Proof Plans Research Articles

From Editor-in-Chief’s Keyboard (December 2022)

The Covid-19 pandemic has obliterated all previous histories of development. In an effort to stem the tide of the pandemic, governments on every continent have ordered the strictest lockdowns in recorded history. Since nearly half of the world's population put unprecedented constraints on travel, the effects of this pandemic may impact many facets of human life and trade, including tourist management. Many experts fear that the new Covid-19 pandemic will have a depressing effect on international travel and the economy. Reductions in financial development and unfavourable attitudes toward citizens of countries hardest hit by the Covid-19 pandemic are predicted, according to economic estimates. The economic, tourist, and social effects of the pandemic are catastrophic for all nations.
 Therefore, the December issue emphasises issues related to the business strategies specialisation in tourism industry. Article by Wang Haouran (page 22-30) study on the Impact of Covid-19 Epidemic on Public Views of Tourist Travel Danger and Management where there is speculation among vacationers that health concerns associated with the Covid-19 pandemic have led some to cancel their trips. These results may be helpful to policymakers and healthcare providers in identifying those most at risk for developing maladaptive levels of anxiety in response to the Covid-19 epidemic. Healthcare professionals can enhance the quality of their educational interventions by focusing on the needs of out-of-country tourists. Tourists worry about how the Covid-19 epidemic may change their vacation plans in the post-pandemic era. Because of the severity of the Covid-19 outbreak, this study offers useful information for developing more fool proof plans to restore travellers' faith in the tourism industry after they've been through a health crisis and a frightening experience abroad.
 Let us unwind and have fun by reading the current issue. This is the final issue for 2022. My team and I hope that the content of our journal during the year will greatly contribute to your life improvement. We'll see you in 2023 and say goodbye in 2022.
 
 Assoc. Prof. Dr. Ilham SentosaEditor-in-Chief
 editor@dreamjournal.my

Review on Applications of Object Detection using Deep Learning

Abstract: Human cerebral mantle not requires a second to separate the area of thing inside the image similarly as recall it when it ensures; in spite of that, machine requires a time and large amount of data to perform a similar task. Deep neural network dependent on convolution neural network allows high accuracy and better results in object discovery .To develop deep neural networks, large amount of information such as images, video recordings are required and also it requires large amount of time. As computational cost of PC vision is incredibly high, highly learning methodology, where a model ready on one endeavor is reused on one more associated task, gives improved results. Through the survey and investigation of deep learning-based article recognition techniques recently, this work integrates the going with parts: spine interconnection, setback limits and planning procedures, customary thing distinguishing proof plans, multi-layered issues, the datasets and appraisal aspects, applications, and future headway headings. We belief this overview paper will be helpful for experts in the field of object detection. Keywords: Artificial Intelligence, Deep Learning, Neural Network, Object Detection

Two proving strategies of highly successful mathematics majors

We examined the proof-writing behaviors of six highly successful mathematics majors on novel proving tasks in calculus. We found two approaches that these students used to write proofs, which we termed the targeted strategy and the shotgun strategy. When using a targeted strategy students would develop a strong understanding of the statement they were proving, choose a plan based on this understanding, develop a graphical argument for why the statement is true, and formalize this graphical argument into a proof. When using a shotgun strategy, students would begin trying different proof plans immediately after reading the statement and would abandon a plan at the first sign of difficulty. The identification of these two strategies adds to the literature on proving by informing how elements of existing problem-solving models interrelate.

On the Comparison of Proof Planning Systems: , Ωmega and IsaPlanner

We present a framework for describing proof planners. This framework is based around a decomposition of proof planners into planning states, proof language, proof plans, proof methods, proof revision, proof control and planning algorithms.We use this framework to motivate the comparison of three recent proof planning systems, λCLaM, Ωmega and IsaPlanner, and demonstrate how the framework allows us to discuss and illustrate both their similarities and differences in a consistent fashion. This analysis reveals that proof control and the use of contextual information in planning states are key areas in need of further investigation.

Combining Proof Plans with Partial Order Planning for Imperative Program Synthesis

The structured programming literature provides methods and a wealth of heuristic knowledge for guiding the construction of provably correct imperative programs. We investigate these methods and heuristics as a basis for mechanizing program synthesis. Our approach combines proof planning with conventional partial order planning. Proof planning is an automated theorem proving technique which uses high-level proof plans to guide the search for proofs. Proof plans are structured in terms of proof methods, which encapsulate heuristics for guiding proof search. We demonstrate that proof planning provides a local perspective on the synthesis task. In particular, we show that proof methods can be extended to represent heuristics for guiding program construction. Partial order planning complements proof planning by providing a global perspective on the synthesis task. This means that it allows us to reason about the order in which program fragments are composed. Our hybrid approach has been implemented in a semi-automatic system called Bertha. Bertha supports partial correctness and has been tested on a wide range of non-trivial programming examples.

