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We apply a paraconsistent logic to reason about fractions.

We apply a paraconsistent logic to reason about fractions.

Plaatsbepaling van Rekenen-Informatica als perspectief op elementair rekenen vanuit de informatica.

Six assertions concerning the status of Bitcoin are formulated and defended: (i) Bitcoin is not and will not become a currency-like informational commodity, (ii) currency-like informational commodities that aren’t currencies must be frauds, (ii) specific BTC amounts may become monetized and thus may be turned into financial assets, (iii) currently no BTC amounts are monetized in any currency area and therefore none are financial assets, (iv) by means of burocratic steps only some BTC volumes can be turned in to an informational currency within a given currency area, modified client software is not required for that step, (v) if a specific amount of BTC qualifies as currency, it also qualifies as money, (vi) moneyness of Bitcoin, or rather of a specific occurrence of an amount of BTC, should be questioned only after one has agreed positively on its status as a financial asset, and negatively on its status as an amount of currency. Factions in the Bitcoin promoting movement are viewed from a perspective of organizational multi-threading. Different factions of the Bitcoin movement may wish to see status issues about Bitcoin settled in different ways. Overall consistency in these matters should not be expected from the union of factions in the Bitcoin movement.

We add probabilistic features to basic thread algebra and its extensions with thread-service interaction and strategic interleaving. Here, threads represent the behaviours produced by instruction sequences under execution and services represent the behaviours exhibited by the components of execution environments of instruction sequences. In a paper concerned with probabilistic instruction sequences, we proposed several kinds of probabilistic instructions and gave an informal explanation for each of them. The probabilistic features added to the extension of basic thread algebra with thread-service interaction make it possible to give a formal explanation in terms of non-probabilistic instructions and probabilistic services. The probabilistic features added to the extensions of basic thread algebra with strategic interleaving make it possible to cover strategies corresponding with probabilistic scheduling algorithms.

Integer arithmetic is specified according to three views: unary, binary, and decimal notation. In each case we find a ground confluent and terminating datatype defining rewrite system. In each case the resulting datatype is a canonical term algebra which extends a corresponding canonical term algebra for natural numbers. For each view, we also consider an alternative rewrite system.

We present a formal system for proving the partial correctness of a single-pass instruction sequence as considered in program algebra by decomposition into proofs of the partial correctness of segments of the single-pass instruction sequence concerned. The system is similar to Hoare logics, but takes into account that, by the presence of jump instructions, segments of single-pass instruction sequences may have multiple entry points and multiple exit points.

Natural numbers with zero, one, successor, addition and multiplication, constitute a classic example of an abstract datatype amenable for equational initial algebra specification. Datatype defining rewrite systems provide a specification which at the same time is a complete, that is confluent and strongly terminating, rewrite system thereby providing means for automatic implementation. Syntax for unary, binary, decimal, and hexadecimal notation is introduced and corresponding rewrite systems are designed.

It is argued that a Bitcoin-style money-like informational commodity may constitute an effective instrument for the further development of Islamic Finance. The argument involves the following elements: (i) an application of circulation theory to Bitcoin with the objective to establish the implausibility of interest payment in connection with Bitcoin, (ii) viewing a Bitcoin-like system as a money-like exclusively informational commodity with the implication that such a system need not support debt, (iii) the idea that Islamic Finance imposes different requirements compared to conventional financial policies on a money concerning its use as a tool for achieving social and economic objectives, and (iv) identification of two aspects of mining, gambling and lack of trust, that may both be considered problematic from the perspective of compliance with the rules of Islamic Finance and a corresponding proposal to modify the architecture of mining in order to improve compliance with these rules.

Deze paper bevat een verkorte beschrijving van de Nakamoto architectuur voor informational money, een positionering van Bitcoin, een "money-like informational commodity", als een verschijningsvorm van iGoud, en een bespiegeling over de vraag hoe hoe informational money het einde van Gewoon Geld in kan luiden.

