N. Bidoit and C. Froidevaux. General logical databases and programs: Default logic semantics and stratification. Information and Computation, 91:15--54, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Besnard [6] and Etherington [26] are good sources on default logic. There is a body of results indicating that default logic can capture a large number of different forms of nonmonotonic reasoning. Default logic is especially closely related to reasoning in logic programs and deductive databases [8, 9, 33]. Default logic has been applied in formalizing inheritance reasoning and truth maintenance systems [24, 49] Connections have been established between default logic and autoepistemic logic and McDermott and Doyle style nonmonotonic modal logics [61, 84, 86, 89, 144, 145] circumscription [25, ....

....rules in the framework based on autoepistemic logic but these expressions can be approximated, for example in the following two different ways. In the other interpretation proposed by Gelfond et al. 34] the expression means f:LOE ; L OEg and in the other suggested by Bidoit and Froidevaux [8] it means fOE g [ MIN(fOE; g) Other embeddings of logic programs into autoepistemic logic have been proposed besides (7.41) Gelfond [29] proposes an embedding where rules of a general logic program are translated by interpreting negation as failure as disbelief. tr G (a 0 a 1 ; am ....

N. Bidoit and C. Froidevaux. General logical databases and programs: Default logic semantics and stratification. Information and Computation, 91:15--54, 1991.

....for specifying the semantics of logic programs. Most approaches can be seen as either to restrict the class of programs to ensure that a canonical model for this restricted class exists, or to associate to a program a set of models. The first idea led to various forms of stratification semantics ([ABW88,CB94,Ros90,BF91]) The second idea led to the discovery of two quite dominant approaches: the wellfounded semantics WFS ( vGRS91] and the stable semantics STABLE ( GL88] The well founded semantics for logic programs with negation has received great interest since its introduction, because it has several ....

Nicole Bidoit and Christine Froidevaux. General logical Databases and Programs: Default Logic Semantics and Stratification. Information and Computation, 91:15--54, 1991.

....of logic program and related structures in nonmonotonic reasoning. Stable models are closely related to extensions [Rei80] the principal structure in default logic. Extensions play a similar role as sets of consequences of a theory in propositional logic [MT93] It has been shown [MT90, BF91b, BF91a] that there is a 1 1 correspondence between extensions of certain default theories and stable models of logic programs [GL88] Unfortunately, to decide for a given default theory whether it possesses an extension is 6 P 2 complete problem [Got92] We shall use the connectionist technique to ....

N. Bidoit and Ch. Froidevaux. General logical databases and programs: Default logic semantics and stratification. Information and Computation, 91:15--54, 1991.

....and Marek and Truszczy#ski [76] are good sources on default logic. There is a body of results indicating that default logic can capture a large number of dioeerent forms of nonmonotonic reasoning. Default logic is especially closely related to reasoning in logic programs and deductive databases [10, 11, 32]. Default logic has been applied in formalizing inheritance reasoning and truth maintenance systems [23, 42] Connections have been established between default logic and autoepistemic logic and McDermott and Doyle style nonmonotonic modal logics [51, 70, 71, 75, 118, 119] circumscription [24, ....

N. Bidoit and C. Froidevaux. General logical databases and programs: Default logic semantics and stratication. Information and Computation, 91:1554, 1991.

....concept of representational succinctness, another one that of pfm translations. Both notions allow to create hierarchies of formalisms, in the first option of succinctness, in the second one of expressiveness. TECHNICAL REPORT DBAI TR 2000 40 75 For some results on translatability issues, refer to [Bidoit and Froidevaux, 1991; Inoue and Sakama, 1993] 4.9.1 Representational Succinctness Definition 4.9.1 [Gogic et al. 1995] Let A and B be formalisms for knowledge representation, A ; B be knowledge bases, i.e. specific theories like default theories: We say that B is at least as (equally or more) succinct as A, ....

N. Bidoit and C. Froidevaux. General Logical Databases and Programs: Default Logic Semantics and Stratification. Information and Computation 91 (1991) 15-54.

....using default assumptions about the same propositions are not allowed. The notion of strati cation has its origins in the logic programming community [CHA 85, APT 88, VG88] and it has also been studied in the context of other forms of nonmonotonic reasoning such as default logic [BID 87, BID 91a, FRO 88, FRO 92] and autoepistemic logic [GEL 87, MAR 91a] A knowledge base is stratied if it can be partitioned into a sequence of levels (strata) so that on every level default assumptions are made only about propositions which have already been idenedj on preceding levels. As an example of a ....

