## Why parallel processing?(English)Zbl 0845.68039

Casati, Roberto (ed.) et al., Philosophy and the cognitive sciences. Proceedings of the 16th international Wittgenstein symposium, 15-22 August 1993, Kirchberg am Wechsel, Austria. Vienna: Hölder-Pichler-Tempsky. Schriftenreihe der Wittgenstein-Gesellschaft. 21, 265-272 (1994).
The author contributes to the question whether parallel distributed processing (PDP) offers a better model for human information handling than sequential processing of the Turing machine kind. Without finally deciding this question he offers a logical-combinatorial argument for a certain advantage of PDP as modelling tool, using the partial correlation between logical formulas and distributed processing devices. The author especially considers a system of two parallel units $$U_1$$ and $$U_2$$. Its output will be an ordered pair of numbers $$y$$, $$u$$ obtained from two separate inputs $$x$$, $$z$$. The objects $$x$$, $$y$$, $$z$$, $$u$$ will satisfy a certain condition $$C_0[x, y, z, u]$$. The modus operandi of the combined system $$U_0$$ is expressed by the second-order formula $(\exists f_1)(\exists f_2)(\forall x)(\forall z) C_0[x, f_1(x), z, f_2(z)].$ Statements of that form do not have in general first-order equivalents, but they can be expressed using a branching-quantifier notation, or a slash notation introduced by the author (the informational independence of, say, the quantifiers $$Q_1$$ and $$Q_2$$ is indicated by $$Q_1/Q_2$$): $(\forall x)(\forall z)(\exists y/\forall z)(\exists u/\forall x) C_0[x, y, z, u].$ This “independent-friendly (IF) first-order logic” is claimed to be the “natural logic” if first-order logic fails (due to incompleteness). The notion spells out the parallel processing character of a system, and “we can thus reach means of representing by means of possible parallel processing systems modes of thinking and reasoning which are beyond the purview of first-order logic”. This is the author’s reason to prefer parallel processing as a modelling device to sequential processing (p. 269).
For the entire collection see [Zbl 0849.00032].

### MSC:

 68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.) 03B80 Other applications of logic 03C85 Second- and higher-order model theory 68Q05 Models of computation (Turing machines, etc.) (MSC2010) 68-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science 68W15 Distributed algorithms 68T01 General topics in artificial intelligence