Przymusinski, T. 1988. On the declarative semantics of deductive databases and logic programs. In J. Minker Ed., Foundations of Deductive Databases, pp. 193--216. San Mateo: Morgan Kaufmann.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....reduction gives the same meaning to TSSs as the original one. 19 5 Solutions based on stratification Here I review two methods to assign meaning to transition system specifications based on the technique of (local) stratification, as proposed in the setting of logic programming by Przymusinski [12]. This technique was tailored for TSSs by Groote [9] Definition 14 (stratification) A function S : T(#) T(#) #, where # is an ordinal, is called a stratification of a TSS P = #, R) if for every rule R and every substitution # : V T(#) it holds that for all positive literals ....

....2.5.4 in [9] Here it is an immediate corollary of Proposition 24. # The last proposition says that for a stratified TSS the choice of the stratification in the construction of the transition relation is immaterial. This enables the following solution to (1) and (2) Solution 10 (Stratified) [12, 9]. A TSS is meaningful i# it is stratified. The associated transition relation is given in Definition 15. Proposition 26 Solution 10 strictly extends Solution 1 and is strictly extended by Solution 7. Proof: If P is positive take S(#) 0 for all #. This is a stratification and T P,S = T 0 = ....

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T.C. Przymusinski (1988): On the declarative semantics of deductive databases and logic programs. In Jack Minker, editor: Foundations of Deductive Databases and Logic Programming, Morgan Kaufmann Publishers, Inc., Los Altos, California, pp. 193--216.

....are also logically equivalent. They have the same model theory (set of models) but not the same computational meaning. Obviously, the computational meaning does not have a purely model theoretic speci cation. A construction that produces a single model is the so called strati ed semantics [2, 10], which uses a mixture of syntactic and model theoretic concepts. This semantics fails for programs in which some variables are de ned (directly or indirectly) in terms of their own negations. For such programs we need an extra intermediate (neutral) truth value for certain of the negatively ....

....of the rst widely accepted approaches to negation. Informally speaking, a program is strati ed if it does not contain cyclic dependencies of predicates through negation. Every strati ed logic program has a unique perfect model. An extension of the notion of strati cation is local strati cation [10]; in a locally strati ed program, predicates may depend negatively on themselves as long as no cycles are formed when the rules of the program are instantiated. Again, every locally strati ed program has a unique perfect model [10] Strati cation is a syntactically determinable condition; local ....

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T. Przymusinski. On the Declarative Semantics of 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.

....9 associates the LTS faP 1 ; aP 2 g with T 1 , and the LTS faP 1 g with T 2 and T 4 . 22 3. 3 Answers Based on Stratification Finally, we review two methods to assign meaning to TSSs based on the technique of (local) stratification, as proposed in the setting of logic programming by Przymusinski [182]. This technique was adapted to TSSs in [107, 108] Definition 3.13 (Stratification) A mapping S from transitions to ordinal numbers is a stratification of a TSS T if for every transition rule H=ff in T and every closed substitution oe: ffl for positive premises fi in H, S(oe(fi) S(oe(ff) ....

T. Przymusinski, On the declarative semantics of deductive databases and logic programs, in Foundations of Deductive Databases and Logic Programming, J. Minker, ed., Morgan Kaufmann Publishers, Inc., Los Altos, California, 1988, pp. 193--216.

....usage, e.g. as we have found at IBM in our agent building experience. 2 Preliminary Definitions; Extended LP s Background: We assume the reader is familiar with extended LP s [ 11 ] with the semantics of stratified (ordinary, non extended) logic programs with negation as failure (e.g. [ 33 ] ) and with the standard concepts in the logic programming literature (e.g. as reviewed in [ 2 ] including predicate atom dependency graph and its acyclicity non recursiveness; and instantiation. Appendix A contains some review of these concepts. In this section, we introduce some ....

....LP that is E consistent, i.e. whenever LP lacks labels. A further special case is whenever LP , or its unlabelled version, is (syntactically) an acyclic general LP, i.e. whenever LP lacks classical negation. Remark: Here, we interpret general LP s under the locally stratified semantics [ 1 ] [ 33 ] , the stable semantics [ 10 ] or the well founded semantics [ 37 ] These semantics all coincide for the acyclic case since that is a special case of locally stratified (see, e.g. 2 ] for review of relevant concepts and literature) General LP s are syntactically a special case of extended ....

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Teodor Przymusinski. On the declarative semantics of deductive databases and logic programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming. Morgan Kaufmann, San Francisco, CA., 1988.

