We will extend Floyd's proof system for flow diagrams to handle commands Which process lists. McCarthy and Painter (1967) deal with arrays by introducing'change' and'access' functions so as to write a[i]: a[j] 1 as a: change (a, i, access 24 BURSTALL King (1969) in mechanising Floyd's technique gives a method for such assignments which, however, introduces case analysis that sometimes becomes unwieldy. Let us recall briefly the technique of Floyd (1967) for proving correctness of programs in flow diagram form. We will here retain the inductive method of Floyd for dealing with flow diagrams containing loops, but give methods for coping with more complex kinds of assignment command.
For the past several years research on robot problem-solving methods has centered on what may one day be called'simple' plans: linear sequences of actions to be performed by single robots to achieve single goals in static environments. This process of forming new subgoals and new states continues until a state is produced in which the original goal is provable; the sequence of operators producing that state is the desired solution. In the case of a single goal wff, the objective is quite simple: achieve the goal (possibly while minimizing some combination of planning and execution cost). The objective of the system is to achieve the single positive goal (perhaps while minimizing search and execution costs) while avoiding absolutely any state satisfying the negative goal.
This paper describes a computer system for understanding English. It is based on the belief that in modeling language understanding, we must deal in an integrated way with all of the aspects of language--syntax, semantics, and inference. It enters into a dialog with a person, responding to English sentences with actions and English replies, asking for clarification when its heuristic programs cannot understand a sentence through the use of syntactic, semantic, contextual, and physical knowledge. By developing special procedural representations for syntax, semantics, and inference, we gain flexibility and power.
We were led to this comparison by the observation that the computer model is weaker in three important ways: search depth is not unbounded, structures matching variables cannot be compared, and structures matching variables cannot be moved. Thus, every recursively enumerable language is generated by a transformational grammar with limited search depth, without equality comparisons of variables, and without moving structures corresponding to variables. On the other hand, both mathematical models allow unbounded depth of analysis; both allow equality comparisons of variables, although the Ginsburg-Partee model.compares