By H. Andreka, J.D.Monk, I.Nemeti (eds.)

The János Bolyai Mathematical Society held an Algebraic good judgment Colloquium among 8-14 August, 1988, in Budapest. An introductory sequence of lectures on cylindric and relation algebras used to be given by means of Roger D. Maddux.

The current quantity isn't limited to papers provided on the convention. in its place, it truly is aimed toward supplying the reader with a comparatively coherent examining on Algebraic good judgment (AL), with an emphasis on present learn. shall we now not hide the entire of AL, the most vital omission being that the class theoretic types of AL have been taken care of simply of their connections with Tarskian (or extra conventional) AL. the current quantity was once ready in collaboration with the editors of the lawsuits of Ames convention on AL (Springer Lecture Notes in machine technological know-how Vol. 425, 1990), and a quantity of Studia Logica dedicated to AL which used to be scheduled to visit press within the fall of 1990. many of the papers initially submitted to the current quantity look in a single of the latter.

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305). Usually, one is only interested in postconditions q asserting that the loop-condition b is violated and that the precondition p holds: q — p Ab. Limiting ourselves to such cases we derive a satisfying result about the weakest precondition of while-loops: (3) { b A p } B { p } => p A w p ( a , L ) C w p ( a , b A p ) . R ELA TIO N A L G E B R A AND LO G IC OF PR O G RA M S 53 P ro o f. 3 it is shown that {p}a{bAp} if {bAp}B{p}. 6 that a is totally correct wrt. the precon dition p A wp(o:, L) and the postcondition b A p.

We have to distinguish between two cases: Firstly, we consider the case that every finite computation sequence ix i,S i)i*l with state si G p be finite and ends additionally with a situation (xn, s n) the state component sn of which is contained in q. 3) Non-terminal output situations are interesting in the case of recursive programs. R ELA TIO N A L G E B R A AND LO G IC OF PR O G RA M S 45 P a rtia l C o rrectn ess. *

1. Introduction Abstract relation algebra is proposed as a means to describe semantics, cor rectness, and termination of programs. As an example we choose a language of flowchart-program schemata. We concentrate entirely on the semantic level and interpret programs essentially as pairs of directed graphs, viz. a control flow graph and a situation transition graph. , we do not have an exactly defined program syntax but use an informal transition from syntax to the graphs. Nevertheless, it is also possible to define this transition in ductively assuming a set of automatic statements and certain program form ing constructs like sequential composition R ; S', non-deterministic branching Гр : R | q : s j , and so on.