E. Chan. A Possible Worlds Semantics for Disjunctive Databases. IEEE Transactions on Data and Knowledge Engineering, 1991. To appear.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....reasoning based on model minimality. The (total) circumscription Circ(T ) of a theory T , which is a finite set of sentences, consists of a formula whose set of models is equal to the set of all minimal models of T . For various variants of circumscription, see [14] As noted by various authors [5, 6, 17 20], reasoning under minimal models runs into problems in connection with disjunctive information. The minimality principle of circumscription often enforces the exclusive interpretation of a disjunction a b by adopting the models in which either a or b is true but not both. There are many ....

....holds that Curb(T ) is logically equivalent to Curb(T 0 ) Curbing can be applied to arbitrary logical theories and not just to logic programs. In the context of disjunctive logic programming, various syntax dependent methods of reasoning that do not treat disjunction exclusively were defined in [5, 18, 17, 19, 20, 6]. In [8] the following two major reasoning problems under curbing where shown to be in PSPACE: Curb Model Checking: Given a propositional theory T , an interpretation M of T , and disjoint lists p and z of propositional variables, decide whether M is a good model of T w.r.t. p and z (i.e. ....

E. Chan. A Possible Worlds Semantics for Disjunctive Databases. IEEE Trans. Knowledge and Data Engineering, 5(2):282--292, 1993.

....the reader to the literature [29, 31] 3 Paraconsistent Semantics for Extended Disjunctive Programs This section extends the results presented in the previous section to extended disjunctive programs in general. 3 The possible model semantics is equivalent to the possible world semantics in [6]. 9 3.1 Paraconsistent Stable Models An extended disjunctive program is a finite set of clauses of the form: L 1 . L l L l 1 . Lm notLm 1 . notL n (n m l 0) 2) where L i s are literals and not is a connective representing default negation. The notions of heads, bodies, ....

E. P. F. Chan. A possible world semantics for disjunctive databases. IEEE Transactions on Knowledge and Data Engineering, 5, 282-292, 1993.

.... [41, 42] and further variants such as the Disjunctive Database Rule (DDR) of Ross and Topor [55] which is equivalent to the Weak GCWA (WGCWA) of Rajasekar, Lobo, and Minker [51] and the Possible Models Semantics (PMS) of Sakama [56] which is equivalent to Chan s Possible Worlds Semantics (PWS) [13]. For each semantics S, we consider the following problems. Given a nite propositional disjunctive logic program P , decide whether P has a model under semantics S (S Consistency) and deciding whether a given propositional formula F is satis ed by all legal models of P according to the semantics ....

.... whether P has a model under semantics S (S Consistency) and deciding whether a given propositional formula F is satis ed by all legal models of P according to the semantics S (S Entailment) Basic complexity results for the last group (various forms of the CWA) have already been derived in [60, 11, 13, 21]. In the present paper we sharpen some of the known results and state, for the sake of completeness of the analysis, some minor new results. All other results are novel. This paper complements recent surveys on complexity results for nonmonotonic reasoning and logic programming [12, 59] By the ....

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E. Chan. A Possible Worlds Semantics for Disjunctive Databases. IEEE Transactions on Data and Knowledge Engineering, 5(2):282-292, 1993.

....in infinite ones. This is intuitively explained by the fact that DLP under SMS corresponds to a weak fragment of Pi 1 2 which can be recursively translated to Pi 1 1 . Many other semantics for DLP have been analyzed, some having lower complexity than SMS, e.g. the possible model semantics [27, 116] and the causal model semantics [42] and others higher, e.g. the regular model semantics [57] However, typically they are Pi p 2 complete in the propositional case. cf. 49, 100] 6. Expressive power of logic programming The expressive power of query languages such as datalog is a topic ....

E. Chan. A Possible Worlds Semantics for Disjunctive Databases. IEEE Transactions on Knowledge and Data Engineering, 5(2):282--292, 1993.

....the answer sets of the program are fpg, fqg, and fp; qg, where the third one represents the inclusive model. Classical logic programming semantics based on minimal models are always minimal hence cannot represent such inclusive disjunctions in general. By contrast, the possible model semantics [11, 53, 55] has a non minimal feature, and can represent both inclusive and exclusive disjunctions. We will show that the possible model semantics for positive normal disjunctive programs are characterized by the answer set semantics for GEDPs. On the third point, the fact that q is fixed in circumscription ....

....Here, we show that the possible model semantics for NDPs by Sakama and Inoue [55] can be characterized by the answer set semantics for GEDPs. The possible model semantics was initially introduced for PDPs to enable one to specify both inclusive and exclusive interpretations of disjunctions [53, 11]. 4 Sakama and Inoue [56] have presented the equivalence between the possible model semantics for NDPs and the belief model semantics for abductive NLPs. Utilizing this result and Theorem 3.7, the embedding of the possible model semantics in 4 Possible model semantics is also called possible ....