....one possible set of correct conclusions. For example, in the case of logic programs with negation as failure stratication implies a unique canonical model. There are several alternative approaches to characterizing the canonical model of a stratied program [APT 88, VG88, LIF 88, PRZ 88, BID 87, BID 91a, GEL 87, GEL 88b, VG91] It seems, however, that there are natural situations where competing sets of correct conclusions canonical models emerge. A typical example is inheritance hierarchies with multiple inheritance. Consider a variant of the iNixon diamondj [REI 81] We extend the logic ....

Bidoit N. and Froidevaux C., General logical databases and programs: Default logic semantics and stratication, Information and Computation, 91:1554, 1991.

....semantics agree on the meaning of stratied programs. A good discussion of this subject and the above semantics can be found in [ Przymusinska and Przymusinski, 1990 ] Stratication conditions for nonmonotonic logics based on the similar concept for logic programs have been presented e.g. in [ Bidoit and Froidevaux, 1991; Gelfond, 1987; Marek and Truszczy#ski, 1991 ] The denitions of stratication for autoepistemic logic and some of the denitions for default logic are suOEcient conditions for the uniqueness of stable expansions and extensions. In this work we show that they also give the decision procedures an ....

N. Bidoit and C. Froidevaux. General logical databases and programs: Default logic semantics and stratication. Information and Computation, 91:1554, 1991.

.... semantics for stratified logic programs [Apt89] Almost immediately after this notion was introduced, stratified logic programs were mapped into the three major nonmonotonic formalisms investigated at that time: circumscription [Lif88] Prz88a] autoepistemic logic [Gel87] and default theories [BF91], MT89] Research in this area was stimulated by the workshop on Foundations of Deductive Databases and Logic Programming [Min88] and by the workshops on Logic Programming and Nonmonotonic Reasoning [NMS91, PN93] Collection of important papers can also be found in the forthcoming special issue ....

....is an extension of Pi; ii) every extension of Pi is the deductive closure of exactly one answer set of Pi. Thus, the deductive closure operator establishes a one to one correspondence between the answer sets of a program and its extensions. This result is a simple extension of results from [BF91], and [MT89] Perhaps somewhat surprisingly, it is not easily generalized to disjunctive databases. One of the problems in finding a natural translation from such databases into default theories is related to the inability to use defaults with empty justifications in reasoning by cases: the ....

N. Bidoit and C. Froidevaux. General logical databases and programs: Default logic semantics and stratification. Journal of Information and Computation, 91(1):15--54, 1991.

....faster. A common technique is to stratify a theory. Stratification consists of partitioning a given theory into a sequence of smaller theories for which extensions can be computed faster. This approach was widely studied in the cases of logic programming and autoepistemic logic ( 1] 2] [3], 7] 14] Some results of applying this approach to default logic were obtained by Etherington [6] and Kautz and Selman [9] Their results were based on restricting the syntactic forms of formulas used in default theories. In [5] we studied the class of seminormal default theories. We did not ....

N. Bidoit and Ch. Froidevaux. General logical databases and programs: Default logic semantics and stratification. Information and Computation, 91:15--54, 1991.

....in defaults are disjunctive free . We allow arbitrary seminormal defaults but we impose more restrictive conditions on dependencies between defaults. We will adopt the concept of stratification, which was used in the context of logic programming and various nonmonotonic modal logics [2] 1] [4], 6] 11] to the case of seminormal default logic. Informally, a default theory is stratified if its set of defaults can be partitioned into strata . Defaults which have a common propositional variable in their consequents must appear in the same strata. Moreover, all defaults having in their ....

N. Bidoit and Ch. Froidevaux, General logical databases and programs: Default logic semantics and stratification, Information and Computation 91(1991)15.

....of default theories [11] 12] One common technique to overcome difficulties of extensive computations is to decompose a given theory into several subtheories. This approach, commonly referred to as stratification, was widely described for logic programming and autoepistemic logic [2] 1] [4], 9] 16] 3] Etherington [8] and Kautz and Selman [11] applied this approach to some classes of default theories. Their results were based on restricting the syntactic forms of formulas used in default theories. Finally, in [6] and [7] another way of stratification was proposed for arbitrary ....

N. Bidoit and Ch. Froidevaux. General logical databases and programs: Default logic semantics and stratification. Information and Computation, 91:15--54, 1991.

