George W. Ernst

The role of analogy in transfer between similar problem states

Abstract The study investigated the effect of transfer between two problems having similar (homomorphic) problem states. The results of three experiments revealed that although transfer occurred between repetition of the same problems, transfer occurred between the Jealous Husbands problem and the Missionary—Cannibal problem only when (a) Ss were told the relationship between the two problems and (b) the Jealous Husbands problem was given first. The results are related to the formal structure of the problem space and to alternative explanations of the use of analogy in problem solving. These include memory for individual moves, memory for general strategies, and practice in applying operators.

Sufficient Conditions for the Success of GPS

A formal model of a problem is developed and its relationship to the General Problem Solver (GPS) is discussed. Before GPS can work on a problem it must be given differences, a difference-ordering, and a table of connections, in addition to the specifications of a problem. Formal definitions of this additional information are given, and sufficient conditions for the success of GPS are derived. These conditions point out the utility of differences and a difference-ordering that yield a “triangular” table of connections. Several different formulations of the Tower of Hanoi are given to illustrate the formal concepts. The use of subproblems in narrowing search is discussed.

Modular verification of Ada generics

Abstract This paper develops modular verification rules for Ada generics which are proven to be sound and complete. The generic mechanism in Ada allows modules to be parameterized by types, procedures and functions. The modularity property allows a generic to be verified once, and then exported to other modules which assume that it is correct. This requires the generic to have a specification which is used in verifying other modules, but its implementation cannot be used for this purpose. Thus, modular verification cannot be based on removing generics by macro expansion which requires the use of the generics implementation. The main difficulty with specifying and verifying a generic is that the specification language may need to be extended with a new theory for specifying and reasoning about properties of objects whose type is a parameter to the generic. Such theories must be part of the specification of the generic, and this raises the possibility that the extended specification language may not be expressive, even if it was before the extension. The use of strings in our specification language prevents this from happening, which is proven in the paper; this is a major step toward establishing the completeness of our rules. Modularity also had a large impact on our semantics for programming constructs which is quite different from the usual semantics in the literature, even though it is still based the denotational semantics of Scott and Strachey. The main reason for this is that we had to modify the standard definition of validity. Modularity requires that validity depend on certain internal assertions in a program, such as the precondition of a procedure invoked in the program.

The utility of independent subgoals in theorem proving

This paper views theorem proving as a two-level process. The top level breaks theorems into subgoals which are achieved by contemporary theorem proving methods. A method for generating an AND/OR tree of subgoals is described. It is emphasized that all of the subgoals generated by this method are “independent.” This is important because solving independent subgoals may yield an exponential savings. Examples are given to illustrate the subgoal generation method and its utility.

Verification of programs with procedure-type parameters

SummaryA verification system is developed for proving the correctness of programs containing procedures with procedure-type parameters. The system, which reduces programs and their specifications to assertions to be proved in ordinary logic, is shown to be logically sound. The reduction process is controlled by the syntax of the program and is completely mechanical, requiring no human intervention. The resulting assertions involve higher-order predicates, but they engender no significant difficulties which are not already present in ordinary first-order theories.Our system views the intermediate objects in the reduction process as extended programs, thereby making verification a much less abstruse process. Treating logical assertions as commands appeals strongly to a programmers intuition.

Specification of Abstract Data Types in Modula

The programming language MODULA is extended to permit the formal specification of the structure and functional capabilities of modules. This makes true hierarchical programming possible in MODULA by allowing programmers of higher level parts of a system to ignore completely the internal structure of lower level modules and to rely entirely on the specifications of the capabilities of these modules. An example is included to illustrate this technique. We show that our specification mechanisms are sufficiently powerful to support formal verification rules for modules that have disjoint representations for abstract objects.

The role of common sense knowledge in menu planning

Abstract Planning nutritious and appetizing menus is a task at which experts consistently outperform computer systems, making it a challenging domain for AI research. This paper describes lessons learned through the sequential construction of four expert systems for menu planning. The first of these systems, ESOMP (Expert System on Menu Planning), was built to plan menus for patients on severely restricted low protein diets. A need for common sense in structuring “sensible” looking meals was identified and addressed via meal patterns and food exchange groups. PRISM (Pattern Regulator for the Intelligent Selection of Menus) expanded upon ESOMP by planning menus to meet a broad range of dietary requirements and personal preferences. Simple knowledge representation structures, implemented in PRISM 1.0, proved inadequate for the expanded task. A hierarchical network structure was developed and implemented in PRISM 2.0 and PRISM 3.0. This structure captures the common sense concept of menu form and describes context-sensitive relationships among menu parts. A major contribution of this paper is showing how to represent common sense knowledge about food and menus in a form amenable to successful menu planning.

Rules of inference for procedure calls

SummaryThe semantics of procedures and parameters were formalized by Hoare [2] in terms of axioms and rules of inference. Igarashi et al. [4] reformulated Hoares system. This paper extends their rule of inference for procedure calls to allowi)actual variable parameters to occur in actual value parameters;ii)the body of a procedure to contain global variables that do not occur in assignment positions;iii)post-conditions and “internal” assertions of a procedure to refer to the initial values of variable parameters. None of these are allowed in Hoares system or the system of Igarashi, London and Luckham. An attractive feature of these extensions is that they do not increase the complexity of the rules of inference.

Learning problem solving strategies using refinement and macro generation

This research develops a method for learning efficient strategies (search-control knowledge) for solving a certain class of problems. The input to this system is a description of a problem and its output is a strategy for solving the problem. Several such techniques have already been developed. These methods have some good features as well as some deficiencies. These techniques are analyzed in detail to understand what mechanisms are necessary for learning efficient strategies. The method developed here is called RWM. It incorporates two separate methods, namely, Refinement and Macro Generation. The former is a method for partitioning a given problem into a sequence of easier subproblems which constitutes a raw strategy to solve that problem. The latter is for efficiently learning composite moves which are useful in solving the problem. These methods and a system that incorporates them are described in detail. The kind of strategies learned by RWM are based on the GPS problem solving method. Examples of different types of problems are given for motivation. RWM has learned good strategies for some problems that have not been learned by other strategy learning systems.

Learning patterns in terms of other patterns

Abstract This paper investigates the learning of patterns in terms of previously learned patterns. The main problem is to efficiently select from the set of all previously learned patterns a few in terms of which the pattern to be learned can be described. A computer program for doing this is described and the importance of its memory organization is discussed.