New York: American Elsevier.

New York: McGraw-Hill.

JOINDER OF CLAIMS, COUNTERCLAIMS, AND CROSS-COMPLAINTS: SUGGESTED REVISION OF THE CALIFORNIA PROVISIONS. Research in artificial intelligence, a branch of computer science, has illuminated our capacity to use computers to model human thought processes. In this Article we will argue that the time has come for serious interdisciplinary work between lawyers and computer scientists to explore the computer's potential in law. Interdisciplinary work between the lawyer and the computer scientist has floundered on the misconceptions that each has of the other's discipline. As a result, no one has yet attempted computer programs incorporating complex techniques of legal reasoning. Even efforts in legal information retrieval have been hampered by these misconceptions. In retrieval, lawyers have viewed the computer as, at most, a storehouse from which cases and statutes might be retrieved by skillfully designed indexing systems. But the lawyer rarely looks for, or even expects, clear answers. So far, the efforts in legal retrieval have given little consideration to the possibility that computers might operate on the legal data base the way a lawyer does. Yet the work in both fields law and computer science -,suggests that the computer modeling of legal reasoning would be a fruitful area for research. In this Article we speculate about the dimensions and possible directions of this research. Under the most promising of outcomes, interdisciplinary research could lead both to a greater understanding of the legal reasoning process and to the design of machine methods for performing parts of it. The prospect of using computers to model legal reasoning processes is likely to prompt a typically lawyer-like response: So what if we understand legal reasoning or legal argument formation better? Knowing more about the ways in which lawyers search and manipulate the legal data base might lead to improving the lawyer's skill at his work. We recognize the possibility that the work of many lawyers might actually involve little use of the legal data base for argument construction or dispute resolution.

Russian Mathematical Surveys, 25, 221-262

In Linguaggi nella Societ`a e nella Tecnica, pp. 189– 224. Edizioni di Comunit`a.

Ph.D. dissertation "Bi-directional and heuristic search in path problems" (Stanford, Computer Science, 1970) summarized in this article in Machine Intelligence 6 (1971).In the uni-directional algorithms, the search proceeds from an initial nodeforward until the goal node is encountered. Problems for which the goal nodeis explicitly known can be searched backward from the goal node. Analgorithm combining both search directions is bi-directional.This method has not seen much use because book-keeping problems werethought to outweigh the possible search reduction. The use of hashingfunctions to partition the search space provides a solution to some of theseimplementation problems. However, a more serious difficulty is involved.To realize significant savings in bi-directional search, the forward andbackward search trees must meet in the 'middle' of the space. The potentialbenefits from this technique motivates this paper's examination of thetheoretical and practical problems in using bi-directional search.

Inference systems Τ and search strategies E for T are distinguished from proof procedures β = (T,E) The completeness of procedures is studied by studying separately the completeness of inference systems and of search strategies. Completeness proofs for resolution systems are obtained by the construction of semantic trees. These systems include minimal α-restricted binary resolution, minimal α-restricted M-clash resolution and maximal pseudo-clash resolution. Certain refinements of hyper-resolution systems with equality axioms are shown to be complete and equivalent to refinements of the pararmodulation method for dealing with equality. The completeness and efficiency of search strategies for theorem-proving problems is studied in sufficient generality to include the case of search strategies for path-search problems in graphs. The notion of theorem-proving problem is defined abstractly so as to be dual to that of and" or tree. Special attention is given to resolution problems and to search strategies which generate simpler before more complex proofs. For efficiency, a proof procedure (T,E) requires an efficient search strategy E as well as an inference system T which admits both simple proofs and relatively few redundant and irrelevant derivations. The theory of efficient proof procedures outlined here is applied to proving the increased efficiency of the usual method for deleting tautologies and subsumed clauses. Counter-examples are exhibited for both the completeness and efficiency of alternative methods for deleting subsumed clauses. The efficiency of resolution procedures is improved by replacing the single operation of resolving a clash by the two operations of generating factors of clauses and of resolving a clash of factors. Several factoring methods are investigated for completeness. Of these the m-factoring method is shown to be always more efficient than the Wos-Robinson method. The University of Edinburgh

This paper describes an effort to design a heuristic problem-solving program which accepts problems stated in a nondeterministic programming language and applies constraint satisfaction methods and heuristic search methods to find solutions. The use of nondeterministic programming languages for stating problems is discussed, and ref, the language accepted by the problem solver arf, is described. Various extensions to ref are considered. The conceptual structure of the program is described in detail and various possibilities for extending it are discussed. The use of the input language and the behaviour of the program are described and analyzed in sixteen sample problems.

The game of Go invites analysis. The rules seem few and simple, suggesting that the game may have helpful theorems. Tens of millions of people play and skill has developed over centuries to extraordinary levels. Thus, computer analysis can be tested against analysis by highly skilled human players. We study M × N boards, rather than the usual 19 × 19.

This paper investigates the problem of implementing machine learning of heuristics. First, a method of representing heuristics as production rules is developed which facilitates dynamic manipulation of the heuristics by the program embodying them. Second, procedures are developed which permit a problem-solving program employing heuristics in production rule form to learn to improve its performance by evaluating and modifying existing heuristics and hypothesizing new ones, either during an explicit training process or during normal program operation. Third, the feasibility of these ideas in a complex problem-solving situation is demonstrated by using them in a program to make the bet decision in draw poker. Finally, problems which merit further investigation are discussed, including the problem of defining the task environment and the problem of adapting the system to board games.