O. Shmueli, S. Tsur, and C. Zaniolo. Compilation of Set Terms in the Logic Data Language (LDL). JLP, 12(1/2):89--119.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....problem involving positive and negative equality literals. Notice that in the framework of general ACI1 unification, we can encode all (A b ) C ) unification problems, since, if f( Delta) is a unary (free) function symbol, then fX j Y g is equivalent to f(X) Y (cf. also Footnote 1 and [19]) In [12] ACI1 constraints (including unification) for the general case are studied and solved. 5 Multisets Expressiveness results similar to those of the previous sections can be obtained in a multiset framework. However, while the meaning of set operators is a common and unambiguous ....

O. Shmueli, S. Tsur, and C. Zaniolo. Compilation of set terms in the logic data language (LDL). Journal of Logic Programming, 12(1-2):89--119, 1992.

....instead, sets are intended as subsets of a finite domain D of objects. At the language level, each ground set is represented as an individual constant (where all constants are partially ordered to reflect the lattice) 41 ffl using an infinite collection of function symbols of different arity [17, 25] the set fa 1 ; a n g is encoded by the term f n (a 1 ; a n ) using the n ary functor f n . We will concentrate on the first two methods only. The third one, in fact, does not suit to our purposes. In particular, stating equality in axiomatic form would require a non trivial ....

O. Shmueli, S. Tsur, and C. Zaniolo. Compilation of Set Terms in the Logic Data Language (LDL). J. of Logic Programming, 12(1):89--120, 1992.

....must exhibit the permutativity property fX j fY j Zgg = fY j fX j Zgg and the absorption property fX j fX j Zgg = fX j Zg : Solution (3) requires the introduction of an in nite signature, with a di erent set constructor for each possible nite set cardinality. This approach has been adopted in [51]. In order to use this solution it is necessary to introduce a complex (in nite) equational theory capable of specifying the uni ability of set terms with di erent main functors, like in fg 3 (X; Y; Z) fg 2 (a; b) Representation (2) has been frequently used in the context of logic languages ....

Shmueli, O., Tsur, S., and Zaniolo, C. Compilation of Set Terms in the Logic Data Language (LDL). Journal of Logic Programming, 12(1/2):89-119, 1992.

....must exhibit the permutativity property fX j fY j Zgg = fY j fX j Zgg and the absorption property fX j fX j Zgg = fX j Zg : Solution (3) requires the introduction of an in nite signature, with a di erent set constructor for each possible nite set cardinality. This approach has been adopted in [47]. In order to use this solution it is necessary to introduce a complex (in nite) equational theory capable of specifying the uni ability of set terms with di erent main functors, like in fg 3 (X; Y; Z) fg 2 (a; b) Representation (2) has been frequently used in the context of logic languages ....

Shmueli, O., Tsur, S., and Zaniolo, C. Compilation of Set Terms in the Logic Data Language (LDL). In Journal of Logic Programming, 12(1/2):89-119, 1992.

....[36] 5 Overview ffl Magic Sets and Related Research (e.g. Alexander Method) Formulation [102] 7] 111] 124] 20] 87] 85] 10] 70] 91] 117] 47] 60] 96] 11] 114] 104] 84] References are a little dated. Implementation and Systems [8] 25] 125] 97] [113], 130] 131] 44] 59] 63] 86] LDL, Aditi, Coral and others. Optimizations [95] 88] 105] 106] 103] 72] 116] 62] 61] 118] 15] 6 Overview ffl Practical and Research Applications ffl Parsing [1] 78] 30] Tabling eliminates need for transformations from ....

O. Shmueli, S. Tsur, and C. Zaniolo. Compilation of set terms in the logic data language (LDL). Journal of Logic Programming, 12:89--119, 1992.

.... [121] 45] 83] 95] 92] Optimizations [30] 6 Motivation Magic Sets and Related Research (e.g. Alexander Method) Formulation [87] 5] 97] 111] 18] 69] 67] 8] 59] 73] 103] 39] 49] 79] 9] 101] 89] 66] Implementation and Systems [6] 24] 112] 80] [99], 118] 119] 37] 48] 52] 68] Optimizations [78] 70] 90] 91] 88] 61] 102] 51] 50] 104] 16] ffl Bibliography is incomplete: it considers only formulations of evaluation strategies and not general theories of Datalog, updates, etc. Does not consider some newer ....

O. Shmueli, S. Tsur, and C. Zaniolo. Compilation of set terms in the logic data language (LDL). Journal of Logic Programming, 12:89--119, 1992.