Every partial function from bit strings of a given length to bit strings of a possibly different given length can be computed by a finite instruction sequence that contains only instructions to set and get the content of Boolean registers, forward jump instructions, and a termination instruction. We look for an equivalence relation on instruction sequences of this kind that captures to a reasonable degree the intuitive notion that two instruction sequences express the same algorithm.

Een weide is zowel een generalisatie als een expansie van een lichaam. Als generalisatie is de weide bekend als von Neumann reguliere ring, voor de expansie met inverse heeft de wiskunde geen naam. Van het daarvoor gebruikte Engelse "meadow" maak ik hier "weide". In een weide bestaat de expressie 1/0 en is de vraag naar de betekenis ervan onontkoombaar. In een conservatieve weide geldt 1/0 = 0, en in een gewone weide geldt 1/0 = a, een nieuwe waarde van het type getal. Rekenen in een weide heeft als bijzondere eigenschap in vergelijking met rekenen in een lichaam dat er een duidelijke notie van expressies is waarbij de status van inverse of deling volstrekt vergelijkbaar is met de status van optellen (som) en vermenigvuldigen (product). Het rekenen in een weide kan worden gezien als werken met een beperkt en overzichtelijk aantal herschrijfregels.

Een poging tot beschrijven en duiden van Bitcoin, een "money-like informational commodity". Voordracht College Tour, Spui 2, 5 februari 2014, 20.00-20.45.

Promises, impositions, proposals, predictions, and suggestions are categorized as voluntary co-operational methods. The class of voluntary co-operational methods is included in the class of so-called directionals. Directionals are mechanisms supporting the mutual coordination of autonomous agents. Notations are provided capable of expressing residual fragments of directionals. An extensive example, involving promises about the suitability of programs for tasks imposed on the promisee is presented. The example illustrates the dynamics of promises and more specifically the corresponding mechanism of trust updating and credibility updating. Trust levels and credibility levels then determine the way certain promises and impositions are handled. The ubiquity of promises and impositions is further demonstrated with two extensive examples involving human behaviour: an artificial example about an agent planning a purchase, and a realistic example describing technology mediated interaction concerning the solution of pay station failure related problems arising for an agent intending to leave the parking area.

Promise Theory bridges the worlds of semantics and dynamics to describe interactions between autonomous agencies within a system. It provides a semi-formal language for modelling intent and its outcome, which results in a chemistry for cooperative behaviour. This book is aimed at scientists and engineers. It introduces readers to promises in a practical manner, keeping within the paradigm of `voluntary cooperation'. The book draws on examples from the real world, with a special emphasis on computers and information systems.

A survey is given of issues regarding division by zero, in particular in connection with the presentation of elementary mathematics. The viewpoint is defended that accepting 1/0 as a valid expression is harmless, and that setting its value equal to 0 is useful.

We consider the signatures Σm=(0,1,−,+,⋅, −1) of meadows and (Σm,s) of signed meadows. We give two complete axiomatizations of the equational theories of the real numbers with respect to these signatures. In the first case, we extend the axiomatization of zero-totalized fields by a single axiom scheme expressing formal realness; the second axiomatization presupposes an ordering. We apply these completeness results in order to obtain complete axiomatizations of the complex numbers.

The Kolmogorov axioms for probability mass functions are phrased in the context of signed meadows.

The Karatsuba multiplication algorithm is an algorithm for computing the product of two natural numbers represented in the binary number system. This means that the algorithm actually computes a function on bit strings. The restriction of this function to bit strings of any given length can be computed according to the Karatsuba multiplication algorithm by a finite instruction sequence that contains only instructions to set and get the content of Boolean registers, forward jump instructions, and a termination instruction. We describe the instruction sequences concerned for the restrictions to bit strings of the different lengths by uniform terms from an algebraic theory.

We present an approach to non-uniform complexity in which single-pass instruction sequences play a key part, and answer various questions that arise from this approach. We introduce several kinds of non-uniform complexity classes. One kind includes a counterpart of the well-known non-uniform complexity class P/poly and another kind includes a counterpart of the well-known non-uniform complexity class NP/poly. Moreover, we introduce a general notion of completeness for the non-uniform complexity classes of the latter kind. We also formulate a counterpart of the well-known complexity theoretic conjecture that NP is not included in P/poly. We think that the presented approach opens up an additional way of investigating issues concerning non-uniform complexity.

