Artificial Intelligence, Vol. 2, pp. 79-116, 1971.

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

Full text available for a fee. "The use of augmented transition network grammars for the analysis of natural language sentences is described. Structure-building actions associated with the arcs of the grammar network allow for the reordering, restructuring, and copying of constituents necessary to produce deep-structure representations of the type normally obtained from a transformational analysis, and conditions on the arcs allow for a powerful selectivity which can rule out meaningless analyses and take advantage of semantic information to guide the parsing. The advantages of this model for natural language analysis are discussed in detail and illustrated by examples. An implementation of an experimental parsing system for transition network grammars is briefly described." Communications of the ACM, Vol. 13, No. 10, October, 1970, pp. 591-606 (reprinted in RNLP: 71-88).

See also: CACM, 13 (2), 94-102

Artificial Intelligence 1:121-170

In R. B. Banerji and M. D. Mesarovic (Eds.), Theoretical approaches to non-numerical problem solving. Berlin: Springer-Verlag, 303-343.

Arguably the first article discussing the uses of AI in the law beyond straightforward information retrieval.Although the computer has worked its way out of the laboratory and into common experience, lawyers have made slim progress towards finding useful computer applications. Research in artificial intelligence, a branch of computer science, has illuminated our capacity to use computers to model human thought processes. This research suggests that computer science may assist lawyers in both the study and performance of their reasoning 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.Stanford Law Review vol.23, no.1, November, 1970

This paper explores new approaches to the symmetric traveling-salesman problem in which 1-trees, which are a slight variant of spanning trees, play an essential role. A 1-tree is a tree together with an additional vertex connected to the tree by two edges. We observe that (i) a tour is precisely a 1-tree in which each vertex has degree 2, (ii) a minimum 1-tree is easy to compute, and (iii) the transformation on “intercity distances” cij → Cij + πi + πj leaves the traveling-salesman problem invariant but changes the minimum 1-tree. Operations Research, 18, 1138–1162.