Przymusinski, T.C. On the declarative semantics of stratified deductive databases. In Minker (ed) Foundations of Deductive Databases and Logic Programming, (1988), 193--216.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....programming is closely related to memoing or tabling for Prolog programs [10, 9, 1] The bottom up language described here allows deletion. Our notion of deletion is superficially similar to widely studied notions of negation in logic programming such as well founded (stratified) programs [8, 4] and stable model semantics [3] Here, however, we use a don t care nondeterministic semantics which does not require the program to be well founded and where the final database need not be stable. Deletion in logic programming has also been modeled with linear logic [7] The linear logic ....

T. Przymusinski. the declarative semantics of stratified deductive databases and logic programs, 1988.

....of that generalization process. We will show: 1) the correctness of our transformation rules w.r.t. the least Z) model in the case of definite CLP programs [39] 2) the correctness of our transformation rules w.r.t. the perfect model in the case of programs with locally stratified negation [6, 65], and (3) the termination of our program specialization strategies. 1.4 Verification of Concurrent Systems We will also study how to apply the techniques for transforming constraint logic programs to the automatic verification of temporal properties of finite or infinite state concurrent ....

....it is expressive enough to contain many of the constraint logic programs which are used in practice. Moreover all major approaches to the semantics of negation coincide for locally stratified CLP programs. In particular given a locally stratified constraint logic program P the unique perfect model [65] of P is equal to the unique stable model [34] of P and to the well founded model [83] of P. The perfect model of a locally stratified constraint logic program is constructed in a way which is very similar to the case of locally stratified logic programs and most approaches for dealing with ....

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PRZYMUSINSKI, T. C. On the declarative semantics of stratified deductive databases and logic programs. In Foundations of Deductive Databases and Logic Programming, J. Minker, Ed. Morgan Kaufmann, 1987, pp. 193-216.

....with positive loops or loops through weak negation. The latter allows positive loops while rejecting negative loops over weak negation. For the case of weakly well founded XDBs Wagner defines the concept of perfect model, which is the immediate translation of Przymusinski s perfect model notion [46] into the XDB setting. Given this notion, Wagner then defines a new inference system (let us designate it by loop l ) which is adequate with respect to the perfect model MX , i.e. MX j= F iff X loop l F . Inference system loop l is l plus loop checking, failing all positive cycles. ....

....every occurrence of 1, a, a, Gammaa, and Gamma a, respectively by true, a p , a n , not a p , and not a n , where a is an arbitrary atom. It is immediately recognizable that an XDB X is well founded iff P l is acyclic [4] and weakly well founded iff P l is locally stratified [46]. Therefore P l is locally stratified and has a unique perfect model which is equivalent to the well founded model of P l [45] It is not difficult to see that the following correspondence holds: Theorem 32. Let X be a weakly well founded XDB. Then the following equivalences hold, where a is ....

T. Przymusinski. On the declarative semantics of stratified deductive databases. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 193--216. Morgan Kaufmann, 1988.

....clauses to obey a local stratification condition: All circular function calls must be defined in terms of one another through subsetmonotonic functions. Non circular function call dependencies are not restricted in any way. Note that this definition of local stratification is similar to the one in [26]. 2.2. Conditional Subset Clauses The syntax of conditional subset clauses is as follows: f(terms) contains expr : condition where each variable in expr appears either in terms or in condition, and condition is a sequence of one or more goals as defined below: condition : goal j goal, ....

....true. The meaning of a ground expression e is the ground term t that follows from the completion of the program, following the collect all and emptiness as failure assumptions. We require negated goals and function calls to obey the usual local stratification condition for predicates, as given by [26]. We treat negated goals by negation as failure [19] When new variables appear in condition, i.e. those that are not on the left hand side of : then the goals in condition should be processed in such an order so that all negated goals and function calls are invoked with ground terms as ....

T. Przymusinski, On the Declarative Semantics of Stratified Deductive Databases and Logic Programs, Proc. Foundations of Deductive Databases and Logic Programming, J. Minker (ed.), pp. 193--216, Morgan-Kaufmann, 1988.

....function p in the above syntax can also be replaced by a composition of monotonic functions without any change in semantics. Second, it suffices if the ground instances of program assertions are stratified in the above manner. This idea is, of course, analogous to the that of local stratification [P88]. Henceforth, we will use the term general stratified language to refer to this extended language. It is straightforward to show that the presence of monotonic functions does not call for any alteration of the model theoretic semantics. The operational semantics, however, must be modified to ....

