K.R. Apt. Logic Programming, Handbook of Theoretical Computer Science. J. Van Leeuwen, Elsevier, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....greatest fixpoint typel contains Ol and 02; type2 contains o2; type3 contains o2 and o3. Thus, even if we delete type2 every object will still be assigned to at least one type. In that case, o2 will loose its original home type but will be assigned two home types, namely type1 and type3. Remark 4.4 Because of the special form of the type predicates it can be shown that eliminating types corresponding to multiple role objects is not very hard. It can be done in at most O(n 2) where n is the number of types. Of course, there is still the problem of choosing a particular set of types for ....

....fixpoint typel contains Ol and 02; type2 contains o2; type3 contains o2 and o3. Thus, even if we delete type2 every object will still be assigned to at least one type. In that case, o2 will loose its original home type but will be assigned two home types, namely type1 and type3. Remark 4. 4 Because of the special form of the type predicates it can be shown that eliminating types corresponding to multiple role objects is not very hard. It can be done in at most O(n 2) where n is the number of types. Of course, there is still the problem of choosing a particular set of types for the ....

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K.R. Apt. Logic Programming, Handbook of Theoretical Computer Science. J. Van Leeuwen, Elsevier, 1991.

....worthwhile. Moreover, since interpreters exist for most of these languages, or at least for subsets of them, logic based descriptions of MAS can be seen as executable specifications, and executable specifications are prototypes. The paper focused on the adoption of Logic Programming (LP) [2] for developing MAS prototypes. Besides the already observed features common to all the logic based frameworks, other characteristics make LP suitable for our purposes. MAS execution: the evolution of a MAS consists of non deterministic succession of events; from an abstract point of view an LP ....

K. R. Apt. Introduction to Logic Programming, volume B of Handbook of Theoretical Computer Science. Elsevier, Amsterdam and The MIT Press, Cambridge, 1990.

....programming is not necessary in order to understand our algorithm. Its relevance is that these techniques can be used as one approach to solving the constraints generated by our algorithm. Constraint logic programming (CLP) 17, 16, 6, 7, 18] is a generalization of classical logic programming [37, 1, 25], whereby the equality constraints between terms e.g. father of(X) father of(henry) and their solution by unification algorithms are replaced by generic constraint domains and their associated constraintprocessing methods. Van Hentenryck observed that this generalization has simplified the ....

....1.5. 2 The result of the query diagline(1,X,Y) can be represented by the primitive rule: result(X, Y ) # X # 0, X # 1, Y = 1 X 33 Even though the point set for this rule is infinite, it is still directly usable, because it expresses a function from the independent variable x ranging over [0,1] to the dependent variable y. Example 1.5.3 The answer to the query diamond(1,X,Y) # Y # 0 is representable by the two primitive rules: result(X, Y ) # X # 1, X # 0, Y = X 1 result(X, Y ) # X # 0, X # 1, Y = X 1 For an example where there is no useful constraint ....

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K.R. Apt. Logic programming. Handbook of theoretical computer science, Volume B, van Leeuwen, J. ed., pages 493--574, 1990.

....Section 6. In Section 7, we establish the soundness and completeness issues of the method. Section 8 discusses the heuristics for arriving at the pre and the postassertions followed by a discussion of the method in section 9. Throughout the paper, we follow the definitions and notation given in [3, 27] unless otherwise stated. 2 Termination of Logic Programs In this section, we provide a brief account of the spectrum of methods that have been used for proving termination of logic programs. Our primary aim is to highlight different techniques that have been used for proving termination of ....

Apt, K.R., Logic Programming, Handbook of Theoretical Computer Science, Edited by J. van Leeuwen, Elsevier Science Publishers, 1990, pp. 494-574.