Discovering applications of higher order functions through proof planning

Abstract. The close association between higher order functions (HOFs) and algorithmic skeletons is a promising source of automatic parallelisation of programs. A theorem proving approach to discovering HOFs in functional programs is presented. Our starting point is proof planning, an automated theorem proving technique in which high-level proof plans are used to guide proof search. We use proof planning to identify provably correct transformation rules that introduce HOFs. The approach has been implemented in the λ Clam proof planner and tested on a range of examples. The work was conducted within the context of a parallelising compiler for Standard ML.

The Use of Proof Planning for Co-operative Theorem Proving

We describebarnacle: a co-operative interface to theclaminductive theorem proving system. For the foreseeable future, there will be theorems which cannot be proved completely automatically, so the ability to allow human intervention is desirable; for this intervention to be productive the problem of orienting the user in the proof attempt must be overcome. There are many semi-automatic theorem provers: we call our style of theorem provingco-operative, in that the skills of both human and automaton are used each to their best advantage, and used together may find a proof where other methods fail. The co-operative nature of thebarnacleinterface is made possible by the proof planning technique underpinningclam. Our claim is that proof planning makes new kinds of user interaction possible.Proof planning is a technique for guiding the search for a proof in automatic theorem proving. Common patterns of reasoning in proofs are identified and represented computationally as proof plans, which can then be used to guide the search for proofs of new conjectures. We have harnessed the explanatory power of proof planning to enable the user to understand where the automatic prover got to and why it is stuck. A user can analyse the failed proof in terms ofclam's specification language, and hence override the prover to force or prevent the application of a tactic, or discover a proof patch. This patch might be to apply further rules or tactics to bridge the gap between the effects of previous tactics and the preconditions needed by a currently inapplicable tactic.

Proof planning: A methodology for developing AI systems incorporating design issues

AbstractIn cases where a domain theory can be successfully expressed in a logical formalism and can be used to formulate a task in that domain in mathematical terms, the task of building sound knowledge-based systems is greatly facilitated. However, it is not immediately obvious how the design aspects of such tasks, where these are an important feature of problem solving, can be incorporated in this approach. Design issues differ from search problems in that there may be several choices, each valid in some sense, but not (necessarily) equally good or equally appropriate in the current context. A case study is described in which a methodology is used based on the development of proof plans. The ability to conduct research according to the Popperian framework of hypothesis, validation, testing, and modification in response to empirical evidence – the hypothetico-deductive approach – seems essential to any rigorous scientific endeavor. It is believed that proof planning is a method which readily exploits this inherently incrementalist approach and could prove to be a powerful tool in designing AI systems.

Experiments with proof plans for induction

The technique of proof plans is explained. This technique is used to guide automatic inference in order to avoid a combinatorial explosion. Empirical research is described to test this technique in the domain of theorem proving by mathematical induction. Heuristics, adapted from the work of Boyer and Moore, have been implemented as Prolog programs, called tactics, and used to guide an inductive proof checker, Oyster. These tactics have been partially specified in a meta-logic, and the plan formation program, CLAM, has been used to reason with these specifications and form plans. These plans are then executed by running their associated tactics and, hence, performing an Oyster proof. Results are presented of the use of this technique on a number of standard theorems from the literature. Searching in the planning space is shown to be considerably cheaper than searching directly in Oyster's search space. The success rate on the standard theorems is high.

EXTENDING THE PROOF PLAN METHODOLOGY TO COMPUTER CONFIGURATION PROBLEMS

Can the technique of proof plans, developed originally for use in theorem proving, be successfully applied outside mathematics? We look at a problem associated with the configuration of large computer systems, namely that of checking orders drawn up by sales people on behalf of customers. Strategies exist for this task which may be explicitly encoded. We discuss the formation of plans for order checking and the factors involved in determining whether such plans can be guaranteed to succeed.

Meta-level inference: Two applications

We describe two uses of meta-level inference: to control the search for a proof; and to derive new control information, and illustrate them in the domain of algebraic equation solving. The derivation of control information is the main focus of the paper. It involves the proving of theorems in the Meta-Theory of Algebra. These proofs are guided by meta-meta-level inference. We are developing a meta-meta-language to describe formulae, and proof plans, and have built a program, IMPRESS, which uses these plans to build a proof. We describe one such proof plan in detail. IMPRESS will form part of a self-improving algebra system.

AN ANATOMY OF ABSTRACTION

The use of the abstraction in resolution theorem proving is pro posed in order to obtain some global proof plans. Then the problem is how to avoid the false proof. We give a new definition of the shapes of proofs so that we can make use of unifiers occurring in the proofs and discuss some typical abstractions. Then we can clarify that such abstractions are concerned with the unifiers. Moreover, we can give a complete strategy with matching. Our formalization will be useful to the further discussions on abstractions.