T. Przymusinski, "On the Declarative Semantics of Stratified Deductive Databases and Logic Programs," Proc. Foundations of Deductive Databases and Logic Programming, J. Minker (ed.), pp. 193-216, Morgan-Kaufmann, 1988.

....monotonic functions is monotonic, the function m in the above syntax can also be replaced by a composition of monotonic functions. Second, it suffices if the ground instances of program clauses are stratified in the above manner. This idea is, of course, analogous to that of local stratification [25], except that we are working with functions rather than predicates. It should be clear that the presence of monotonic functions does not call for any alteration of the model theoretic semantics. The operational semantics, however, must be modified to incorporate monotonically updatable ....

T. Przymusinski, On the Declarative Semantics of Stratified Deductive Databases and Logic Programs, Proc. Foundations of Deductive Databases and Logic Programming, J. Minker (ed.), pp. 193-216, Morgan-Kaufmann, 1988.

....model semantics based purely on logical implication, and so the meaning of a program is defined either as the result of some normal form computation, or as the set of facts in some intended model. Early approaches restricted the class of programs to those that are stratified in some fashion [ABW88, Prz88, Ros90, PP88]. More recent approaches, such as the well founded semantics [VRS91] the three valued stable model semantics [Prz90] and the valid semantics [BRSS92a] define semantics for all logic programs with negation and set grouping. Recently, there have been several proposals to extend the semantics to ....

T.C. Przymusinski. On the declarative semantics of stratified deductive databases. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 193--216, 1988.

.... Instead of using various circumscription policies, a logic program uses an operator called negation as failure (not) The YSP can be expressed as a logic program (see, for example, 20, 4] The resulting logic program can be proved to be locally stratified and thus has a unique perfect model [57] as intended 1 . Because there are so many different approaches to reasoning about actions and changes, it is very difficult, if not impossible, to compare and contrast them with each other, although they share a few basic assumptions. Instead of constructing new special purpose formalisms, ....

T. Przymusinski, On the declarative semantics of stratified deductive databases and logic programs, In J. Minker, editor, , Foundations of Deductive Databases and logic Programming, Morgan Kaufmann, 1987, 193-216

....does not appear, it collapses to a definite logic program; if the body of every rule is empty, it collapses to a relational database. For many interesting domains, relational databases are too weak and extended logic programs are not necessary, but locally stratified logic programs [10] are sufficient 1 . Anyway extended logic programs are sufficient to subsume many other knowledge bases. The semantics of an extended logic program P is defined to be the well founded semantics of P incorporated with a coherence principle [3] The coherence principle relates two forms of ....

T. Przymusinski. On the declarative semantics of stratified deductive databases and logic programs. In J. Minker, editor, Foundations of Deductive Databases and logic Programming, pages 193--216. Morgan Kaufmann, 1987.

....operator does not appear, it collapses to a definite logic program; if the body of every rule is empty, it collapses to a relational database. For many interesting domains, relational databases are too weak and extended logic programs are not necessary, but locally stratified logic programs [16] are sufficient 3 . The semantics of an extended logic program P is defined to be the well founded model semantics of P incorporated with a coherence principle [2] relating two forms of negation: For any interpretation I = T [ not F and any objective literal L, if :L 2 T then L 2 F . Let P be ....

Przymusinski, T., On the declarative semantics of stratified deductive databases and logic programs, In J. Minker, editor, , Foundations of DeductiveDatabasesand logic Programming, Morgan Kaufmann, 1987, 193-216

....1 Introduction In recent years there has been much interest in defining semantics for deductive databases logic programs that use negation and aggregation. We call such programs extended logic programs. Early approaches restricted the class of programs to those that are stratified in some fashion [1, 8, 12]. More recent approaches, such as the well founded semantics [15] and the 0 The first author, on behalf of all those alphabetic order challenged, led a successful crusade to have the names in reverse alphabetical order. three valued stable model semantics [9] provided semantics for programs ....

T. Przymusinski. On the declarative semantics of stratified deductive databases. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 193--216, 1988.

.... Gardner and Shepherdson, 1991; Seki, 1991 ] the Clark s completion [ Gardner and Shepherdson, 1991 ] the Fitting s and Kunen s three valued extensions of Clark s completion [ Fitting, 1985; Kunen, 1987; Bossi et al. 1992b; Sato, 1992; Bossi and Etalle, 1994a ] the perfect model semantics [ Przymusinsky, 1987; Maher, 1993; Seki, 1991 ] the stable model semantics [ Gelfond and Lifschitz, 1988; Maher, 1990; Seki, 1990 ] and the well founded model semantics [ Van Gelder et al. 1989; Maher, 1990; Seki, 1990; Seki, 1993 ] A uniform approach for proving the correctness of the unfold fold ....

