Why parallel processing? (English) Zbl 0845.68039

Hintikka, Jaakko

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].

Reviewer: V.Peckhaus (Erlangen)

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

Keywords:

independent-friendly first-order logic; parallel distributed processing; branching-quantifier