a calculus of program transformations. These are declarative since they express precise semantical properties (e.g. partial evaluation) But they are also procedural because they can be ....

....Clark s comp [16] Norm. no ffl no ffl WFS [41] Norm. ffl ffl no ffl WFS [17] 7 Norm. ffl no no ffl GCWA [27] Pos. ffl ffl triv. ffl WGCWA [36] 8 Pos. no ffl triv. no Positivism [6] Dis. no ffl no ffl STABLE [25, 33] Dis. ffl ffl ffl ffl Strong WFS [37] Dis. no no no no STATIONARY [34] Dis. ffl ffl no ffl STATIC [35] Dis. ffl ffl no ffl D WFS [8] Dis. ffl ffl no ffl REG SEM [42] Dis. ffl ffl no ffl already decide many queries without fully computing the semantics. Therefore, putting something on top of res( Phi) should make it possible to obtain these stronger semantics ....

Teodor Przymusinski. Stationary Semantics for Normal and Disjunctive Logic Programs. In C. Delobel, M. Kifer, and Y. Masunaga, editors, DOOD '91, Proceedings of the 2nd International Conference, Berlin, December 1991. Muenchen, Springer. LNCS 566.

....to the operation of union on programs. Some compositionality results for extended logic programs, including general programs, were established by Brogi et al. in [7] The authors showed that many semantics for general programs (such as stable models, well founded models, stationary expansions [27], complete scenaria [15] can be defined in terms of the Herbrand models of (the positive version of) a program. The compositionality of Herbrand models w.r.t. the union of programs then induces general compositionality results for the various semantics considered. While these results can be ....

T. Przymusinski. Stationary semantics for normal and disjunctive logic programs. In C. Delobel, M. Kifer, and Y. Masunagar, editors, Proceedings of DOOD'91. SpringerVerlag, 1991.

....all stable models of a program. This work was further extended and generalized by Teusink [168] who characterized all stationary models by means of fixpoints of another nondeterministic, non monotonic operator. The following characterization of stationary models, proposed by Przymusinski [126], stays within 2 valued logic. First we identify a program with the program obtained by replacing every occurrence of a negative literal :A by the new atom not A. This gives a positive program, in which the atoms of the form not A occur only in the bodies of clauses. A stationary expansion is ....

....C j= min :A if :A is true in all minimal models of P [ C. ffl A stationary expansion of P is a consistent theory E(P ) which satisfies E(P ) P [ fnot A j E(P ) j= min :Ag: ffl The least stationary expansion of P is called its stationary completion. 2 Theorem 7. 14 (Correspondence) Przymusinski [126]) Let P be a program. There is the following one to one correspondence between stationary models and stationary expansions of P . ffl If M is a stationary model of P , then P [ fnot A j M j= 3 :Ag is a stationary expansion of P . ffl If E(P ) is a stationary expansion of P , then fA j E(P ) j= ....

[Article contains additional citation context not shown here]

T. C. Przymusinski. Stationary semantics for normal and disjunctive logic programs. In C. Delobel, M. Kifer, and Y. Masunaga, editors, DOOD'91, Proc. of the Second International Conference, LNCS 566, Munchen, December 1991. Springer.

....Properties of Logic Programming Semantics Semantics Taut. GPPE Red. Nonmin. Clark s comp [7] ffl ffl ffl WFS [19] ffl ffl ffl ffl GCWA [11] ffl ffl ffl ffl WGCWA [16] ffl ffl Positivism [2] ffl ffl ffl STABLE [10, 13] ffl ffl ffl ffl Strong WFS [17] ffl STATIONARY [14] ffl ffl ffl ffl STATIC [15] ffl ffl ffl ffl D WFS [6] ffl ffl ffl ffl REG SEM [20] ffl ffl ffl ffl ACKNOWLEDGEMENTS We are grateful to some anonymous referees as well as to Teodor Przymusinski for their useful comments. We are also indebted to Ilkka Niemela for pointing out two weaknesses in ....

Teodor Przymusinski, `Stationary Semantics for Normal and Disjunctive Logic Programs', in DOOD '91, Proceedings of the 2nd International Conference, eds., C. Delobel, M. Kifer, and Y. Masunaga, Berlin, (December 1991). Muenchen, Springer. LNCS 566.

....of Logic Programming Semantics Semantics Reference Domain Taut. GPPE Red. Non Min. Rel. comp [Cla78] Nondis. ffl ffl ffl GCWA [Min82] Pos. ffl ffl ffl ffl ffl WGCWA [RT88] Pos. ffl ffl ffl DSTABLE [GL91] Dis. ffl ffl ffl ffl WFS [vGRS91] Nondis. ffl ffl ffl ffl ffl ST N [Prz91b] Dis. ffl ffl ffl ffl ffl STATIC [Prz95] Dis. ffl ffl ffl ffl ffl D WFS [BD95d] Dis. ffl ffl ffl ffl ffl DWFS [Dix92b] Dis. ffl ffl ffl ffl ffl Strong WFS[Ros92] Dis. ffl ffl WD WFS [BD95d] Dis. ffl ffl ffl WDWFS [Dix92b] Dis. ffl ffl ffl PMS [SI93] Dis. ....

....are some implemented systems. Inoue et al. show in [IKH92] how to compute stable models for extended disjunctive programs in a bottom upfashion using a theorem prover. The approach of Bell et al. NNS91] was used by Dix Muller to implement versions of the stationary semantics of Przymusinski ([Prz91b]) MD93, DM92, Mul92] Brass Dix have implemented both D WFS and DSTABLE for allowed DATALOG programs ( BD95a] 23 ) An implementation of static semantics is described in [BDP96b] 24 . 23 ftp: ftp.informatik.uni hannover.de software index.html 24 ....