T. Przymusinsky. On the declarative semantics of stratified deductive databases and logic programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 193-- 216. Morgan Kaufmann, 1987.

.... b; b ag is call consistent but not stratified. 2.1. Theorem [9] 22] If Pi is stratified then the stratified model of Pi (see [1] is the unique stable model of Pi. 2.2. Theorem [18] 10] 2] If Pi is call consistent then comp( Pi) has a Herbrand model. The atom dependency graph of Pi [15], denoted by G( Pi) is analogous to the predicate dependency graph. The nodes are the ground atoms of the Herbrand universe. There is a positive (resp. negative) edge from A to B if there is a rule R 2 Ground( Pi) with A 2 pos(R) resp. A 2 neg(R) and B = concl(R) By abuse of notation we ....

....A to B if there is a rule R 2 Ground( Pi) with A 2 pos(R) resp. A 2 neg(R) and B = concl(R) By abuse of notation we define also the relations , 0 , and Gamma , on ground atoms, in the same way as in the predicate dependency graph . A logic program Pi is said to be locally stratified [15] if the relation of dependency through at least one negative edge in G( Pi) is well founded. Pi is said to be negative cycle free [17] if Gamma is irreflexive in G( Pi) Pi is said to be order consistent [17] if the relation ( and Gamma ) in G( Pi) is well founded (this condition is called ....

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T. Przymusinski, On the declarative semantics of stratified deductive data-bases and logic programming, in Foundations of deductive databases and logic programming, Minker, J. (ed.), Morgan Kaufmann, Los Altos (1987).

.... P is equivalent to the following (under the special conditions mentioned in each case) 1) the weakly perfect model of P , if P is weaklystratified ( PP88] 2) the modularly stratified model of P , if P is modularly stratified ( Ros90] 3) the perfect model of P , if P is locally stratified ([Prz88]) and (4) the stratified model of P , if P is stratified ( ABW88] 2 The above semantics are also equivalent to well founded models under the special conditions mentioned in each case. The class of modularly stratified programs contains the class of locally stratified programs, which in turn ....

T.C. Przymusinski. On the declarative semantics of stratified deductive databases. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 193-- 216, 1988.

....Revised: Nov. 30, 1991 1 Introduction During the last couple of years a significant body of knowledge has been accumulated providing us with a much better understanding of semantic issues in logic programming and theory of deductive databases. In particular, the class of perfect models [ABW88, VG89, Prz88] was shown to provide a suitable semantics for stratified logic programs. Subsequently, two competing, but closely related [Prz91c, Prz91a] extensions of the class of perfect models to normal (i.e. non disjunctive) logic programs were introduced and thoroughly investigated. One of them was the ....

....stable and well founded models, stationary expansions also provide a natural extension of the classes of stable and well founded models to disjunctive programs and databases. Moreover, stationary expansions also extend the class of perfect models of stratified disjunctive programs introduced in [Prz88]. In addition to extending these important classes of models to disjunctive programs, stationary expansions also preserve their various attractive features. However, the original definition of stationary expansions was given in terms of 3 valued models and 3 valued theories and therefore seemed to ....

[Article contains additional citation context not shown here]

T. C. Przymusinski. On the declarative semantics of stratified deductive databases and logic programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 193--216. Morgan Kaufmann, Los Altos, CA., 1988.

...., Artificial Intelligence. 1 Introduction During the last couple of years a significant body of knowledge has been accumulated providing us with a better understanding of semantic issues in logic programming and the theory of deductive databases. In particular, the class of perfect models [ABW88, VG89, Prz88] was shown to provide a suitable semantics for stratified logic programs. Subsequently, two competing, but closely related [Prz91d, Prz91a] extensions of the class of perfect models to normal, non disjunctive logic programs were introduced and extensively investigated. One of them is the class of ....

.... P 1 j= min :C andthus P 2 = Psi P (P 1 ) P 1 [ fD:C g: It is easy to see that P 2 = Psi P (P 2 ) P 3 is a fixed point and therefore: P = P [ fDAB ; D:A:B ; D:C g: The resulting semantics coincides with the perfect model semantics of disjunctive programs introduced in [Prz88]. One easily verifies that P does not have any other (consistent) static expansions. 4 We recall again Convention 4.1. Example 6.3 Consider now the following non negative generalized logic program P describing the state of mind of a person planning a trip to either Australia or Europe. ....

