Read more
The calculus of relations has been an important component of the development of logic and algebra since the middle of the nineteenth century, when Augustus De Morgan observed that since a horse is an animal we should be able to infer that the head of a horse is the head of an animal. For this, Aristotelian syllogistic does not suffice: We require relational reasoning. George Boole, in his Mathematical Analysis of Logic of 1847, initiated the treatment of logic as part of mathematics, specifically as part of algebra. Quite the opposite conviction was put forward early this century by Bertrand Russell and Alfred North Whitehead in their Principia Mathematica (1910 - 1913): that mathematics was essentially grounded in logic. Logic thus developed in two streams. On the one hand algebraic logic, in which the calculus of relations played a particularly prominent part, was taken up from Boole by Charles Sanders Peirce, who wished to do for the "calculus of relatives" what Boole had done for the calculus of sets. Peirce's work was in turn taken up by Schroder in his Algebra und Logik der Relative of 1895 (the third part of a massive work on the algebra of logic). Schroder's work, however, lay dormant for more than 40 years, until revived by Alfred Tarski in his seminal paper "On the calculus of binary relations" of 1941 (actually his presidential address to the Association for Symbolic Logic).
List of contents
I. Introduction.- 1 Background Material.- II. Algebras.- 2 Relation Algebras.- 3 Heterogeneous Relation.- 4 Fork Algebras.- III. Logics.- 5 Relation Algebra and Modal Logics.- 6 Relational Formalisation of Nonclassical Logics.- 7 Linear Logic.- IV. Programs.- 8 Relational Semantics of Functional Programs.- 9 Algorithms from Relational Specifications.- 10 Programs and Datatypes.- 11 Refinement and Demonic Semantics.- 12 Tabular Representations in Relational Documents.- V. Other Application Areas.- 13 Databases.- 14 Logic, Language, and Information.- 15 Natural Language.- Bibliography (compiled by Wolfram Kahl, Thomas Ströhlein).- Symbol Table.- Addresses of Contributors.
About the author
Dr. Gunther Schmidt gilt international als einer der maßgeblichen Pioniere in der Entwicklung einer Integration systemischer (auch familientherapeutischer) Modelle und der kompetenzfokussierenden Konzepte Erickson'scher Hypnotherapie zu einem ganzheitlich-lösungsfokussierenden Konzept für Beratung und Psychotherapie. Im deutschsprachigen Raum begründete er mit seinen, durch Milton Erickson angeregten Beiträgen die 'lösungsorientierte Wende' in der systemischen Familientherapie ebenso wie den Aufbau kompetenz- und lösungsorientierter Kurzzeittherapie im Bereich z.B. von Suchtproblemen, Psychosomatik und der Therapie von massiv traumatisierten Menschen. Die von ihm entwickelten systemisch- hypnotherapeutischen Modelle für Organisationsberatung, Team- und Gruppenarbeit und Coaching tragen wesentlich zu einem intensivierten ressourcenorientierten Beratungsverständnis bei. 2011 wurde Schmidt für sein Lebenswerk mit dem Life Achivement Award ausgezeichnet.
