Search

Lewis Carroll has been credited for developing a “Method of Trees” for solving multi-literal sorites problems, which anticipates several aspects of contemporary “tableau” or tree systems of logical proof. In particular, Carroll’s method pioneers the use of branching paths as a means of displaying or illustrating inclusive disjunction. However, rather than focusing on the respects in which Carroll’s tree diagrams resemble contemporary tree systems, I propose to focus instead on significant aspects in which they differ. In particular, I will show how the sorts of multi-literal sorites problems that Carroll’s method of trees is designed to solve are particularly ill-suited for resolution by more contemporary tree methods. I will also show how Carroll likely used something like this method, not only to solve but also to craft some of the trickier logical puzzles for which he is also famous.

This article examines the evolution of the concept of existence in modern visual representation and reasoning, highlighting important milestones. In the late eighteenth century, during the so-called golden age of visual reasoning, nominalism reigned supreme and there was limited scope for existential import or individuals in logic diagrams. By the late nineteenth century, a form of realism had taken hold, whose existential commitments continue to dominate many areas in logic and visual reasoning to this day. Physical, metaphysical, epistemological, and linguistic positions underlie both nominalist and realist views. Since the paradigmatic works on visual reasoning in the 1990s, formal diagram systems have been developed that revive either the nominalist or realist perspectives. Unlike in the nineteenth century, these are not motivated by philosophical views. Nevertheless, they may still have an impact on many areas of philosophy and science outside logic.

Logic diagrams have been increasingly studied and applied for a few decades, not only in logic, but also in many other fields of science. The history of logic diagrams is an important subject, as many current systems and applications of logic diagrams are based on historical predecessors. While traditional histories of logic diagrams cite pioneers such as Leibniz, Euler, Venn, and Peirce, it is not widely known that Kant and the early Kantians in Germany and England played a crucial role in popularising Euler(-type) diagrams. In this paper, the role of the Kantians in the late eighteenth and early nineteenth centuries will be analysed in more detail. It shows that diagrams (or intuition in general) were a highly contentious topic that depend on the philosophical attitude and went beyond logic to touch on issues of physics, metaphysics, linguistics and, above all, mathematics. [ABSTRACT FROM AUTHOR]

This paper analyses a hitherto unknown technique of using logic diagrams to create argument maps in eristic dialectics. The method was invented in the 1810s and -20s by Arthur Schopenhauer, who is considered the originator of modern eristic. This technique of Schopenhauer could be interesting for several branches of research in the field of argumentation: Firstly, for the field of argument mapping, since here a hitherto unknown diagrammatic technique is shown in order to visualise possible situations of arguments in a dialogical controversy. Secondly, the art of controversy or eristic, since the diagrams do not analyse the truth of judgements and the validity of inferences, but the persuasiveness of arguments in a dialogue. [ABSTRACT FROM AUTHOR]

The present text discusses whether there is a tension between aphorisms 6.1-6.13 of the Tractatus and the Church-Turing theorem about the decidability of predicate logic. We attempt to establish the following points: (i) Aphorisms 6.1-6.13 are not consistent with the Church-Turing theorem. (ii) The logical symbolism of the Tractatus, built from the N-operator, can (and should) be interpreted as expressively complete with respect to first-order formulas. (iii) Wittgenstein's reasons for believing that Logic is decidable were purely philosophical and the undecidability result shows that there are aspects of his criticisms of Frege and Russell that become unjustified in light of these results. [ABSTRACT FROM AUTHOR]

In the vein of a renewed interest in diagrammatic reasoning, this paper challenges an opposition between logic diagrams and formal languages that has traditionally been the common view in philosophy of logic and linguistics. We examine, from a philosophical point of view, what we call five dogmas of logic diagrams. These are as follows: (1) diagrams are non-linguistic; (2) diagrams are visual representations; (3) diagrams are iconic, and not symbolic; (4) diagrams are non-linear; (5) diagrams are heterogenous, and not homogenous. Using historical examples, we argue that none of these dogmas is an adequate criterion to distinguish logic diagrams from formal languages. Instead, we advocate that there is a common core between linguistic and diagrammatic representation and reasoning. • We critically examine, from a philosophical point of view, five dogmas in current research on logic diagrams that have been proposed as criteria to establish an opposition between formal language and logic diagrams. • The dogmas we consider are: (1) diagrams are non-linguistic ; (2) diagrams are visual representations; (3) diagrams are iconic , and not symbolic ; (4) diagrams are non-linear; (5) diagrams are heterogenous , and not homogenous. • We present historical examples which are not met by these criteria. • We provide a positive outlook by arguing that there is a common core between linguistic and diagrammatic representation and reasoning, which can be called 'invariance'. [ABSTRACT FROM AUTHOR]