....widely recognized as a valuable feature of high level programming languages. And logic programming languages seem to be the right candidates for hosting such a feature due to their potentially high declarative nature. Attention to this problem has come first from the field of deductive databases [1, 4, 14, 22]. However many other fields, including rapid software prototyping and knowledge based systems, may benefit from the availability of sets constructs. And, recently, a number of papers have addressed the problem also in a wider setting. General purpose set constructs and basic 1 Read setlog . ....

O. Shmueli, S. Tsur, and C. Zaniolo. Compilation of set terms in the logic data language (LDL). J. of Logic Programming, vol.12, n.1, 1992.

....for data intensive applications, it is assumed that only ground answers are of interest. ffl Set unification is not required in LDL. The bottom up semantics allows matching to be used in place of full unification, by guaranteeing that one of the terms to be compared is ground. Furthermore, in [47], it is shown that a program can be rewritten at compile time into an equivalent one in which each rule containing set terms is replaced by a set of rules, each containing first order, i.e. nonset, terms only. ffl LDL offers a built in set collection mechanism. The class of acceptable programs ....

Shmueli, O., Tsur, S., and Zaniolo, C., Compilation of set terms in the logic data language (LDL). J. Logic Programming, 12(1):89--119 (1992).

....one is more general than the other. Unification algorithms for functions with the associativity, commutativity, and idempotency properties have been proposed [9] however, these algorithms cannot be adopted for set term unification since functions and set terms have different semantics (See [11], P. 93) 5, 12] propose set term unification algorithms that compute unifiers for a given pair of set terms with the commutative and idempotent properties; however, these algorithms have several problems. One of the problems is that duplicated unifiers, which are generated for a given pair of ....

....p(s 1 ; s n ) p(t 1 ; t n ) is a term called tuple term, where t i is of type s i , 1 i n. 2 A set term (subset, multiset, or permutation as defined in Section 3) is treated as the concatenation of a number of elements, with the properties of commutativity and idempotency [5, 11]. The commutative and idempotent property of a set term S allows elements in S to be arranged in any order and treats duplicated elements in S as a single element, respectively. Definition 3 A set term S satisfies the commutative property if given any two elements e 1 and e 2 , concat(e 1 ; ....

O. Shmueli, S. Tsur, and C. Zaniolo. Compilation of Set Terms in the Logic Data Language (LDL). Journal of Logic Programming, 12(1):89--119, 1992.

....Relational query languages typically deal with tuples of atomic values like strings or integers. Applications require to handle more complex values, for example sets or multisets. Various kinds of complex values in databases and logic programming have been considered in many papers, including [2, 3, 15, 6, 22, 20, 16, 5, 1, 14, 13, 10, 9, 23]. Our paper studies complexity aspects of databases with complex values. There are two main kinds of complexity in databases: 1) query evaluation complexity that measures time or space needed to evaluate a query, and (2) descriptive complexity that characterizes the expressive power of query ....

O. Shmueli, S. Tsur, and C. Zaniolo. Compilation of set terms in the logic data language (LDL). Journal of Logic Programming, 12(1):89--119, 1992.

....relations, and is simpler in notation than HILOG R [5] which requires type and named attribute to be attached to each argument of a type declaration, and named attribute to each data value in a tuple. In addition, LDL=NR is more complete in terms of language structure for nested relations than LDL [14] which allows only nested tuples rather than nested sets. Furthermore, the semantics of sets in the logic database language defined by [9] is different from the semantics of set terms as defined in LDL=NR. From the theoretical point of view, set terms as defined in [9] cannot handle the nested ....

O. Shmueli, S. Tsur, and C. Zaniolo. Compilation of Set Terms in the Logic Data Language (LDL). Logic Programming, 12(1):89--119, 1992.

....lem in the context of the logic data language LDL. This problem asks: given a system of elementary ACI equations, does there exist an ACI matcher such that every variable is instantiated by a single constant This restricted ACI matching problem has been introduced by Shmueli, Tsur, and Zaniolo [STZ92], and also studied by Arni, Greco, and Sacc a [AGS96] under the name bounded set term matching. Here, we show that restricted ACI matching with two free constants and an unbounded number of equations is NP complete, but restricted ACImatching with a fixed number of free constants and a fixed ....

....its computational complexity has been investigated by Kapur and Narendran [KN86] who showed that this problem is NP complete. Set matching, as well as certain variants of it, arise naturally in deductive database systems and in logicbased languages that support complex objects. Shmueli et al. [STZ92] studied set matching problems in the context of LDL, a Horn clause programming language for deductive database systems. The semantics of LDL require that set terms consisting of variables and constants be matched in such a way that variables are instantiated only by individual constants. In ....

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O. Shmueli, S. Tsur, and C. Zaniolo. Compilation of set terms in the logic data language (LDL). J. Logic Prog., 12(1 & 2):89--119, 1992.