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Chan, E. P. F., A Possible World Semantics for Disjunctive Databases, IEEE Transactions on Data and Knowledge Engineering 5(2):282--292 (1993).

....for the possible model semantics. We have also presented the NAFP rule as a sound procedure for computing the GCWAP . A disjunctive database is a database containing incomplete information and we consider the possible model semantics can provide natural meaning to such databases. Recently, Chan [Cha89] has independently proposed the possible world semantics for disjunctive databases, which turned equivalent to our possible model semantics in positive disjunctive databases. The result of this paper is directly extended to non stratifiable general disjunctive databases using the techniques of ....

Chan, E. P. F., A Possible World Semantics for Disjunctive Databases, Research Report CS-89-47, Dept. of Computer Science, Univ. of Waterloo, 1989.

.... to disjunctive programs ( 53] and there are also frameworks based on autoepistemic logic ( 19] as well as approaches to reduce the disjunctive case to normal programs [38] In addition, there are works where different sorts of disjunction, ranging from exclusive to inclusive are allowed ([75, 76, 29]) The reason why we focused on D WFS is that (1) some of the semantics mentioned above are not wellbehaved (see [39 41] and (2) there is strong evidence that this semantics is the natural disjunctive counterpart of WFS. Also we can show that any semantics satisfying some natural conditions is ....

Edward P.F. Chan. A Possible World Semantics for Disjunctive Databases. IEEE Trans. on Knowledge and Data Engineering, 5(2):282--292, 1993.

....the number of disjuncts and and the depth in building minimal upper bounds can be used to cut down the set of good models. 6 Related work and conclusion Inclusive interpretation of disjunctive models has been investigated in logic programming [ Ross and Topor, 1988; Sakama, 1989; Ross, 1989; Chan, 1991 ] The Disjunctive Database Rule (DDR) Ross and Topor, 1988 ] has been proposed to allow cautious derivation of negative literals from a disjunctive database. The DDR allows all models in Examples 1 and 2, hence also the unintuitive ones. Moreover, it depends on syntactical representation [ ....

....1991 ] The Disjunctive Database Rule (DDR) Ross and Topor, 1988 ] has been proposed to allow cautious derivation of negative literals from a disjunctive database. The DDR allows all models in Examples 1 and 2, hence also the unintuitive ones. Moreover, it depends on syntactical representation [ Chan, 1991 ] which however is customary for semantics of logic programming. Thus, the DDR is basically different from our method. A more sophisticated approach that allows also to deal with negative clauses was introduced in [ Sakama, 1989; Chan, 1991 ] by the equivalent concepts Possible Models ....

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E.P.F. Chan. A Possible Worlds Semantics for Disjunctive Databases. IEEE Transactions on Data and Knowledge Engineering, 1991. To appear.

....model semantics has 4 Note that an answer set al..so provides an inclusive interpretation of disjunctions in the program a b #, a # b, b # a . However, minimality based semantics interprets disjunctions as exclusive as possible [41] 7 some nice properties for inferring negation [35,4,37] and also has theoretical relation to autoepistemic logic [20] Recent study [40] presents that the possible model semantics is useful for representing product configuration applications. 2.2 Abductive Logic Programming An abductive program is defined as a pair # = # P, A # where P is a ....

....at least one normal rule L i # # is included in E for each r. In this case, there is a split program P # of P in which each ground instance of the rule r is split into a ground instance of the rule L i # # in E. Thus S is also an answer set of P # , hence a possible model of P . # Example 4. 1 ([4]) Let P be the program: violent psychopath # suspect, dangerous # violent, psychopath, suspect # . Then it becomes ks(P ) # T, H # where T : dangerous # violent, psychopath, suspect #, # suspect, not violent, not psychopath . H : violent # suspect, psychopath # suspect. The ....

E. P. F. Chan, A possible world semantics for disjunctive databases, IEEE Transactions on Data and Knowledge Engineering 5(2) (1993) 282--292.

....a disjunctive logic program Pi and a literal l, determine whether l is a consequence of Pi in the given semantics. Then the following holds: Theorem 10.7 (a) the decision problem for Pi under the disjunctive database rule [RT88] and the equivalent weak generalized CWA [RLM89] is polynomial [Cha93] (co NP complete if heads can be empty) b) the decision problem for Pi under the possible models semantics [Sak89] and the equivalent possible worlds semantics [Cha93] is polynomial (co NP complete again if heads can be empty) c) the decision problem for Pi under the careful CWA [GP86] ....