....semantics M supp P ( ABW88] in the latter sense. 2.1 Stable Semantics vs. Well founded Semantics One of the central ideas of the stable semantics is that any atom in a potential model should have a definite reason to be true or false. This idea was made explicit by Bidoit and Froidevaux [BF91] and, independently, by Gelfond and Lifschitz [GL88] as follows: for a program P and a model N BP we define P N : frule N : rule 2 Pg; where (a b 1 ; bn ; c 1 ; cm ) N : ae a b 1 ; bn ; if 8j : c j 62 N, t; otherwise. P N is called the ....

Nicole Bidoit and Christine Froidevaux. General logical Databases and Programs: Default Logic Semantics and Stratification. Information and Computation, 91:15--54, 1991.

....6.1 Stratified Programs and the Standard Model Let us first agree on the desired properties of the natural model. Clearly, for every fact in the model we would like to have some explanation why it is there. The following definition suggested by Apt, Blair and Walker [9] and Bidoit and Froidevaux [21] attempts to formalize this requirement. Definition 6.1 (Supported interpretation) A Herbrand interpretation I is called supported if A 2 I ) 9 L (A L 2 ground(P ) I j= L) 2 Intuitively, L is an explanation for A. We clearly have Lemma 6.2 I is a supported model of P iff T P (I) I. 2 ....

....stable expansions of auto epistemic logic (Moore [111] inspired Gelfond [67, 68] to define the stable semantics. A parallel work on connections between the default logic of Reiter [145] and stable model semantics was carried out by Marek and Truszczy nski [105] and by Bidoit and Froidevaux [21]. Recently, Przymusinski [135, 127] explained the stationary semantics by means of auto epistemic logic (see also Bonatti [26] In the other direction, Przymusinski [139] introduced 3 valued versions of default logic and auto epistemic logic, based on the well founded semantics for logic ....

N. Bidoit and C. Froidevaux. General logical databases and programs: Default logic semantics and stratification. Information and Computation, 91:15--54, 1991.

.... by Reiter [Rei80] is an effective nonmonotonic reasoning system (cf. Eth87, Eth88] In addition to being a stand alone paradigm for nonmonotonic reasoning, default logic has also been used to represent other nonmonotonic reasoning systems such as the stable model semantics ( MT89] LS92] [BF91]) and the well founded semantics [Bar94] of logic programs. We complement this integral relationship between default logic and logic programming by developing a sound and complete proof procedure for certain default theories. Readers familiar with proof procedures for logic programs will notice ....

N. Bidoit and C. Froidevaux. General logical databases and programs: Default logic semantics and stratification. Information and Computation, 91:15--54, 1991.

....a regular move, given by the relation move from to( 4 This means that there are no infinite descending chains. 3.2 STABLE The idea of the stable semantics is that in an intended (two valued) model any atom should have a definite reason to be true or false. This idea was made explicit in [BF91a] and, independently, GL88] We use the latter terminology and introduce the Gelfond Lifschitz transformation: for a program P and a model N B P we define P N : frule N : rule 2 Pg where (A B 1 ; B n ; C 1 ; Cm ) N : A B 1 ; B n ; if 8j : C j 62 N , ....

Nicole Bidoit and Christine Froidevaux. General logical Databases and Programs: Default Logic Semantics and Stratification. Information and Computation, 91:15-- 54, 1991.

.... semantics for stratified logic programs [Apt89] Almost immediately after this notion was introduced, stratified logic programs were mapped into the three major nonmonotonic formalisms investigated at that time: circumscription [Lif88] Prz88a] autoepistemic logic [Gel87] and default theories [BF91], MT89] Research in this area was stimulated by the workshop on Foundations of Deductive Databases and Logic Programming [Min88] and by the workshops on Logic Programming and Nonmonotonic Reasoning [NMS91, PN93] Collection of important papers can also be found in the forthcoming special issue ....

....of S is an extension of 5; ii) every extension of 5 is the deductive closure of exactly one answer set of 5. Thus, the deductive closure operator establishes a one to one correspondence between the answer sets of a program and its extensions. This result is a simple extension of results from [BF91], and [MT89] Perhaps somewhat surprisingly, it is not easily generalized to disjunctive databases. One of the problems in finding a natural translation from such databases into default theories is related to the inability to use defaults with empty justifications in reasoning by cases: the ....

N. Bidoit and C. Froidevaux. General logical databases and programs: Default logic semantics and stratification. Journal of Information and Computation, 91(1):15--54, 1991.