....of Q. LDL=NR restricts HILOG [CC90] to nested relations, and is simpler in notation than HILOG R [CK91] which requires type and named attribute to be attached to each argument of a type declaration and named attribute to each data value in a tuple. Furthermore, LDL=NR is more complete than LDL [STZ92] which allows only nested tuples rather than nested sets. 2.3.1 Syntax of Rule Expressions in LDL=NR Rule expressions REs in LDL=NR are based on the notions of type, term, and formula which in turn are defined on an alphabet in LDL=NR. Constants and variables in REs are of atomic type. There are ....

O. Shmueli, S. Tsur, and C. Zaniolo. Compilation of Set Terms in the Logic Data Language (LDL). Logic Programming, 12(1):89--119, 1992.

....in old team consists of a set of people. An ok team tuple additionally must contain an engineer, a pilot and a doctor. Note that a team containing a single member who is an engineer, a pilot and a doctor would qualify as an ok team. This program is a translation into CORAL of an LDL program from [STZ92] the semantics of the original LDL program required that a team contain at most three members. The addition of count(S; C) C 3 to the body of the rule ensures this. 2.5 Persistent Relations The schema of a persistent relation must be declared, e.g. schema(employee(string; int; f loat; ....

Oded Shmueli, Shalom Tsur, and Carlo Zaniolo. Compilation of set terms in the logic data language (LDL). Journal of Logic Programming, 12(1&2):89--120, 1992.

....33, 25] as well as with associativity, commutativity and idempotency [26] such algorithms cannot be extended to deal with commutativity and idempotency only. A technique to extend the deductive database resolution strategy to deal with set terms, for the case of matching, has been proposed in [31] where the anomaly of the set term unification is removed at compilation time using rewriting techniques to transform set terms into standard terms. This technique generates a number of rules that is exponential in the size of the rewritten terms. The case of set term matching has been studied ....

O. Shmueli, S. Tsur and C. Zaniolo, Compilation of Set Terms in the Logic Data Language (LDL), Journal of Logic Programming, Vol. 12, No 1 & 2, Jan.Feb., 1992, pages 89-119.

....general unifier (mgu) of two set terms is unique modulo renaming of variables. Unification algorithms for functions with the associativity, commutativity, and idempotency properties have been proposed [Sti81, Fag84, LC88] however, these algorithms cannot be adopted to handle set term unification [STZ92] since functions and set terms have different semantics. In [DOPR91, Sto93] set term unification algorithms that compute unifiers for a given pair of set terms with commutative and idempotent properties were presented. However, these algorithms have several problems. One of these problems is that ....

.... is dept(cs, projectsfdb; se; lpg, employees femployee(smith; 123) employee(jones; 567) employee(snow; 201)g) 2 A set term (subset, multiset, or permutation) is treated as the concatenation of a number of elements, i.e. as an ordered list, with the properties of commutativity and idempotency [DOPR91, STZ92, AGS92]. The commutative property of a set term S in LDL=NR allows elements in S to be arranged in any order, while the idempotent property of S treats duplicated elements in S as a single element. Definition 3 A set term S in LDL=NR satisfies the commutative property if given any two elements e 1 and ....

O. Shmueli, S. Tsur, and C. Zaniolo. Compilation of Set Terms in the Logic Data Language (LDL). Journal of Logic Programming, 12(1):89--119, 1992.

....sets (where one or both of the sets can have variables) is not supported in CORAL, unlike in LDL, which supports set matching. The evaluation mechanism for set matching in LDL generates a number of rules at compile time that is exponential in the size of the largest set term in the program text [STZ92] The use of set matching is limited in CORAL to avoid this problem. A set term is restricted to be ground (as in LDL) and to match either another (identical) ground set term or a variable. We believe that most, if not all, uses of set matching can be implemented naturally using the suite of ....

....in old team consists of a set of people. An ok team tuple additionally must contain an engineer, a pilot and a doctor. Note that a team containing a single member who is an engineer, a pilot and a doctor would qualify as an ok team. This program is a translation into CORAL of an LDL program from [STZ92] the semantics of the original LDL program required that a team contain at most three members. The literals count(S; C) C 3 in the body of the rule ensure this. 3 Interactive System Environment CORAL presents users with an interactive environment for program development and ad hoc querying. ....

Oded Shmueli, Shalom Tsur, and Carlo Zaniolo. Compilation of set terms in the logic data language (LDL). Journal of Logic Programming, 12(1&2):89--120, 1992.

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O. Shmueli, S. Tsur, and C. Zaniolo. Compilation of Set Terms in the Logic Data Language (LDL). JLP, 12(1/2):89--119.

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Shmueli, O., Tsur, S., and Zaniolo, C. Compilation of Set Terms in the Logic Data Language (LDL). Journal of Logic Programming 12, 1/2 (1992), 89-119.

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