.... Royer, 1992] Geffner, 1992] conditional logics, e.g. cf. Delgrande, 1987a] Delgrande, 1987b] Geffner, 1992] and argument systems, e.g. cf. Loui, 1987] aggregation principles for modelpreference logics [Brown and Shoham, 1989] including for logic programming with negation as failure [Przymusinski, 1988] and terminological logics [Quantz and Royer, 1992] possibilistic logic [Dubois and Prade, 1988] syntax based belief revision formalisms, e.g. Nebel, 1989] and a variety of others, e.g. Brewka, 1989a] Brewka, 1989b] Brewka, 1994] Ginsberg, 1988] Zadrozny, 1987] Pollock, 1987] ....

.... antecedent over a default with a more general class antecedent) and, in stratified logic programs, to represent recursive depth in negation as failure use (i.e. deeper strata in backward inferencing have higher precedence associated with their predicates minimization) Lifschitz, 1987] [Przymusinski, 1988] . More generally, precedence appears to be an important expressive aspect of defaults needed or useful to represent many domains. Bases for precedence information include not only specificity dominance but also reliability and authority of sources [Grosof, 1993] decision theoretic utility ....

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Teodor Przymusinski. On the declarative semantics of deductive databases and logic programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming. Morgan Kaufmann, San Francisco, CA., 1988.

.... for de nite programs [4] and for normal programs the stable [5] and the well founded semantics [6] Of lesser importance, albeit still acknowledged in particular for their relation to resolutionbased logic programming, are the Fitting semantics [7] and approaches based on strati cation [8, 9]. The semantics just mentioned are closely connnected by a number of well (and some lesser ) known relationships, and many authors have contributed to this understanding. Fitting [10] provides a framework using Belnap s four valued logic which encompasses supported, stable, Fitting, and ....

....3. Let P be a normal logic program with Fitting model M . Then M is the greatest model among all models I, for which there exists an I partial level mapping l for P such that P satis es (F) with respect to I and l. Let us recall next the de nition of a (locally) strati ed program, due to [8, 9]: A normal logic program is called locally strati ed if there exists a (total) level mapping l : BP , for some ordinal , such that for each clause A A 1 ; An ; B 1 ; Bm in ground(P ) we have that l(A) l(A i ) and l(A) l(B j ) for all i = 1; n and j = 1; ....

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

.... We assume the reader is familiar with: the previous published version of courteous logic programs [ 4 ] 3 ] extended logic programs [ 2 ] the concept of ordinary, non extended logic programs, the semantics of stratified (ordinary, non extended) logic programs with negation as failure (e.g. [ 7 ] ) and the standard concepts in the logic programming literature (e.g. as reviewed in [ 1 ] including predicate atom dependency graph and its acyclicity non recursiveness; and instantiation. Appendix A contains some review of these concepts. In this section, we introduce some preliminary ....

Teodor Przymusinski. On the declarative semantics of deductive databases and logic programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming. Morgan Kaufmann, San Francisco, CA., 1988.

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ACM Transactions on Computational Logic, Vol. V, No. N, Month 20YY. Przymusinski, T. 1988. On the Declarative Semantics of Deductive Databases and Logic Programs. In Foundations of Deductive Databases and Logic Programming, J. Minker, Ed. Morgan Kaufmann, Los Altos, CA, 193-216.

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Przymusinski, T. 1988. On the declarative semantics of deductive databases and logic programs. In J. Minker Ed., Foundations of Deductive Databases, pp. 193--216. San Mateo: Morgan Kaufmann.

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

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

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Przymusinski T., On the declarative semantics of deductive databases and logic programs, In Minker J., editor, Foundations of Deductive Databases and Logic Programming, pages 193216, Morgan Kaufmann Publishers, Los Altos, 1988.

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T. C. Przymusinski. On the declarative semantics of deductive databases and logic programs. In [20].

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

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T. C. Przymusinski. On the declarative semantics of deductive databases and logic programs. In [20].

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

No context found.

T. C. Przymusinski. On the Declarative Semantics of Deductive Databases and Logic Programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 193--216. Morgan Kaufman, Washington DC, 1988.

No context found.

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

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T. Przymusinski. On the declarative semantics of deductive databases and logic programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, chapter 5, pages 193--216. Morgan Kaufmann, 1988.

No context found.

T. Przymusinski. On the declarative semantics of deductive databases and logic programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, chapter 5, pages 193--216. Morgan Kaufmann, 1988.

No context found.

T.C. Przymusinski (1988): On the declarative semantics of deductive databases and logic programs. In Jack Minker, editor: Foundations of Deductive Databases and Logic Programming, Morgan Kaufmann Publishers, Inc., Los Altos, California, pp. 193-216.

No context found.

T. C. Przymusinski. On the declarative semantics of deductive databases and logic programs. In [20].

No context found.

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

No context found.

T.C. Przymusinski. On the declarative semantics of deductive databases and logic programming. In [Min88b], Chapter 5, pp. 193-216. 1988.

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