....we shall not resort to such proofs by contradiction when presenting the inference algorithm, but rather, we shall use the notion of rule trees as the basis for the development. The two approaches are equivalent, but the positive approach is more directly visualizable. The reader is referred to [Apt90] for a lucid survey of classical logic programming. LLo87] investigates the foundations of classical logic programming. SS86] is a standard introductory textbook on Prolog programming. JM94] is a comprehensive survey on constraint logic programming. The early chapters in [SAJ97] present a ....

K.R. Apt. Logic programming. Handbook of theoretical computer science, Volume B, van Leeuwen, J. ed., pages 493--574, 1990.

....to [HHK98a] would be a good way. However we have not yet implemented this translation and we think that LP is finer on some aspects than OCL. Thus the problem of consistency of such class diagrams is related to the consistency of first order predicate logic. This kind of problem is not decidable [Apt90] It exists several useful approaches to detect either consistency or inconsistency. For example, techniques based on Herbrand s Theorem may detect inconsistency [DJ90] but they require process termination because this problem is semi decidable. Here we use LP and under some hypotheses it can ....

K. R. Apt. Logic rogramming, volume B of Handbook of Theoretical Computer Science, chapter 10, pages 495--574. Elsevier, 1990. Jan Van Leeuwen, Editor.

....in Vickers [Vic89] There has been much investigation into the use of domain logics as logics of types and of program correctness, mainly for imperative and functional languages. Surprisingly, though, there has been relatively little work tying domain theory to the semantics of logic programming [Apt90], in particular disjunctive logic programming [LMR92] Most of this work focuses on first order logic. Extensions to higher types have been made for example, Prolog [NM98] but domain theory has not played as much of a role here as it has for functional programming. In this paper we offer ....

K. R. Apt, Logic programming, Handbook of Theoretical Computer Science, vol. B, MIT Press/Elsevier, 1990, pp. 495--571.

....reader is assumed to have a certain knowledge of the main concepts and terminology in the areas of algebraic specification and logic programming. In addition, certain familiarity with basic constructs from category theory is required. For more details on some of these topics the reader may consult [1, 3, 8, 20, 25]. Due to lack of space, most of the results and the discussions have been only sketched. The reader is addressed to the long version of this paper for more detail. ACKNOWLEDGEMENTS Some initial work in this subject was done together with Andrea Corradini. This work has been partially supported ....

....institution for defining the (declarative) semantics of definite logic programs is Horn Clause Logic. Actually, this is what is (implicitly) done by most authors. In particular, the standard declarative meaning of a logic program P is defined as the least Herbrand model of P (see, for instance, [20, 1]) In algebraic terms, this is equivalent to defining the semantics of P as the initial model in Mod(P) where Mod corresponds to the model functor of HCL. This kind of semantics is the most reasonable one when defining the meaning of a logic programming language as a logic language. However, if ....

K. R. Apt. Logic Programming. Handbook of Theoretical Computer Science, Vol B, chapter 10. 1990.

....E is obtained by the set difference of BE(F ) and the heads of F instantiated by the Herbrand base of E. 16 4. 2 Operational Semantics Wenow present a top down semantics for the extended language by means of a set of inference rules, which directly extend the standard notion of SLD refutation [4]. SLD refutations may be defined by means of inference rules of the form P remise Conclusion with the meaning that Conclusion holds whenever Premise holds. We will write E # G if there exists a top down refutation for the goal G in the program (expression) E with computed substitution #. Let ....

K. R. Apt. Logic programming.InJ.van Leeuwen, editor, Handbook of Theoretical Computer Science, pages 493--574. Elsevier, 1990. Vol. B.

....the standard traversal and handling the cut are described. Finally, in Section 4 some more examples show the need of control information for ensuring completeness and explain its use. 1 Preliminaries The reader is assumed to be familiar with the basic concepts of Logic Programming, see [1, 12]. V is an infinite set of variables. A substitution is a mapping from V to T ( Sigma; V) which acts as the identity almost everywhere. A renaming is a bijection on variables. With Subst we denote the set of all idempotent substitutions and with j V the restriction of to the set of variables ....