We develop an algebraic theory of synchronous dataflow networks. First, a basic algebraic theory of networks, called BNA (Basic Network Algebra), is introduced. This theory captures the basic algebraic properties of networks. For synchronous dataflow networks, it is subsequently extended with additional constants for the branching connections that occur between the cells of synchronous dataflow networks and axioms for these additional constants. We also give two models of the resulting theory, the one based on stream transformers and the other based on processes as considered in process algebra.

An alignment is developed between the terminology of outcome oriented decision taking and a terminology for promise issuing. Differences and correspondences are investigated between the concepts of decision and promise. For decision taking, two forms are distinguished: the external outcome delivering form and internalized decision taking. Internalized decision taking is brought in connection with Marc Slors' theory of self-programming. Examples are produced for decisions and promises in four different several settings each connected with software technology: instruction sequence effectuation, informational money transfer, budget announcement, and division by zero.

A program is a finite piece of data that produces a (possibly infinite) sequence of primitive instructions. From scratch we develop a linear notation for sequential, imperative programs, using a familiar class of primitive instructions and so-called repeat instructions, a particular type of control instructions. The resulting mathematical structure is a semigroup. We relate this set of programs to program algebra (PGA) and show that a particular subsemigroup is a carrier for PGA by providing axioms for single-pass congruence, structural congruence, and thread extraction. This subsemigroup characterizes periodic single-pass instruction sequences and provides a direct basis for PGA's toolset.

The famous new money Bitcoin is classified as a technical informational money (TIM). Besides introducing the idea of a TIM, a more extreme notion of informational money will be developed: exclusively informational money (EXIM). The informational coins (INCOs) of an EXIM can be in control of an agent but are not owned by any agent. INCOs of an EXIM cannot be stolen, but they can be lost, or thrown away. The difference between an EXIM and a TIM shows up when considering a user perspective on security matters. Security for an EXIM user is discussed in substantial detail, with the remarkable conclusion that computer security (security models, access control, user names, passwords, firewalls etc.) is not always essential for an EXIM, while the application of cryptography based information security is unavoidable for the use of an EXIM. Bitcoin seems to meet the criteria of an EXIM, but the assertion that "Bitcoin is an EXIM", might also be considered problematic. As a thought experiment we will contemplate Bitguilder, a hypothetical copy of Bitcoin that qualifies as an EXIM. A business ethics assessment of Bitcoin is made which reveals a number of worries. By combining Bitguilder with a so-called technical informational near-money (TINM) a dual money system, having two units with a fluctuating rate, may be obtained. It seems that a dual money can remedy some, but not all, of the ethical worries that arise when contemplating Bitcoin after hypothetically having become a dominant form of money. The contributions that Bitcoin's designers can potentially make to the evolution of EXIMs and TIMs is analyzed in terms of the update of the portfolio of money related natural kinds that comes with Bitcoin.

A collection of questions about Bitcoin and its hypothetical relatives Bitguilder and Bitpenny is formulated. These questions concern technical issues about protocols, security issues, issues about the formalizations of informational monies in various contexts, and issues about forms of use and misuse. Some questions are formulated in the more general setting of informational monies and near-monies. We also formulate questions about legal, psychological, and ethical aspects of informational money. Finally we formulate a number of questions concerning the economical merits of and outlooks for Bitcoin.

The secure hash function SHA-256 is a function on bit strings. This means that its restriction to the bit strings of any given length can be computed by a finite instruction sequence that contains only instructions to set and get the content of Boolean registers, forward jump instructions, and a termination instruction. We describe such instruction sequences for the restrictions to bit strings of the different possible lengths by means of uniform terms from an algebraic theory.

