Hogger, C.J. (1990). Essentials of Logic Programming. Oxford University Press.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....logics and the resolution principle is well established. Since [Lee72] one of the pioneering works in the area, several proposals have been made, aiming at richer languages in respect of both the logical and the fuzzy relations supported. In [Lee72] the language is limited to definite clauses [Apt87, Hog90] allowing fuzzy predicates with truth values always greater than 0.5 . The semantics of the relevant connectives is defined according to Zadeh s triangular norms and conorms and resolution is extended to propagate truth values in a way that is sound and complete with respect to the Herbrand ....

C. J. Hogger. Essentials of Logic Programming. Oxford Univ. Press, 1990.

....exists a computed answer for it via SLD resolution. Proof. See [Cla79, Llo87] Theorem 2.3. Semi decidability of SLD resolution) There is no decision procedure for obtaining terminating inferences for general program goals and programs. Proof. Horn clause logic is Turing powerful. See [Hog90]. It is convenient to denote logic programs directly within predicate logic derivations, without explicitly using the notation for SLD resolution. The following definition denotes logic programs in such a form. Definition 2.17. program completion) The completion Comp(P) of a logic program P ....

C.J. Hogger. Essentials of Logic Programming. Oxford University Press, 1990.

....In this case, the events are called conditioned events. For example, in Table 1 the mode transition defined in the second row is caused by the occurrence of conditioned event F(Ignited) whose condition is that Running is false. Different semantics have been used for conditioned events [21], all of which are expressible in our Event Calculus approach. In this specific case study, we have adopted the same interpretation as used in [4] An event T(C) conditional on D means that C is false in the current mode and is changed to true in the new mode, while D is true in the ....

....in the Event Calculus; e.g. HoldsAt(Off,0) so that system invariants may be checked with respect to the initial state separately 3.2.2 Translation of an alternative SCR semantics. As mentioned in Section 3. 1, different semantics for conditioned events have been used in the literature [21], all of which are expressible in our Event Calculus approach. In recent years, one of these semantics has become widely used. According to this semantics, two basic assumptions are made when representing systems specifications as SCR mode transition tables. The first is that events are ....

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Hogger, C. (1990). Essentials of Logic Programming. Clarendon Press, Oxford.

....The minimum development to achieve a reasonably efficient executable program is carried out and a rigorous argument [11] is presented to help ensure the correctness of the compiler. 1. 1 Logic programming and Prolog As the name suggests, logic programming has a well established mathematical basis [12, 13, 14]. Prolog [15] is the most widely available logic programming language. However, Prolog includes many non logical features in an attempt to make it into a usable, practical and efficiently executable language. Even so, if the features used in Prolog are restricted, it is possible to use it in a ....

Hogger CJ. Essentials of Logic Programming. Oxford University Press, 1990

....to tri logical disjunctions of each of the quantification s elements, which in turn derive built in disjunctions that may compromise performance due to backtracking. In some situations, existential quantifiers are transformed into conjunctions of two constraints by a process known as Skolemization [10]. This transformation is possible if the set of the quantification is not empty and the applicability expression of the SPL rule does not depend on the quantification variable. Under these conditions, the existential quantification # x # A : rule(x) is equivalent to c # A and rule(c) ....

C. J. Hogger. Essential of Logic Programming. Oxford University Press, 1990.

....used as a programming language. The scheme was based on SLD resolution.The first implementation of PROLOG, the language that realised the scheme, existed before the publication of the Kowalski scheme [BM73] In the following the main elements of a logic program are formally defined. Llo84] and [Hog90] are excellent textbooks about Logic Programming, its syntax, declarative and procedural semantics. Definition 1.1.1 (Clauses) A clause is of the form p 0 : Gamma p 1 ; p n where p i ; 0 i n, are atoms. p 0 is the head of the clause and p 1 ; pn is the body of the clause. ....

....the above example, the failed unification of variable W with constant e during resolution of t(Y,W,X) with t(b,e,c) creates the unification conflict set fs, tg. During the resolution of a call with the head of a clause the unification algorithm stops when identifying the first unification failure [Llo84, Hog90]. However, if all the unification steps are applied and all unification failures for a call are identified then all the individual unification conflict sets can be combined and form the resolution conflict set. Resolution conflict sets will be defined a little later on. The reason for not stopping ....

C.J Hogger. Essentials of Logic Programming. Oxford University Press, 1990.