In this paper risk assessment for ship to ship LNG bunkering is carried out by exploiting the results of the projects "Risk management system for design and operation of installations for LNG refuelling" (TRiTON) financed by the Greek government, and the "SUstainability PERformance of LNG-based maritime mobility -- Plus" (SUPERLNG PLUS) financed by Interreg-Adrion. Ship to ship bunkering constitutes a simple method when it is difficult to install new storage tanks in the port areas. In brief, risk assessment is conducted including five basic steps: a) hazard identification, b) accident sequence modeling and quantification, c) damage states identification, d) consequence assessment, and e) risk evaluation. First, the Master Logic Diagram (MLD) technique is used to identify the initial events that create a disturbance in the installation and may lead to an LNG release. Corrosion in tanks, pipelines and other parts, and excess external heat owing to a nearby external fire are some of the identified initial events. Moreover, safety functions and systems for preventing LNG release, such as emergency shut-down and pressure safety valves, are identified. Event trees are developed to describe the accident sequence from the initial event occurrence until the LNG release and define the final damage states. By exploiting available failure rate data, the frequency of each damage state is estimated. In parallel, the consequences of LNG release are assessed on the basis of the heat radiation or overpressure dose an individual receives. Finally, risk is calculated by combining the frequencies of the various damage states with the corresponding consequences. A case study for a Greek port is, herein, presented. [ABSTRACT FROM AUTHOR]

Reism or concretism are the labels for a position in ontology and semantics that is represented by various philosophers. As Kazimierz Ajdukiewicz and Jan Woleński have shown, there are two dimensions with which the abstract expression of reism can be made concrete: The ontological dimension of reism says that only things exist; the semantic dimension of reism says that all concepts must be reduced to concrete terms in order to be meaningful. In this paper we argue for the following two theses: (1) Arthur Schopenhauer has advocated a reistic philosophy of language which says that all concepts must ultimately be based on concrete intuition in order to be meaningful. (2) In his semantics, Schopenhauer developed a theory of logic diagrams that can be interpreted by modern means in order to concretize the abstract position of reism. Thus we are not only enhancing Jan Woleński’s list of well-known reists, but we are also adding a diagrammatic dimension to concretism, represented by Schopenhauer.

Logicians have often suggested that the use of Euler-type diagrams has influenced the idea of the quantification of the predicate. This is mainly due to the fact that Euler-type diagrams display more information than is required in traditional syllogistics. The paper supports this argument and extends it by a further step: Euler-type diagrams not only illustrate the quantification of the predicate, but also solve problems of traditional proof theory, which prevented an overall quantification of the predicate. Thus, Euler-type diagrams can be called the natural basis of syllogistic reasoning and can even go beyond. In the paper, these arguments are presented in connection with the book Nucleus Logicae Weisaniae by Johann Christian Lange from 1712. [ABSTRACT FROM AUTHOR]

Petri nets have been extensively applied for specification, design, verification, performance evaluation, and simulation of discrete event control systems (DECS). The usual way to verify the dynamic behaviour of DECS design is to employ a process-based model, which proves to be impractical in application because the process-based model does not usually fully correspond to the control programming behaviour. This paper proposes a sensor-based stage Petri net (SBSPN) to represent a programmable logic controller (PLC) stage logic diagram (LD) for discrete-event control design. The new technique is able to simplify the modelling process of the complex PLC program without considering the interlocking problem within the ladder diagram. An illustrated example is used to explore the new methodology. The proposed method contains the power and flexibility of the Petri net analysis prior to the PLC implementation. It is believed that this technique is significant for industry practice. [ABSTRACT FROM AUTHOR]

Logicians commonly speak in a relatively undifferentiated way about pre-Euler diagrams. The thesis of this paper, however, is that there were three periods in the early modern era in which Euler-type diagrams (line diagrams as well as circle diagrams) were expansively used. Expansive periods are characterized by continuity, and regressive periods by discontinuity: While on the one hand an ongoing awareness of the use of Euler-type diagrams occurred within an expansive period, after a subsequent phase of regression the entire knowledge about the systematic application and the history of Euler-type diagrams was lost. I will argue that the first expansive period lasted from Vives (1531) to Alsted (1614). The second period began around 1660 with Weigel and ended in 1712 with Lange. The third period of expansion started around 1760 with the works of Ploucquet, Euler and Lambert. Finally, it is shown that Euler-type diagrams became popular in the debate about intuition which took place in the 1790s between Leibnizians and Kantians. The article is thus limited to the historical periodization between 1530 and 1800.