Motivated by an intention to remedy current complications with Dutch terminology concerning informatics, the term informaticology is positioned to denote an academic counterpart of informatics where informatics is conceived of as a container for a coherent family of practical disciplines ranging from computer engineering and software engineering to network technology, data center management, information technology, and information management in a broad sense. Informaticology escapes from the limitations of instrumental objectives and the perspective of usage that both restrict the scope of informatics. That is achieved by including fiction science in informaticology and by ranking fiction science on equal terms with computer science and data science, and framing (the study of) game design, development, assessment and distribution, ranging from serious gaming to entertainment gaming, as a chapter of fiction science. A suggestion for the scope of fiction science is specified in some detail. In order to illustrate the coherence of informaticology thus conceived, a potential application of fiction to the ontology of instruction sequences and to software quality assessment is sketched, thereby highlighting a possible role of fiction (science) within informaticology but outside gaming.

Decision Taking is discussed in the context of the role it may play for a selling agent in a search market, in particular for agents involved in the sale of valuable and relatively unique items, such as a dwelling, a second hand car, or a second hand recreational vessel. Detailed connections are made between the architecture of decision making processes and a sample of software technology based concepts including instruction sequences, multi-threading, and thread algebra. Ample attention is paid to the initialization or startup of a thread dedicated to achieving a given objective, and to corresponding decision taking. As an application, the selling of an item is taken as an objective to be achieved by running a thread that was designed for that purpose.

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.

This book demonstrates that the concept of an instruction sequence offers a novel and useful viewpoint on issues relating to diverse subjects in computer science. Selected issues relating to well-known subjects from the theory of computation and the area of computer architecture are rigorously investigated in this book thinking in terms of instruction sequences. The subjects from the theory of computation, to wit the halting problem and non-uniform computational complexity, are usually investigated thinking in terms of a common model of computation such as Turing machines and Boolean circuits. The subjects from the area of computer architecture, to wit instruction sequence performance, instruction set architectures and remote instruction processing, are usually not investigated in a rigorous way at all.

In a previous paper, we presented several extensions of ACP with conditional expressions, including one with a retrospection operator on conditions to allow for looking back on conditions under which preceding actions have been performed. In this paper, we add a constant for a process that is only capable of terminating successfully to those extensions of ACP, which can be very useful in applications. It happens that in all cases the addition of this constant is unproblematic. 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.

Decision taking can be performed as a service to other parties and it is amenable to outtasking rather than to outsourcing. Outtasking decision taking is compatible with selfsourcing of decision making activities carried out in preparation of decision taking. Decision taking as a service (DTaaS) is viewed as an instance of so-called decision casting. Preconditions for service casting are examined, and compliance of decision taking with these preconditions is confirmed. Potential advantages and disadvantages of using decision taking as a service are considered.

Decision taking is discussed in the context of the role it may play for various types of agents, and it is contrasted with action determination. Some remarks are made about the role of decision taking and action determination in the ongoing debate concerning the reverse polder development of the hertogin Hedwige polder.

The strong, intermediate, and weak Turing impossibility properties are introduced. Some facts concerning Turing impossibility for stack machine programming are trivially adapted from previous work. Several intriguing questions are raised about the Turing impossibility properties concerning different method interfaces for stack machine programming.

The behaviour produced by an instruction sequence under execution is a behaviour to be controlled by some execution environment: each step performed actuates the processing of an instruction by the execution environment and a reply returned at completion of the processing determines how the behaviour proceeds. The increasingly occurring case where the processing takes place remotely involves the generation of a stream of instructions to be processed and a remote execution unit that handles the processing of this stream of instructions. We use process algebra to describe the behaviours produced by instruction sequences under execution and to describe two protocols implementing these behaviours in the case of remote processing. We also show that all finite-state behaviours considered in process algebra can be produced by instruction sequences under execution.

It is argued that arguments for strict prohibition of interests must be based on the use of arguments from authority. This is carried out by first making a survey of so-called dialectical roots for interest prohibition and then demonstrating that for at least one important positive interest bearing financial product, the savings account with interest, its prohibition cannot be inferred from a match with any of these root cases.