.... problem for Pi under the disjunctive database rule [RT88] and the equivalent weak generalized CWA [RLM89] is polynomial [Cha93] co NP complete if heads can be empty) b) the decision problem for Pi under the possible models semantics [Sak89] and the equivalent possible worlds semantics [Cha93] is polynomial (co NP complete again if heads can be empty) c) the decision problem for Pi under the careful CWA [GP86] is Pi P 2 hard and in Delta P 3 [O(log n) and (d) the decision problem for Pi is Pi P 2 complete for the following semantics [EG93a, EG93c, EG93d] the ....

E. Chan. A Possible Worlds Semantics for Disjunctive Databases. IEEE Transactions on Data and Knowledge Engineering, 5(2):282--292, 1993.

.... ffl The Extended Closed World Assumption (ECWA) by Gelfond, Przymusinska, and Przymusinski [12] which is in the finite propositional case equivalent to McCarthy s circumscription as defined by Lifschitz in [14] CIRC) ffl The Possible Worlds Semantics (PWS) by Chan [5], which turned out equivalent to the independently developed Possible Models Semantics (PMS) of Sakama [24] ffl The Perfect Models Semantics (PERF) by Przymusinski [19] and the Iterated Closed World Assumption (ICWA) by Gelfond, Przymusinska, and Przymusinski [12] introduced for capturing PERF ....

....syntactically restricted cases. Eiter and Gottlob complemented their work with results for arbitrary propositional databases [7] Marek and Truszczy nski [15] and Bidoit and Froidevaux [2] independently showed that deciding whether a nondisjunctive database has a stable model is NP complete. Chan [5] considered the complexity of inference of a literal under GCWA, DDR and PWS. He proved that inferring a literal from a propositional database in which no integrity clauses (i.e. clauses with empty heads) occur is coNP hard under GCWA, but polynomial under DDR and PWS. Chan proved that if ....

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E. Chan. A Possible Worlds Semantics for Disjunctive Databases. IEEE Transactions on Data and Knowledge Engineering, 1991. To appear.

....by unbounded disjuncts. Limiting simultaneously the number of disjuncts and and the depth in building minimal upper bounds can be used to cut down the set of good models. 6 Related work and conclusion Inclusive interpretation of disjunctive models has been investigated in logic programming [8, 9, 1]. The Disjunctive Database Rule (DDR) 8] has been proposed to allow cautious derivation of negative literals from a disjunctive database. If the clause a 1 Delta Delta Delta a n is in the database, then a 1 ; a n are considered possible, and if b 1 Delta Delta Delta b m a 1 ....

....DDR adds all literals :a to the database such that atom a is not possible. It is easy to see that in Examples 1 and 2 all atoms are possible, and hence application of the DDR adds nothing to the theories; all unintuitive models are admitted. Moreover, the DDR depends on syntactical representation [1]. Thus, the DDR is basically different from our method. The DDR has been refined to deal properly with negative clauses : a 1 Delta Delta Delta a n ) in [9, 1] which present the equivalent concepts Possible Models Semantics (PMS) and Possible Worlds Semantics (PWS) They work as the ....

[Article contains additional citation context not shown here]

E. Chan. A Possible Worlds Semantics for Disjunctive Databases. IEEE Transactions on Data and Knowledge Engineering, 1991. To appear.

....given a disjunctive logic program 5 and a literal l, determine whether l is a consequence of 5 in the given semantics. Then the following holds: Theorem 10.7 (a) the decision problem for 5 under the disjunctive database rule [RT88] and the equivalent weak generalized CWA [RLM89] is polynomial [Cha93] (co NP complete if heads can be empty) b) the decision problem for 5 under the possible models semantics [Sak89] and the equivalent possible worlds semantics [Cha93] is polynomial (co NP complete again if heads can be empty) c) the decision problem for 5 under the careful CWA [GP86] is 5 ....

.... decision problem for 5 under the disjunctive database rule [RT88] and the equivalent weak generalized CWA [RLM89] is polynomial [Cha93] co NP complete if heads can be empty) b) the decision problem for 5 under the possible models semantics [Sak89] and the equivalent possible worlds semantics [Cha93] is polynomial (co NP complete again if heads can be empty) c) the decision problem for 5 under the careful CWA [GP86] is 5 P 2 hard and in 1 P 3 [O(log n) and (d) the decision problem for 5 is 5 P 2 complete for the following semantics [EG93a, EG93c, EG93d] the generalized CWA ....

E. Chan. A Possible Worlds Semantics for Disjunctive Databases. IEEE Transactions on Data and Knowledge Engineering, 5(2):282--292, 1993.