K. Apt: Introduction to Logic Programming. Handbook of Theoretical Computer Science, J.van Leeuwen, editor, North Holland, 1990.

....with any of the previously published OSC synthesis algorithms because of loops and uncontrollable events (AV engine failures) in the plant transition relation. 2 Basic Definitions In this section we review standard definitions from First Order Logic (FOL) and Logic Programming (e.g. see [12] [3]) and adapt them to our case: Boolean First Order Logic (BFOL) BFOL is simply FOL on the boolean domain f0, 1g. BFOL syntax is the same as that for FOL with the following provisions: the only constants in BFOL alphabet are 0; 1 (propositional constants) there are no function symbols in BFOL ....

....predicate symbol p occurring in a program statement in P there is exactly [at most] one program statement in P with p occurring in the head. Note that we call program what in logic programming is usually called (up to statement ordering) the completion of a logic program (e.g. see [12] sec. 17 or [3]) Note that a program is a module, but the converse is false. e.g. P = p = q] is a module but it is not a program since in P there is no program statement with q as head (i.e. q is not defined in P ) ffl Let P be a module. A predicate symbol p is in P iff p occurs in a statement in P . The ....

K. R. Apt, Logic Programming, Handbook of Theoretical Computer Science, Elsevier 1990

....give extensive references for points 2 6. For point 1(a) one can find several good books on firstorder logic, for example [53] or good surveys on constraint logic programming and fixpoint semantics [42, 75, 153, 154] There are also good introductions to logic programming (without constraints) in [10, 50, 101] and to database query languages (also without constraints) in [3, 79, 149] One can also find an earlier tutorial on constraint databases in [80] and an applications oriented survey in [61] Points 1(b) and 1(c) will be illustrated by a new algebra for constraint databases with integer order ....

....query can be expressed as a logic program, but the reverse is not true. Unfortunately, from the database point of view the higher expressive power of logic programs is at the expense of some practicality. The following is a brief historical summary of the developments in the two areas, based on [10]: 1970: Relational Algebra proposed by Codd [41] 1972: Relational Calculus shown equivalent to Relational Algebra by Codd. 1973 74: Prolog by Colmerauer, Kanoui, and Van Caneghem [44] and Kowalski. 1976: Fixpoint Semantics for Prolog by Van Emden and Kowalski. 1979 80: Datalog by Aho and Ullman ....

K.R. Apt. Logic Programming. Handbook of Theoretical Computer Science, Vol. B, chapter 10, (J. van Leeuwen editor), North-Holland, 1990.

.... S gfp(T ) the converse is not valid) 3 Symptom and Error for Logic Programs Obviously we have a first application of this scheme if we consider a definite program P , the Herbrand base H , i.e. the set of the ground atoms, and the rules which are the ground instances of the clauses of P (see [25, 3]) lfp(T ) is the least Herbrand model of P and it is also the set of all the ground atoms which are logical consequences of P . It is a formalization of its (ground, positive) declarative semantics. S is a set theoretical formalization of an expected property. Here a symptom for T wrt S is an ....

K. R. Apt. Handbook of Theoretical Computer Science, volume 2, chapter Logic Programming, pages 493--574. Elsevier, 1990.

....with rules the inference mechanism that apply axioms the program starting from a goal and searching for a proof. We formulate this approach in all its generality and we exemplify it with some systems that are related to SLD(NF ) resolution. We assume some familiarity with logic programming [27, 2] and basic proof theory [38, 42, 16] 2.1 AAR Systems An AAR system is a triple hG; A; Ri where: 1. G is a set of admissible goals. In this paper those will be literals, but more general forms could be used (see [33] Goals are therefore distinct from Prolog goals, denoted as usual by the ....

K.A. Apt. Logic Programming. Handbook of Theoretical Computer Science, J. Leuween, ed., Elsevier, 1990.

