Indeterminacy in Concurrent Computation - A Limitation of Logic Programming

A Limitation of Logic Programming

Patrick Hayes argued that the "usual sharp distinction that is made between the processes of computation and deduction, is misleading". Robert Kowalski developed the thesis that computation could be subsumed by deduction and quoted with approval "Computation is controlled deduction." which he attributed to Hayes in his 1988 paper on the early history of Prolog. Contrary to Kowalski and Hayes, Carl Hewitt claimed that logical deduction was incapable of carrying out concurrent computation in open systems.

Hewitt, Hewitt and Agha, and other published work argued that mathematical models of concurrency did not determine particular concurrent computations as follows: The Actor model makes use of arbitration (often in the form of notional Arbiters) for determining which message is next in the arrival ordering of an Actor that is sent multiple messages concurrently. This introduces indeterminacy in the arrival order. Since the arrival orderings are indeterminate, they cannot be deduced from prior information by mathematical logic alone. Therefore mathematical logic can not implement concurrent computation in open systems.

The authors note that although mathematical logic cannot, in their view, implement general concurrency it can implement some special cases of concurrent computation, e.g., sequential computation and some kinds of parallel computation including the lambda calculus.