....Among others, we note the work by Reiter (1982) where he proves that circumscription, in some cases, implies predicate completion. Gelfond (1987) describes how to interpret stratified programs as autoepistemic theories. A semantics for stratified programs based on default theories is presented in Bidoit Froidevaux (1988) . Przymusinski (1989) shows that the well founded semantics for general Horn programs reduces to suitable forms of circumscription, autoepistemic logic and default theory. Our line of investigation points in this direction. We intend to study the connection between the theories of negation for ....

Bidoit N. and Froidevaux C. (1988). General Logical Databases and Programs: Default Logic Semantics and Stratification, Journal of Information and Computation.

....of Illinois at Chicago 851 S. Morgan Street #1120 SEO Chicago, Illinois 60607 7053 jorge eecs.uic.edu Keywords: Artificial Intelligence, Default Logic, Well Founded Semantics 1 Introduction The power of default logic [Rei80] as a non monotonic reasoning system has been studied extensively [RC85, BF91, Eth87]. The similarity of default logic to other logic programming semantics seems to indicate that default logic is more general than previously thought. Bidoit and Froidevoix [BF91] found that there is a one to one correspondence between default extensions and the stable model semantics [GL88] We ....

....The power of default logic [Rei80] as a non monotonic reasoning system has been studied extensively [RC85, BF91, Eth87] The similarity of default logic to other logic programming semantics seems to indicate that default logic is more general than previously thought. Bidoit and Froidevoix [BF91] found that there is a one to one correspondence between default extensions and the stable model semantics [GL88] We show that this correspondence generalizes to the well founded semantics when the correct translation is used. This result differs from the previous attempts to correlate default ....

N. Bidoit and C. Froidevaux. General logical databases and programs: Default logic semantics and stratification. Information and Computation, 91:15--54, 1991.

....stable classes of a program, P and the extension classes of the translation of P . The following two theorems formalize these relationships. Theorem 7 [BS90] M is a stable class of a program P iff E = fCn(M i ) j M i 2 Mg is an extension class of tr 1 (P ) 2 3 tr1 was first introduced in [BF88]. Theorem 8 [BS90] Suppose M is a collection of interpretations. M is a stable class of program P iff there exists an extension class E of tr 2 (P ) such that M = fE i AT j E i 2 Eg is an extension class of tr 2 (P ) 2 3.2 Well founded semantics for default theories We now show how the ....

N. Bidoit and C. Froidevaux. General Logical Databases and Programs: Default logic semantics and Stratification. Journal of Information and Computation, 1988. (in print).

....atoms p(1; 1) p(2; 1) and p(2; 2) can be assumed false in P. At the same time, they are the ones that destroy local stratifiability of P. Three different extensions of the perfect model semantics have been proposed: the stable model semantics [GL88] equivalent to the default model semantics [BF91]) the weakly perfect model semantics [PP88] and the well founded semantics [VGRS90] While the first two semantics are 2 valued and are defined only for restricted classes of programs, the well founded semantics is 3 valued and is defined for all logic programs. Although the three semantics ....

....P has a unique stable model MP , then its stable model semantics is determined by this unique intended model MP . Stable model semantics is closely related to the autoepistemic approach to non monotonic reasoning (see [Gel87] and Section 7) The same semantics has been independently discovered in [BF91], where it is defined in terms of default logic and thus can be called the default model semantics. Example 6.15 Consider the program P in Example 6.9 and let M = fp(1; 2) q(1)g; fp(1; 1) p(2; 2) p(2; 1) q(2)g be the unique weakly perfect model of P (see Example 6.11) The application ....

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N. Bidoit and C. Froidevaux. General logical databases and programs: Default logic semantics and stratification. Journal of Information and Computation, pages 15--54, 1991.

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N. Bidoit and C. Froidevaux. General logical databases and programs: Default logic semantics and stratification. Information and Computation, 91:15--54, 1991.

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Bidoit N. and Froidevaux C., General logical databases and programs: Default logic semantics and stratication, Information and Computation, 91:1554, 1991.

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N. Bidoit and C. Froidevaux. General logical databases and programs: Default logic semantics and strati cation. Journal of Information and Computation, 91(1):15-54, 1991.

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N. Bidoit and C. Froidevaux. General logical databases and programs : Default logic semantics and stratification. Information and Computation, 91(1):15--54, 1991.

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N. Bidoit and C. Froidevaux. General logical databases and programs: default logic semantics and stratification. Information and Computation, 91:15--54, 1991.

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