.... programs ( GL91] and there are also frameworks based on autoepistemic logic ( BDP96] as well as approaches to reduce the disjunctive case to normal programs [DGM96] In addition, there are works where different sorts of disjunction, ranging from exclusive to inclusive are allowed ( Sak89, SI94, Cha93] The reason why we focused on D WFS is that (1) some of the semantics mentioned above are not well behaved (see [Dix95a, Dix95b, Dix95c] and (2) there is strong evidence that this semantics is the natural disjunctive counterpart of WFS. Also we can show that any semantics satisfying some ....

Edward P.F. Chan. A Possible World Semantics for Disjunctive Databases. IEEE Trans. on Knowledge and Data Engineering, 5(2):282--292, 1993.

....must satisfy IC. The pure consistency approach is that at least one minimal model satisfies IC. In the latter case, the ICs effectively eliminate those models which do not entail them. There exist possible semantics for ICs between the entailment and consistency definitions that are sensible ([13] and [84] but we do not consider them here. Thus once we allow disjunction or default negation in our databases, we may lose the substance of our intuition for integrity constraints, that they only check the database and do not contribute to generate data. Any proof procedure, or query ....

E. Chan. A possible world semantics for disjunctive databases. IEEE Transactions on Data and Knowledge Engineering, 5(2):282--292, 1993.

....1 ; A l g. Then a possible model of P is defined as a stable model of any split program of P . Clearly, possible models reduce to stable models in normal logic programs. In positive disjunctive programs, the notion of possible models also coincides with the possible worlds presented in [Cha93]. Example 2.1 Let P be the program: f a b not c; d a b g: Then the split programs of P are f a not c; d a b g; f b not c; d a b g; f a not c; b not c; d a b g; and fag, fbg, fa; b; dg are the possible models of P . 2 Note that fag and fbg are also disjunctive stable ....

....clause A i 0 is included in F . In this case, there is a split program P 0 of P in which each ground instance of a disjunctive clause C is split into a corresponding ground instance of a normal clause A i 0. Thus I is also a stable model of P 0 , hence a possible model of P . 2 Example 4. 1 [Cha93] Let P = f violent psychopath suspect; dangerous violent psychopath; suspect g: Then, alp(P ) h disj(P ) IC; C i where disj(P ) IC = f dangerous violent psychopath; suspect ; suspect not violent not psychopath g; C = f violent suspect; psychopath suspect g: Thus, ....

Chan, E. P. F., A Possible World Semantics for Disjunctive Databases, IEEE Trans. on Data and Knowledge Engineering 5(2), 282292, 1993.

....IC. In the latter case, the ICs effectively eliminate those 30 April 1997 ICs: Semantics and Applications Godfrey, Grant, Gryz, Minker p. 11 of 46 models which do not entail them. There exist possible semantics for ICs between the entailment and consistency definitions that are sensible ([Chan, 1993] and [Sakama, 1989] but we do not consider them here. Thus once we allow disjunction or default negation in our databases, we may lose the substance of our intuition for integrity constraints, that they only check the database and do not contribute to generate data. Any proof procedure, or ....

Chan, E. (1993). A possible world semantics for disjunctive databases. IEEE Transactions on Data and Knowledge Engineering, 5(2):282--292.

....and Dechter in [11] where they show a polynomial mapping from a subclass of disjunctive logic programs into a propositional theory. Another semantics, called disjunctive database rule has been defined by Ross and Topor in [132] and it has been shown to be polynomially tractable by Chan [31]. Chan has also extended this rule to the possible worlds semantics which correctly handles negative clauses. However, literal inference under this new semantics is co NP complete [31, 42] 6 Circumscription and Closed World Reasoning Circumscription has been defined by McCarthy in [98] and ....

....rule has been defined by Ross and Topor in [132] and it has been shown to be polynomially tractable by Chan [31] Chan has also extended this rule to the possible worlds semantics which correctly handles negative clauses. However, literal inference under this new semantics is co NP complete [31, 42]. 6 Circumscription and Closed World Reasoning Circumscription has been defined by McCarthy in [98] and refined later by McCarthy himself in [99] and Lifschitz in [85] We refer to the definition which can be found in [99, 85] Let T [P ; Z] be a first order formula in which at least the ....

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E. Chan. A possible worlds semantics for disjunctive databases. IEEE Transactions on Data and Knowledge Engineering, 1992. To appear.

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E. Chan. A Possible Worlds Semantics for Disjunctive Databases. IEEE Transactions on Data and Knowledge Engineering, 1991. To appear.

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E. Chan. A possible world semantics for disjunctive databases. IEEE Trans. Data and Knowledge Eng., 5(2): pp. 282-292, 1993.

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Edward P.F. Chan, "A Possible World Semantics for Disjunctive Databases," IEEE, 25 TKDE, Vol. 5, No. 2, pp. 282-292, 1993.

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E.P.F. Chan (1993). A possible world semantics for disjunctive databases. IEEE Trans. Data and Knowledge Engineering, 5(2):282--292.

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