....denotes whether the edge is incoming (left) or outgoing (right) The superscript denotes the type of the object at the other end of the edge. Semantics The semantics of a datalog program P of the form described above for a database D is defined as the greatest fixpoint of P for D. See, e.g. [4]. More precisely, let M be an instance over the schema of P such that M coincides with D on flink; atomicg. Then M is a fixpoint of P for D, if for each IDB c, P(M ) c) M (c) It is the greatest fixpoint, if it contains any other fixpoint of P for D. Note that this definition is correct ....

....atomicg. Then M is a fixpoint of P for D, if for each IDB c, P(M ) c) M (c) It is the greatest fixpoint, if it contains any other fixpoint of P for D. Note that this definition is correct because for a given database D and a datalog program P, there is unique greatest fixpoint of P for D [4]. For the data of Figure 2, and for the program P 0 , the greatest fixpoint consists of fperson(g) person(j) firm(a) firm(m)g, which is as expected. Note that for this program, a least fixpoint semantics would fail to classify any object. The intuition behind the choice of the greatest ....

K.R. Apt. Logic Programming, Handbook of Theoretical Computer Science. J. Van Leeuwen, Elsevier, 1991.

....Tsur, and Zaniolo 1993; Zaniolo 1994) In this section, we will briefly describe some of the salient aspects of the LDL system as relevant to KM and also highlight the benefits of using LDL in the Knowledge Miner framework. The LDL query language is based on Horn clause logic (Lloyd 1984; Apt 1990) and a LDL program is essentially a set of declarative rules. For example, the following rules ancestor(X; Y ) parent(X; Y ) ancestor(X; Y ) ancestor(X; Z) parent(Z; Y ) specify that a new relation ancestor 2 can be defined based on the relation parent 2. X, Y and Z are variables and ....

Apt, Krzysztof R., Logic Programming, Chapter 10, Handbook of Theoretical Computer Science, Ed. J. van Leeuwen, pp. 493-574, 1990.

....n, newsat2(n) is false in the perfect model of the program. As already mentioned, we will describe our generalization technique in Section 6. 3. Preliminaries In this section we recall some basic notions of constraint logic programming. For notions not de ned here the reader may refer to [3, 4, 20, 21, 27]. We also present our notational conventions and we brie y recall the syntax and the semantics of the Computational Tree Logic (CTL, for short) which is the logic we use for expressing properties of reactive systems. For a more detailed treatment of CTL the reader may look at [9] 3.1. Syntax of ....

K. R. Apt, \Introduction to logic programming," in Handbook of Theoretical Computer Science (J. van Leeuwen, ed.), pp. 493-576, Elsevier, 1990.

....about the database, TR uses the closed world assumption. Using the logic programming jargon to define more precisely the meaning of this assumption, we can say that the models of a set of formulae are determined by the least fixpoint of the immediate consequence operator Tp applied to this set [17]. To illustrate the mechanism demanded to update non atomic formulae, let s analyze the following example: suppose there is a database composed of a set of formulae and there are two elementary transactions ff:del 0 and ff:ins 0 which removes and inserts a formula ff in the database. Figure 1 ....

K. R. Apt. Introduction to logic programming. Handbook of Theoretical Computer Science, (J. Van Leeuwen, Managing Editor), North Holland, 1986.

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K.R. Apt, Introduction to Logic Programming, ed. J. van Leeuwen, Handbook of Theoretical Computer Science, volume B: Formal Models and Semantics (Elsevier, Amsterdam and The MIT Press, Cambridge, 1990).

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Apt, K. R. \Logic Programming" in Handbook of Theoretical Computer Science, J. van Leeuwen, ed., Elsevier, 1990, pp. 494-574.

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Apt, K. R.: Logic Programming, Handbook of Theoretical Computer Science (J. van Leeuwen, ed.), Elsevier Science Publishers B.V., 1990.

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K. R. Apt. Logic Programming. Handbook of Theoretical Computer Science, Vol. B: Formal Models and Semantics, Chapter 10, Elsevier, 1990.

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