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T. C. Przymusinski. On the declarative semantics of stratified deductive databases and logic programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 193--216, Morgan Kaufmann, Los Altos, CA., 1988.

....formulae (all queries) are equality definable are called equality definable programs. In Section 3 we give examples of equality definable and non equalitydefinable formulae w.r.t. three semantics of logic programs: Clark s predicate completion COMP(P) Cla79] the perfect model semantics PERF(P) [Prz88, Prz89b] and the first order logic semantics FO(P) We also show that a closed formula G is equality definable if and only if either G or :G is implied by the semantics. In Section 4, we define normal equality formulae a natural and simple class of equality formulae and we show that every ....

....: The semantics of P is thought of as providing the meaning of P. For example, SEM(P) may denote Clark s predicate completion COMP(P) of P [ CET (Clark s semantics [Cla79] or the set PERF(P) of all sentences satisfied in all perfect models of P [ CET (perfect model semantics [Prz89b] see also [ABW88, VG89, Prz88]) or SEM(P) may simply be equal to FO(P ) P [ CET (first order logic semantics) 3 Equality Definable Formulae and Programs Definition 3.1 We will call a formula of L P an equality formula if it does not contain any other predicate symbols except equality, true, and false. As we pointed out ....

T. C. Przymusinski. On the declarative semantics of stratified deductive databases and logic programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 193--216, Morgan Kaufmann, Los Altos, CA., 1988.

....of queries namely existential the results produced by any one of these semantics are exactly identical. This result is not only important in the context of non monotonic reasoning, but it also plays an important role in the problem of finding a proper declarative semantics for logic programs [18, 19, 20]. It is also significant in view of the fact that in many applications existential queries are of main interest. In the second part of the paper we discuss the relationship between semantics of types I III mentioned above for arbitrary universal theories T. The most general formalization of the ....

Przymusinski, T., "On the Declarative Semantics of Stratified Deductive Databases and Logic Programs", in: Foundations of Deductive Databases and Logic Programming (ed. J.Minker), Morgan Kaufmann 1988, 193-216.

....Foundation grant #IRI 9313061. 1 Introduction During the last couple of years a significant body of knowledge has been accumulated providing us with a better understanding of semantic issues in logic programming and the theory of deductive databases. In particular, the class of perfect models [ABW88, VG89, Prz88] was shown to provide a suitable semantics for (locally) stratified logic programs. Subsequently, two closely related [PP90] extensions of the class of perfect models to normal, non disjunctive, logic programs were introduced and extensively investigated. One of them is the class of well founded ....

....P has precisely one static expansion P which describes the minimal model semantics of P . However, when restricted 1 Partial stable models were also called 3 valued stable models. to stratified disjunctive programs, the static semantics is in general weaker than the perfect model semantics [Prz88]. This is the consequence of the fact that the static semantics derives a minimal , in some sense, set of conclusions that can be inferred from a disjunctive program. If a given application area requires us to infer more facts, we can achieve it by explicitly adding additional axioms which then ....

[Article contains additional citation context not shown here]

T. C. Przymusinski. On the declarative semantics of stratified deductive databases and logic programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 193--216. Morgan Kaufmann, Los Altos, CA., 1988.

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Przymusinski, T.C. On the declarative semantics of stratified deductive databases. In Minker (ed) Foundations of Deductive Databases and Logic Programming, (1988), 193--216.

No context found.

T. C. Przymusinski. On the declarative semantics of stratified deductive databases and logic programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pp. 193--216. Morgan Kaufmann, 1988.

No context found.

T. C. Przymusinski. On the declarative semantics of stratified deductive databases and logic programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 193--216. Morgan Kaufmann, 1988.

No context found.

T. C. Przymusinski. On the declarative semantics of stratified deductive databases and logic programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 193--216. Morgan Kaufmann, 1988.

No context found.

T. C. Przymusinski, On the declarative semantics of stratified deductive databases and logic programs, in J. Minker (ed), Foundations of Deductive Databases and Logic Programs, Morgan Kaufmann, Los Altos, CA, 1988, pp. 193-216.

No context found.

Przymusinski, T. C., On the declarative semantics of stratified deductive databases and logic programs, in: Minker, J. (ed), Foundations of Deductive Databases and Logic Programs, Morgan Kaufmann, Los Altos, CA, 1988.

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