An attempt is made to define the concept of execution of an instruction sequence. It is found to be a special case of directly putting into effect of an instruction sequence. Directly putting into effect of an instruction sequences comprises interpretation as well as execution. Directly putting into effect is a special case of putting into effect with other special cases classified as indirectly putting into effect.

Four options for assigning a meaning to Islamic Logic are surveyed including a new proposal for an option named "Real Islamic Logic" (RIL). That approach to Islamic Logic should serve modern Islamic objectives in a way comparable to the functionality of Islamic Finance. The prospective role of RIL is analyzed from several perspectives: (i) parallel distributed systems design, (ii) reception by a community structured audience, (iii) informal logic and applied non-classical logics, and (iv) (in)tractability and artificial intelligence.

The notion of an instruction sequence fault is considered from various perspectives. Four different viewpoints on what constitutes a fault, or how to use the notion of a fault, are formulated. An integration of these views is proposed.

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. A decision effect is any consequence of putting a decision outcome into effect. Decision outcomes must be expected by the decider to lead to certain decision effects, by way of their being put into effect. The availability of a model or of a theory of the causal chain leading from a decision outcome to one or more decision effects is assumed for the decision taker, otherwise the decision outcome is merely an utterance. Decision effectiveness measures the decision effects against objectives meant to be served with the decision. Decision taking is positioned amidst many similar notions including: decision making, decision process, decision making process, decision process making, decision engineering, decision progression, and decision progression production. Decision making is operationally defined as an informatics related activity consisting of the production of progressions from threads, thus casting decision making competence as an informatics competence. Short-circuit logic underlies the production of decision making progressions from instruction sequences that codify prepared decision making processes. Decision taking can constitute the primary task of dedicated agents. Human agents in such roles are professional decision takers. Multi-threading is essential for the professional decision taker.

Interest prohibition theory concerns theoretical aspects of interest prohibition. We attempt to lay down some aspects of interest prohibition theory wrapped in a larger framework of informal logic. The reason for this is that interest prohibition theory has to deal with a variety of arguments which is so wide that a limitation to so-called correct arguments in advance is counterproductive. We suggest that an application specific informal logic must be developed for dealing with the principles of interest prohibition theory.

We give a rough sketch of the Judaic, Greek, Islamic and Christian positions in the matter of interest prohibition during the last few millennia and discuss the way in which interest prohibition is dealt with in Islamic finance, the problems with authority-based arguments for interest prohibition, and the prospects of interest prohibition with the advent of electronic money.

Principles of financial product synthesis from a few basic financial products constitute an interesting research topic inspired by Islamic finance. We make an effort to answer general questions that should be answered before starting to investigate the main issues concerning this topic with the formalization of financial products and principles of financial product synthesis. We also outline the outcome of some preparatory explorations, which have been conducted with the purpose to form a reasonable preliminary picture of the details of financial products that are relevant to the study of the principles of financial product synthesis.

Outsourcing, the passing on of tasks by organizations to other organizations, often including the personnel and means to perform these tasks, has become an important IT-business strategy over the past decades. We investigate imaginative definitions for outsourcing relations and outsourcing transformations. Abstract models of an extreme and unrealistic simplicity are considered in order to investigate possible definitions of outsourcing. Rather than covering all relevant practical cases an imaginative definition of a concept provides obvious cases of its instantiation from which more refined or liberal definitions may be derived. A definition of outsourcing induces to a complementary definition of insourcing. Outsourcing and insourcing have more complex variations in which multiple parties are involved. All of these terms both refer to state transformations and to state descriptions pertaining to the state obtained after such transformations. We make an attempt to disambiguate the terminology in that respect and we make an attempt to characterize the general concept of sourcing which captures some representative cases. Because mereology is the most general theory of parthood relations we coin business mereology as the general theory in business studies which concerns the full variety of sourcing relations and transformations.

A steering fragment of an instruction sequence consists of a sequence of steering instructions. These are decision points involving the check of a propositional statement in sequential logic. The question is addressed why composed propositional statements occur in steering fragments given the fact that a straightforward transformation allows their elimination. A survey is provided of constraints that may be implicitly assumed when composed propositional statements occur in a meaningful instruction sequence.