Extended execution

These proofs have to be performed by an extension to SLD resolution, because the initial goals are here definite clauses, and not mere conjunctions of atoms. An existing such extension is the extended execution mechanism of [Kanamori and Seki 86] [Kanamori and Fujita 86], where theories are definite programs, and goals are so-called S formulas (short for specification formulas). Note that most of the terminology (but not the notation) used hereafter is borrowed from these two original references. This passage only states results, but not their motivations or proofs refer to these references when in need of further explanations. 

Due to our syntactic restriction to implicative goals, only three inference rules of extended execution are actually required in our context. 

This subset of extended execution is sound and complete wrt the Clark completion semantics [Kanamori 86]. Hence, provability by extended execution is equivalent to truth. Moreover, since % is by construction the completion of (Dj, the proofs of (2) thus effectively do amount to the truths of (1). 

SLD resolution is parameterized on a computation rule and a search rule [Lloyd 87]. For extended execution, these rules are, for the purpose of the Proofs-as-Programs Method, instantiated as follows ... 

Note that we could have adapted extended execution to handle our original formalisms without translations. But we feel that re-using (subsets of) existing results (namely [Kanamori and Fujita 86] [Kanamori and Seki 86] for execution, and [Deville 90] for the necessary translations) is a better approach. 

There is independence of the computation rules. But a fairness condition requires that no atom be indefinitely ignored by NFL The completeness proof of extended execution [Kanamori 86] states that every logical consequence is provable by a so-called normalized derivation, in which a sequence of NFI inferences precedes a sequence of DCI inferences, which in turn precedes a sequence of Sim inferences. Hence the idea of a priority ordering between the inference rules, namely NFf > DCI > Sim. 

Proof 9-1 The theorem directly follows from the soundness and completeness of extended execution wrt the Clark completion semantics [Kanamori 86]. ... 

Definition 9-5 The Proofs-as-Programs Method succeeds iff LA r) is proven (by extended execution) to be complete wrt P(r). It fails otherwise. 

Similarly, a set Zof logic algorithms LA(qf) is obtained by translating the definite procedures of the qj into logic algorithms. The used translation rules are the reverse of those used for achieving the applicability of extended execution they amount to... 

The objective is to attempt to prove, by extended execution, that each property P is a logical consequence of theory... 

T. Kanamori. Soundness and completeness of extended execution for proving properties of Prolog programs. TRICOT-TR-175, Tokyo (Japan), May 1986. [Kanamori and Fujita 86]... 

YAcHMOP stands for yet another extended Hiickel molecular orbital package. The package has two main executables and a number of associated utilities. The bind program does molecular and crystal band structure extended Hiickel calculations. The viewkel program is used for displaying results. We tested Version 3.0 of bind and Version 2.0 of viewkel. 

In addition to pressure maintenance in a resei voir, there are other ways to maintain or improve well productivity as the formation pressure falls. A pump can be used to raise the oil, a process called artificial lift. One type is the familiar beam pump with its surface power unit driving up and down one end of a center-mounted beam while the other end executes the opposite down-up motion. The second end is attached to a string of sucker rods that extend down to the bottom of the well and operate a pump arrangement, consisting of a cylinder, plunger, and one-way A alves. Other types of pumps in use eliminate the sucker rod and may have the power unit at... 

The term Brownian motion was originally introduced to refer to the random thermal motion of visible particles. There is no reason why we should not extend its use to the random motion of the molecules and ions themselves. Even if the ion itself were stationary, the solvent molecules in the outer regions of the co-sphere would be continually changing furthermore, the ion itself executes a Brownian motion. We must use the term co-sphere to refer to the molecules which at any time are momentarily in that region of solvent which is appreciably modified by the ion. In this book we are primarily interested in solutions that are so dilute that the co-spheres of the ions do not overlap, and we are little concerned with the size of the co-spheres. In studying any property... 

Scripts are often fairly simple software components that can be generated very quickly to execute recurring operations or collect multiple operations into a large block for efficient usage. Scripts can be simple shell scripts with no graphical output capability, but the use of extended graphical toolbox scripts provides a simple way of implementing software features with easy user interaction. 

First suppose we have paths a and o satisfying (a) - (c). Since o ends at a node that is either dead or loop-alive, o can be extended to an infinite path x (with o as finite initial subpath) which is an execution sequence because P is free. Now o contained one more assignment than a so the values of y under a free interpretation at the end of o and of o must differ. Thus, as the schemes are lanov, any extension of o must be consistent with a. So o,t is a consistent pair. Thus there is a free interpretation I under which computation (P,I,x) follows 0 and so halts and computation (P, I,x) follows t and so diverges. 

HSE, Explosion Hazard Assessment A Study of the Feasibility and Benefits of Extending Current HSE Methodology to Take Account of Blast Sheltering, Health and Safety Executive report HSL/2001/04, Sheffield, 2001. 

On a small scale, pluggable user-interface widgets form components. Several such kits come with visual builders, such as Visual Basic, which help you plug the components together. Kits also may extend to small parts outside the user interface domain (for example, VisualAge and JavaBeans). These components all work within one executable program. 

In Smalltalk/Envy, an executing system is made up of a series of packages (or applications ) loaded in a specific order, starting with the kernel, which defines all the primitives. Each package can extend existing classes and redefine specific methods. 

The whole lake is divided into a number of vertical elements, each comprising a column of water and the top layer of sediment. In this simulation only one such element is considered in order to improve the speed of execution. The general principle however can be extended to many elements. 

The Natural Fibers and Food Protein Commission of Texas, Carl Cox, executive director, supported this work over an extended period of time, which is gratefully acknowledged. Additional support came from Texas Cottonseed Crushers Assoc, and Cotton, Inc. The author acknowledges and expresses appreciation for the cooperation and contributions of graduate students. The contributions of Theresa Smith and Carol Owsiany in preparing this manuscript are appreciated. 

The keystone of managing chemical reactivity hazards is line responsibility. The "line" referred to here is the chain of command and authority that extends from the operator to the chief executive officer of the company. When all the advice and consultation is gathered relative to an issue, such as from relevant area experts and safety personnel, it is the business responsibility to provide leadership. It does so by communicating values, setting policy, making appropriate decisions, allocating the necessary resources, and following up to ensure implementation. 

Special thanks are extended in recognition of the important contributions of the following National Academies staff John Boright, Executive Director of the Office of International Affairs, who provided oversight for the initiative Pat Koshel, who contributed substantially to planning the workshop and Derek Vollmer, who assisted in editing the report. 

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