Teodor Przymusinski. Stationary Semantics for Normal and Disjunctive Logic Programs. In C. Delobel, M. Kifer, and Y. Masunaga, editors, DOOD '91, Proceedings of the 2nd International Conference, Berlin, December 1991. Muenchen, Springer. LNCS 566. REFERENCES 100

....a straightforward extension to disjunctive programs: not even for WFS does there exist a canonical disjunctive version. We claim that our D WFS is this counterpart of WFS. The novelty of our approach is that it is not exclusively declarative (like Przymusinski s stationary or static approach 1 [37, 38]) nor exclusively procedural (like the approaches of Minker and his group 2 [4, 3, 29] We introduced in [8, 11] a calculus of program transformations. These can be seen as declarative because they express precise semantical properties (e.g. partial evaluation) But they are also procedural ....

....Clark s comp [17] Norm. no ffl no ffl WFS [44] Norm. ffl ffl no ffl WFS [20] 10 Norm. ffl no no ffl GCWA [30] Pos. ffl ffl triv. ffl WGCWA [39] 11 Pos. no ffl triv. no Positivism [6] Dis. no ffl no ffl STABLE [28, 36] Dis. ffl ffl ffl ffl Strong WFS [40] Dis. no no no no STATIONARY [37] Dis. ffl ffl no ffl STATIC [38] Dis. ffl ffl no ffl D WFS [8] Dis. ffl ffl no ffl REG SEM [45] Dis. ffl ffl no ffl D WFS. If only our transformation Phi 7 res( Phi) is sound for such a semantics (e.g. STATIONARY, STATIC or STABLE) we can use our calculus and already decide many queries ....

Teodor Przymusinski. Stationary Semantics for Normal and Disjunctive Logic Programs. In C. Delobel, M. Kifer, and Y. Masunaga, editors, DOOD '91, Proceedings of the 2nd International Conference, Berlin, December 1991. Muenchen, Springer. LNCS 566.

....completion is quite natural and straightforward, and, as we have seen above, it can be given without any reference to autoepistemic logic. As we will see in the next section, the definition of well founded completion can, in fact, be even stated without explicitly referring to belief atoms. In [Prz91c] we show that all results contained in this paper can be suitably extended to the class of all disjunctive logic programs (or disjunctive deductive databases) using the stationary semantics defined in [Prz90a] 2 Well Founded Completions of Logic Programs In this section we formally define ....

T. C. Przymusinski. Stationary semantics for normal and disjunctive logic programs. In C. Delobel, M. Kifer, and Y. Masunaga, editors, Proceedings of the Second International Conference on Deductive and Object-Oriented Databases DOOD'91, pages 85--107, Munich, Germany, December 1991. Springer Verlag.

....systems. Inoue et al. show in [IKH92] how to compute stable models for extended disjunctive programs in a bottom up fashion using a theorem prover. The approach of Bell et al. NNS91] was used by Dix Muller [DM93,DM92,Mul92] to implement versions of the stationary semantics of Przymusinski ([Prz91c]. Brass Dix have implemented both D WFS and DSTABLE for allowed DATALOG programs ( BD95] 12 ) An implementation of static semantics ( Prz95b] is described in [BDP96] 13 . Seipel has implemented in his DisLog system various (modified versions of) semantics of Minker and his group. His ....

Teodor Przymusinski. Stationary Semantics for Normal and Disjunctive Logic Programs. In C. Delobel, M. Kifer, and Y. Masunaga, editors, DOOD '91, Proceedings of the 2nd International Conference, Berlin, December 1991. Muenchen, Springer. LNCS 566.

.... VG89, Prz88] and disjunctive perfect model semantics [Prz88] Stable semantics [GL88, BF91] and disjunctive stable semantics [GL90, Prz91b] Well founded semantics [VGRS90] Partial stable semantics [Prz90] and disjunctive partial stable semantics [Prz91b] Stationary semantics [Prz91c]. Static semantics [Prz94b] Extended semantics with classical , or, more precisely, strong negation [GL90, AP92, Prz90, Prz91c] Different approaches are typically based on very different premises and involve different terminology and notation. Their features and mutual relationships ....

.... semantics [GL90, Prz91b] Well founded semantics [VGRS90] Partial stable semantics [Prz90] and disjunctive partial stable semantics [Prz91b] Stationary semantics [Prz91c] Static semantics [Prz94b] Extended semantics with classical , or, more precisely, strong negation [GL90, AP92, Prz90, Prz91c]. Different approaches are typically based on very different premises and involve different terminology and notation. Their features and mutual relationships are not always clear and sometimes confusing. Moreover, their exact relationship to major non monotonic formalisms is often difficult to ....

[Article contains additional citation context not shown here]

T. C. Przymusinski. Stationary semantics for normal and disjunctive logic programs. In C. Delobel, M. Kifer, and Y. Masunaga, editors, Proceedings of the Second International Conference on Deductive and Object-Oriented Databases DOOD'91, pages 85--107, Munich, Germany, December 1991. Springer Verlag.

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T. Przymusinski. Stationary semantics for normal and disjunctive logic programs. In C. Delobel, M. Kifer, and Y. Masunagar, editors, Proceedings of DOOD'91. Springer-Verlag, 1991.

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