Variations on a Theme: A Bibliography on Approaches to Theorem Proving Inspired From Satchmo

This articles is a structured bibliography on theorem provers, approaches to theorem proving, and theorem proving applications inspired from Satchmo, the model generation theorem prover developed in the mid 80es of the 20th century at ECRC, the European Computer- Industry Research Centre. Note that the bibliography given in this article is not exhaustive

Computing cost estimates for proof strategies

In this paper we extend work of Treitel and Genesereth for calculating cost estimates for alternative proof methods of logic programs. We consider four methods: (1) forward chaining by semi-naive bottom-up evaluation, (2) goal-directed forward chaining by semi-naive bottom-up evaluation after Generalized Magic-Sets rewriting, (3) backward chaining by OLD resolution, and (4) memoing backward chaining by OLDT resolution. The methods can interact during a proof. After motivating the advantages of each of the proof methods, we show how the effort for the proof can be estimated. The calculation is based on indirect domain knowledge like the number of initial facts and the number of possible values for variables. From this information we can estimate the probability that facts are derived multiple times. An important valuation factor for a proof strategy is whether these duplicates are eliminated. For systematic analysis we distinguish between in costs and out costs of a rule. The out costs correspond to the number of calls of a rule. In costs are the costs for proving the premises of a clause. Then we show how the selection of a proof method for one rule influences the effort of other rules. Finally we discuss problems of estimating costs for recursive rules and propose a solution for a restricted case

Marvin: A Heuristic Search Planner with Online Macro-Action Learning

This paper describes Marvin, a planner that competed in the Fourth International Planning Competition (IPC 4). Marvin uses action-sequence-memoisation techniques to generate macro-actions, which are then used during search for a solution plan. We provide an overview of its architecture and search behaviour, detailing the algorithms used. We also empirically demonstrate the effectiveness of its features in various planning domains; in particular, the effects on performance due to the use of macro-actions, the novel features of its search behaviour, and the native support of ADL and Derived Predicates

From LCF to Isabelle/HOL

Interactive theorem provers have developed dramatically over the past four decades, from primitive beginnings to today's powerful systems. Here, we focus on Isabelle/HOL and its distinctive strengths. They include automatic proof search, borrowing techniques from the world of first order theorem proving, but also the automatic search for counterexamples. They include a highly readable structured language of proofs and a unique interactive development environment for editing live proof documents. Everything rests on the foundation conceived by Robin Milner for Edinburgh LCF: a proof kernel, using abstract types to ensure soundness and eliminate the need to store proofs. Compared with the research prototypes of the 1970s, Isabelle is a practical and versatile tool. It is used by system designers, mathematicians and many others

Artificial intelligence techniques for assembly process planning

Due to current trends in adopting flexible manufacturing philosophies, there has been a growing interest in applying Artificial Intelligence (AI) techniques to implement these manufacturing strategies. This is because conventional computational methods alone are not sufficient to meet these requirements for more flexibility. This research examines the possibility of applying AI techniques to process planning and also addresses the various problems when implementing such techniques. In this project AI planning techniques were reviewed and some of these techniques were adopted and later extended to develop an assembly planner to illustrate the feasibility of applying AI techniques to process planning. The focus was on assembly process planning because little work in this area has been reported. Logical decisions like the sequencing of tasks which is a part of the process planning function can be viewed as an AI planning problem. The prototype Automatic Assembly Planner (AAP) was implemented using Edinburgh Prolog on a SUN workstation. Even though expected assembly sequences were obtained, the major problem facing this approach and perhaps AI applications in general is that of extracting relevant design data for the process planning function as illustrated by the planner. It is also believed that if process planning can be regarded as making logical decisions with the knowledge of company specific data then perhaps AAP has also provided some possible answers as to how human process planners perform their tasks. The same kind of reasoning for deciding the sequence of operations could also be employed for planning different products based on a different set of company data. AAP has illustrated the potentialities of applying AI techniques to process planning. The complexity of assembly can be tackled by breaking assemblies into sub-goals. The Modal Truth Criterion (MTC) was applied and tested in a real situation. A system for representing the logic of assembly was devised. A redundant goals elimination feature was also added in addition to the MTC in the AAP. Even though the ideal is a generative planner, in practice variant planners are still valid and perhaps closer to manual assembly process planning

A Comparative study of four major knowledge representation techniques used in expert systems with an implementation in Prolog

Knowledge representation is a central issue in Artifical Intelligence (AI) research. In order to solve the diverse and complex problems encountered, one needs both a large amount of knowledge and some mechanism for the management and skillful utilization of that knowledge. The basic problem in knowledge representation is the development of an adequate formalism to represent that knowledge. In this thesis I will discuss four of the major techniques for representing knowledge in expert systems: first order logic, production rules, semantic networks, and frames. Using Prolog as the implementation language, I will demonstrate that all of the above mentioned representation techniques, when used in actual implementations, will be reduced to an equivalency - that being a set of Prolog facts and rules. Prolog limits us to a set of facts expressed as predicate(argumentl, argument, ..., argumentn) and IF ... THEN rules, thus eliminating many of the unique features which characterize the various representation techniques. Therefore, Prolog can be viewed as a representation technique itself

A constraint-based framework for configuration

The research presented here aims at providing a comprehensive framework for solving configuration problems, based on the Constraint Satisfaction paradigm. This thesis is addressing the two main issues raised by a configuration task: modeling the problem and solving it efficiently. Our approach subsumes previous approaches, incorporating both Simplification and further extension, offering increased representational power and efficiency. Modeling. We advance the idea of local, context independent models for the types of objects in the application domain, and show how the model of an artifact can be built as a composition of local models of the constituent parts. Our modeling technique integrates two mechanisms for dealing with complexity, namely composition and abstraction. Using concepts such as locality, aggregation and inheritance, it offers support and guidance as to the appropriate content and organization of the domain knowledge, thus making knowledge specification and representation less error prone, and knowledge maintenance much easier. There are two specific aspects which make modeling configuration problems challenging: the complexity and heterogeneity of relations that must be expressed, manipulated and maintained, and the dynamic nature of the configuration process. We address these issues by introducing Composite Constraint Satisfaction Problems, a new, nonstandard class of problems which extends the classic Constraint Satisfaction paradigm. Efficiency. For the purpose of the work presented here, we are only interested in providing a guaranteed optimal solution to a configuration problem. To achieve this goal, our research focused on two complementary directions. The first one led to a powerful search algorithm called Maintaining Arc Consistency Extended (MACE). By maintaining arc consistency and taking advantage of the problem structure, MACE turned out to be one of the best general purpose CSP search algorithms to date. The second research direction aimed at reducing the search effort involved in proving the optimality of the proposed solution by making use of information which is specific to individual configuration problems. By adding redundant specialized constraints, the algorithm improves dramatically the lower bound computation. Using abstraction through focusing only on relevant features allows the algorithm to take advantage of context-dependent interchangeability between component instances and discard equivalent solutions, involving the same cost as solutions that have already been explored