Abstract:
A decision is an act or event of decision taking. Decision making always includes decision taking, the latter not involving significant exchanges with non-deciding agents. A decision outcome is a piece of storable information constituting the result of a decision. Decision outcomes are typed, for instance: plan, command, assertion, or boolean reply to a question. Decision outcomes are seen by an audience and autonomous actions from the audience is supposed to realize the putting into effect of a decision outcome, thus leading to so-called decision effects. Decision outcomes are supposedly expected by the decider. Using a model or a theory concerning the causal chain leading from a decision outcome to one or more decision effects may support a decision taker decision taker in predicting plausible decision effects for candidate decision outcomes. Decision taking is positioned amidst many related notions including: decision making, decision process, decision making process, decision process making, decision engineering, decision progression, and decision progression production.

Abstract:
Software testing is presented as a so-called theme within which different authors and groups have defined different subjects each of these subjects having a different focus on testing. A uniform concept of software testing is non-existent and the space of possible coherent perspectives on software testing, each fitting within the theme, is viewed as being spanned by five dimensions, each dimension representing two opposite views with a variety of intermediate views in between. Instruction sequences are used as a simple theoretical conceptualization of computer programs. A theory of instruction sequence testing may serve as a model for a theory of software testing. Instruction sequences testing is considered a new topic for which definitions may be freely contemplated without being restricted by existing views on software testing. The problem of developing a theory of instruction sequence testing is posed. A survey is given of motivations and scenarios for developing a theory of instruction sequence testing.

Abstract:
Sequential propositional logic deviates from ordinary propositional logic by taking into account that during the sequential evaluation of a propositional statement,atomic propositions may yield different Boolean values at repeated occurrences. We introduce `free valuations' to capture this dynamics of a propositional statement's environment. The resulting logic is phrased as an equationally specified algebra rather than in the form of proof rules, and is named `proposition algebra'. It is strictly more general than Boolean algebra to the extent that the classical connectives fail to be expressively complete in the sequential case. The four axioms for free valuation congruence are then combined with other axioms in order define a few more valuation congruences that gradually identify more propositional statements, up to static valuation congruence (which is the setting of conventional propositional logic). Proposition algebra is developed in a fashion similar to the process algebra ACP and the program algebra PGA, via an algebraic specification which has a meaningful initial algebra for which a range of coarser congruences are considered important as well. In addition infinite objects (that is propositional statements, processes and programs respectively) are dealt with by means of an inverse limit construction which allows the transfer of knowledge concerning finite objects to facts about infinite ones while reducing all facts about infinite objects to an infinity of facts about finite ones in return.

Abstract:
We introduce an algebra of instruction sequences by presenting asemigroup C in which programs can be represented without directionalbias: in terms of the next instruction to be executed, C has both forwardand backward instructions and a C-expression can be interpretedstarting from any instruction. We provide equations for thread extraction,i.e., C’s program semantics. Then we consider thread extractioncompatible (anti-)homomorphisms and (anti-)automorphisms. Finallywe discuss some expressiveness results.

Abstract:
We study several aspects of the behaviours produced by instruction sequences under execution in the setting of the algebraic theory of processes known as ACP. We use ACP to describe the behaviours produced by instruction sequences under execution and to describe two protocols implementing these behaviours in the case where the processing of instructions takes place remotely. We also show that all finite-state behaviours considered in ACP can be produced by instruction sequences under execution.

Abstract:
This paper concerns instruction sequences that contain probabilistic instructions, i.e. instructions that are themselves probabilistic by nature. We propose several kinds of probabilistic instructions, provide an informal operational meaning for each of them, and discuss related work. On purpose, we refrain from providing an ad hoc formal meaning for the proposed kinds of instructions. We also discuss the approach of projection semantics, which was introduced in earlier work on instruction sequences, in the light of probabilistic instruction sequences.

Abstract:
This paper is concerned with the status of 1/0 and ways to deal with it. These matters are treated in the setting of Komori fields, also known as non-trivial cancellation meadows. Different viewpoints on the status of 1/0 exist in mathematics and theoretical computer science. We give a simple account of how mathematicians deal with 1/0 in which a customary convention among mathematicians plays a prominent part, and we make plausible that a convincing account, starting from the popular computer science viewpoint that 1/0 is undefined, by means of some logic of partial functions is not attainable.

Abstract:
We perceive programs as single-pass instruction sequences. A single-pass instruction sequence under execution is considered to produce a behaviour to be controlled by some execution environment. Threads as considered in basic thread algebra model such behaviours. We show that all regular threads, i.e. threads that can only be in a finite number of states, can be produced by single-pass instruction sequences without jump instructions if use can be made of Boolean registers. We also show that, in the case where goto instructions are used instead of jump instructions, a bound to the number of labels restricts the expressiveness.

Abstract:
We introduce the notion of an ACP process algebra. The models of the axiom system ACP are the origin of this notion. ACP process algebras have to do with processes in which no data are involved. We also introduce the notion of a meadow enriched ACP process algebra, which is a simple generalization of the notion of an ACP process algebra to processes in which data are involved. In meadow enriched ACP process algebras, the mathematical structure for data is a meadow.

Abstract:
We dwell on how a definition of a theoretical concept of an operating system, suitable to be incorporated in a mathematical theory of operating systems, could look like. This is considered a valuable preparation for the development of a mathematical theory of operating systems.