....[Sammut et al. 1992] predictive accuracy is dependent on hypotheses being evaluable in time similar to that of human reaction, and so such hypotheses should be preferred a priori. 2. 1 Bayesian Inductive Logic Programming Familiarity with standard de nitions from Logic Programming [Lloyd 1987; Hogger 1990] is assumed in the following. A Bayesian version of the usual (open world semantics) setting for ILP is as follows. Suppose P , F and V are sets of predicate symbols, function symbols and variables and C d and C h are the classes of de nite and Horn clauses constructed from P , F and V . The ....

Hogger, C. 1990. Essentials of logic programming. Oxford University Press, Oxford.

.... ) X ] where X is the context representing the rst order (say) variables X, is the context representing the propositional assumptions , A is the type representing the proposition and is the realizer representing the proof object ; c) A least xed point semantics (see, for example, [77]) of logic programming with the calculus, i.e. requirement (3) Such a semantics is an essential starting point for understanding logic programming with a formal metatheory; it relies directly on the semantics of we have presented. The details of the ideas described in this section can be ....

....resolution, etc. or in terms of models via a xed point construction of a term model. We also remark that neither of these points of view provides an adequate account of of the execution dynamics of logic programming. For example, least xed point models of the kind described in, for example, [77, 107, 151] provide no account of details such as clause selection, backtracking or, indeed, Prolog s imperative constructs such as assert , retract and . Towards a New Approach. We suggest that one potentially valuable approach towards solving these problems lies in the provision of more ....

C.J. Hogger. Essentials of Logic Programming. Clarendon Pres, Oxford, 1990.

.... include: vEK76] GM87] and [PP91] Egon Borger uses evolving algebras for a semantical analysis of the logic programs, with case studies on (full) Prolog, BABEL and Godel [Bor94, BLR94, BR94] For general background reading I have used the following books: ffl logic programming and Prolog: [Spi96, Llo93, Apt97, SS86, AdBR93, Hog90] (and articles [Rob65, Sha89] ffl functional programming and Gofer: BW88, FWH92] ffl unifying of the theories of programming: HJ98] ffl introduction to operational and algebraic semantics: Hoa85, Ros98] 6.2 Further Work Because of its operational simplicity and transparency, the shallow ....

C.J. Hogger, editor. Essentials of Logic Programming. Clarendon Press, 1990.

....concept, a series of positive and negative examples are presented. FOIL is a general to specific learning system, that is, it searches the hypothesis space from the most general description of a concept to a specific one. 1 A reader unfamiliar with logic programming terminology is referred to [12]. a) b) Figure 2. Extracted edges of cup(a) and its segmentation to straight and curved lines(b) Hypothesis construction consists of two loops, the covering and specialisation loops. Covering loop is responsible for hypothesis construction, while specialisation loop constructs the clauses. ....

C. J. Hogger. Essentials of Logic Programming. Oxford University Press, 1990.

....by Tarski s classical fixpoint theorem. Starting with empty interpretation ; T P arrives at a least fixpoint; however, depending on starting interpretations, there exist numerous fixpoints. The transformation may need infinite iterations before reaching a fixpoint. Details can be found in [Llo84, Hog90] Basically, our algorithm to infer interargument constraints simulates the immediate consequence operator T P . 2.4 Deductive Databases One interpretation of logic is the database interpretation. Here a logic program is regarded as a database. We thus obtain a very natural and powerful ....

C. J. Hogger. Essentials of Logic Programming. Oxford University Press, New York, 1990.

....of beta strand within 40 positions of Pos. Predicates such as pref are defined by the expert using logic program clauses in the background knowledge. Since a logic program is simply a set of logic program clauses, the syntax and semantics of logic programs is very simple, clean and well defined [13, 6]. Despite the simplicity, logic programs are powerful enough for a general purpose programming language. All these properties, together with their ease of comprehension make them ideally suited as a general representation for machine learning within ILP. 2.2 Daimler Benz example Reza ....

C.J. Hogger. Essentials of logic programming. Oxford University Press, Oxford, 1990.

.... representing the first order (say) variables X, Gamma Delta is the context representing the propositional assumptions Delta, A OE is the type representing the proposition OE and oe Phi is the realizer representing the proof object Phi; c) A least fixed point semantics (see, for example, [77]) of logic programming with the Pi calculus, i.e. requirement (3) Such a semantics is an essential starting point for understanding logic programming with a formal metatheory; it relies directly on the semantics of Pi we have presented. The details of the ideas described in this section can ....

