Ranan B. Banerji

Learning by experimentation: acquiring and refining problem-solving heuristics

This chapter concerns learning heuristic problem-solving strategies through experience. In particular, we focus on the issue of learning heuristics to guide a forward-search problem solver, and describe a computer program called lex, which acquires problem-solving heuristics in the domain of symbolic integration. lex acquires and modifies heuristics by iteratively applying the following process: (i) generate a practice problem; (ii) use available heuristics to solve this problem; (iii) analyze the search steps performed in obtaining the solution; and (iv) propose and refine new domain-specific heuristics to improve performance on subsequent problems. We describe the methods currently used by lex, analyze strengths and weaknesses of these methods, and discuss our current research toward more powerful approaches to learning heuristics.

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.

The Logic of Learning: A Basis for Pattern Recognition and for Improvement of Performance.

Publisher Summary This chapter discusses the logic of learning. It defines the phenomenon of pattern recognition. The two initial concepts in a theory of pattern recognition are illustrated by the set of states of a problem and the subsets of it required by the search reduction techniques. In considerations of language, one can describe certain subsets of the universe other than the elementary concepts: any logical statement involving the names of the elementary concepts defines subsets of the universe. Moreover, one can define relations between objects by specifying that the two satisfy two related statements. The chapter classifies the programs along a number of different parameters. One will be according to the language used. There are two aspects to this: One is the nature of the atoms in the language, that is, whether the predicates take only one variable (and thus define classes) or can also define relations by using more than one variable. The other aspect that distinguishes the languages used in different programs is in the nature of the Horn clauses themselves. The chapter concludes that the study of learning has been directed to specific tasks and accordingly many basic problems have been clarified. As this understanding deepens, the field, likened to artificial intelligence, will develop into two branches, applied and pure.

Some linguistic and statistical problems in pattern recognition

Abstract It has been pointed out that all pattern recognition activities depend on writing and reading descriptions of patterns and pattern classes in some special purpose language. This uniform point of view allows all these languages to be considered in terms of some predicate calculus. The feature extraction problem then turns out to be the problem of simplification of sentences by defining new predicates in the language. It has been suggested that the problem can be looked upon as one in the presentation of algebras. A hypothesis has been suggested which might explain the importance of simplicity of description in pattern recognition and in scientific theories.

A language for pattern recognition

Abstract A pattern is defined to be any element of a finite Boolean Algebra generated by the elements of a pre-defined set of partitions on an abstract set. An object is defined to be the “atomic patterns” in this Boolean Algebra, i.e. the elements which cover the least element. A description is a statement obtained from a set of basic predicates by the use of the usual logical connectives. Each basic predicate is true for one and only one element of one of the pre-defined partitions. If the partitions and their elements have names which are themselves objects in another Boolean Algebra, then complex patterns can often be described by comparatively simple statements which express relations in the universe of names. Examples have been given to show how the description language can be used to describe complex patterns in the “character-recognition” environment by comparatively simple statements.

On misere games

Kayles is a nonpartizan two-person game. In such games the moves available to both the players are the same and either the player on move wins or the previous player wins. In the “normal form” of the game, the last player who can make a move is declared the winner. In the “misere form” of the game, the player who makes the last move is declared the loser. The complete analysis of the normal form of the game of Kayles has been described by Berlekamp, Conway, and Guy. This paper completes their analysis of the misere form of Kayles. This is done on the basis of certain properties of what have been called “wild” positions of misere games.

Similarities in Problem Solving Strategies

This is an exposition of a previous paper by Prof. Y. Takahara and its interpretation in the general theory of problem solving. A strategy is defined to be a functor from the category of problems to the category of solutions. Two strategies are considered similar if there is a natural transformation on one into the other.

Changing language while learning recursive descriptions from examples

Shapiro [330] has described a reasonably efficient algorithm for inducing first order theories of models from facts. He proved that the algorithm converges as long as the various parameters appearing in the learning algorithm satisfied certain well defined constraints. Within the limitations of these constraints, however, there was sufficient flexibility in the choice of the parameters.

Developments with GPS

This paper points out that, since its inception, the basic idea of the General Problem Solver (GPS) has been followed and sharpened by a number of researchers. It describes how their research has shed light on various aspects of GPS, examines their limitations, and tries to remove these limitations. Special consideration is given to work aimed at automating the construction of problem dependent heuristic information guidance for GPS.

PERIODICITY OF SPRAGUE-GRUNDY FUNCTION IN GRAPHS WITH DECOMPOSABLE NODES

Abstract Certain games exhibit a periodic behavior that makes it easy to calculate winning strategies for them. Two such classes of games had been analyzed by previous authors. Neither of these two theories included the other as a special case. This paper develops a generalized theory that includes both.