....etc. or in terms of models via a fixed point construction of a term model. We also remark that neither of these points of view provides an adequate account of of the execution dynamics of logic programming. For example, least fixed point models of the kind described in, for example, [77, 107, 151] provide no account of details such as clause selection, backtracking or, indeed, Prolog s imperative constructs such as assert , retract and . Towards a New Approach. We suggest that one potentially valuable approach towards solving these problems lies in the provision of more ....

C.J. Hogger. Essentials of Logic Programming. Clarendon Pres, Oxford, 1990.

....in molecular biology and discusses some of the distributional assumptions used in these applications. Section 4 defines U learnability and describes some general results on U learnable distributions. 2 BAYES ILP DEFINITIONS Familiarity with standard definitions from Logic Programming [22, 14] is assumed in the following. A Bayesian version of the usual (open world semantics) setting for ILP is as follows. Suppose P , F and V are sets of predicate symbols, function symbols and variables and C d and C h are the classes of definite and Horn clauses constructed from P , F and V . The ....

C.J. Hogger. Essentials of logic programming. Oxford University Press, Oxford, 1990.

....functional. Declarative models emphasize state transitions, while functional models emphasize operational or event oriented modelling. Declarative and functional model forms are prevalent in all three disciplines. For instance, programming languages are often categorized into either declarative [1, 49] or functional [48, 6] types. The declarative programming languages (such as Prolog) emphasize changes in state where states are best coded as particular data structures a simple variable being the most commonly used form for a state. Functional programming languages concentrate on ....

Hogger, C. J. Essentials of Logic Programming. Oxford University Press, 1990.

....logics and the resolution principle is well established. Since [Lee72] one of the pioneering works in the area, several proposals have been made, aiming at richer languages in respect of both the logical and the fuzzy relations supported. In [Lee72] the language is limited to definite clauses [Apt87, Hog90] allowing fuzzy predicates with truth values always greater than 0.5 5 . The semantics of the relevant connectives is defined according to Zadeh s triangular norms and conorms and resolution is extended to propagate truth values in a way that is sound and complete with respect to the Herbrand ....

C. J. Hogger. Essentials of Logic Programming. Oxford Univ. Press, 1990.

....ffl Herbrand models and fixed point semantics. We have discussed both prooftheoretic semantics (an abstract operational semantics) and model theoretic semantics for logic programming with BI. We have paid little attention to denotational semantics. In logic programming, as found in, for example, [9], the established method of giving a denotational semantics is to construct a minimal Herbrand or term model as follows: Define a sequence of term models (H n ) n0 such that H n 1 = T (H n ) where T is an operator which corresponds to all of the possible resolution steps, starting from the ....

C.J. Hogger. Essentials of Logic Programming. Oxford University Press, 1990.

....logic programming (CLP) and a simple CLP compiler decompiler are presented. Finally some conclusions are drawn on the possible applicability of the method in practice. 3 Logic programming and Prolog As the name suggests, logic programming has a well established mathematical basis (Lloyd, 1987, Hogger, 1990, van Emden et al. 1976) Prolog (Clocksin et al. 1987) is the most widely available logic programming language. However, Prolog includes many non logical features in an attempt to make it into a practical programming language. Even so, if the features used in Prolog are restricted, it is ....

Hogger, C.J. (1990). Essentials of Logic Programming. Oxford University Press.

....will focus on rather specialized areas within Logic Programming, and as there are already numerous very good introductions to the general field, a basic background knowledge of Logic Programming will be assumed. A reader unfamiliar with the basic notions is referred to books such as [Ko79b] and [Ho90]. The main concepts of Constraint Logic Programming and Abductive Logic Programming will be introduced rather informally motivated by small examples. Readers interested in a more rigorous account of these techniques should consult the references given throughout the text. 1.1 Constraint Logic ....

.... Delta 2 , would have been found. However, this cannot generally be expected. Normally, exactly those predicates for which there are no clauses in the program are the abducibles. An important way of looking at abduction is to regard it as deduction in the completion ( CoDuTo91] see, e.g. [Ho90] for a definition of the completion of a logic program) Abduction can then be performed by forward reasoning from observations using the only if halves of the completed clauses. Basically, abduction as deduction in the completion just means making explicit the so far implicit closedworld ....

Hogger, C. J.: Essentials of Logic Programming, Oxford University Press 1990

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Hogger, C.J. (1990). Essentials of Logic Programming. Oxford University Press.

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