New product ideation might be improved by identifying and applying certain well-defined schemes derived from an historical analysis of product-based trends, termed "templates." These templates might contribute to the understanding and prediction of new product emergence. The authors derive templates in a study that maps the evolution of product changes by adapting a set of intrinsic operations originally designed to uncover hidden logical patterns in technological inventions. They find that the majority of new product versions can be accounted for by as few as five templates. The authors define the five templates and show that they derive from six elementary (first principle) operators. A procedure for using the dominant template, termed "Attribute Dependency," is outlined, followed by a report of two experiments examining its usefulness in the context of product ideation. [ABSTRACT FROM AUTHOR]

The aim of this research paper is to present, on the one hand, the symbolic nature of formal logical reasoning and, on the other hand, its diagrammatic nature. Particularly, this research paper attempts to explain what means to know by means of diagrams and symbols and how this knowledge is linked to the formal nature of logic. As a concrete case of study, will be analyzed Venn diagrams as well as their teaching in the program of High School and College. [ABSTRACT FROM AUTHOR]

A logic machine is a device, electrical or mechanical, designed specifically for solving problems in formal logic. A logic diagram is a geometrical method for doing the same thing. Many ancient machines such as a compass, a clock can be an example of those logic machines. However, logic machines were not restricted to concrete objects but abstract models since ancient times. When many models especially models about learning, teaching styles are investigated, it can be easily seen that they were built on the structure of logic machines such as Kolb's learning Styles, Gregorc Learning Styles, etc. Therefore, it is important to understand the structure of those logic machines to evaluate the epistemological foundations of those models. In this regard, this paper aims to investigate logic machines in the context of learning styles models in comparison with their historical usage and to discuss the epistemological boundaries of logic machines in terms of those educational models. [ABSTRACT FROM AUTHOR]

Taking its point of departure in the origin of the notions of "diagram" and "iconicity" in Peirce's philosophy of logic, this paper reviews and discusses a series of dimensions along which such diagrams may be compared, measured and subdivided: diagrams versus images and metaphors, operational versus optimal iconicity in diagrams, diagram tokens versus diagram types, diagrams as general signs; corollarial versus theorematic diagram reasoning; pure versus applied diagrams; logic diagrams versus diagrams facilitating logical inferences; continuous versus discontinuous diagrams; diagrams in non-deductive reasoning. Most of these developments occur in the mature Peirce after the turn of the century and thus form an important part of his mature semiotics – yet, they do not relate in any simple or straight-forward manner to his attempts at enlarging his combinatorial semiotics from its bases in the three-trichotomy theory of the 1903 Syllabus over the six-trichotomy theory of 1904–1906 to the sketchlike ten-trichotomy version of 1908, where diagrams rarely figure in the names of sign-types discussed – why? [ABSTRACT FROM AUTHOR]

The predominant form of logic before Frege, the logic of terms has been largely neglected since. Terms may be singular, empty or plural in their denotation. This article, presupposing propositional logic, provides an axiomatization based on an identity predicate, a predicate of non-existence, a constant empty term, and term conjunction and negation. The idea of basing term logic on existence or non-existence, outlined by Brentano, is here carried through in modern guise. It is shown how categorical syllogistic reduces to just two forms of inference. Tree and diagram methods of testing validity are described. An obvious translation into monadic predicate logic shows the system is decidable, and additional expressive power brought by adding quantifiers enables numerical predicates to be defined. The system’s advantages for pedagogy are indicated.

Abstract: Influence diagrams (IDs) are one of the most commonly used graphical and mathematical decision models for reasoning under uncertainty. In conventional IDs, both probabilities representing beliefs and utilities representing preferences of decision makers are precise point‐valued parameters. However, it is usually difficult or even impossible to directly provide such parameters. In this paper, we extend conventional IDs to allow IDs with interval‐valued parameters (IIDs) and develop a counterpart method of Copper's evaluation method to evaluate IIDs. IIDs avoid the difficulties attached to the specification of precise parameters and provide the capability to model decision‐making processes in a situation that the precise parameters cannot be specified. The counterpart method to Copper's evaluation method reduces the evaluation of IIDs into inference problems of Bayesian networks with interval‐valued probabilities. An algorithm based on the approximate inference of Bayesian networks with interval‐valued probabilities is proposed, and extensive experiments are conducted. The experimental results indicate that the proposed algorithm can find the optimal strategies effectively in IIDs, and the interval‐valued expected utilities obtained by proposed algorithm are contained in those obtained by exact evaluating algorithms. The newly development approach would significantly extend the range of IDs for managerial decision support applications where parameters of variables can be specifically defined by only estimated intervals. [ABSTRACT FROM AUTHOR]

The paper presents a synthesis strategy oriented to the implementation of multi-output functions into LUT-based FPGA. The key elements of the proposed method include the decomposition of multi-output functions and a technology mapping strategy. The essence of the proposed approach is based on searching for an appropriate decomposition path and the idea of cosharing logic resources. In the process of looking for cosharing logic resources, the algorithm which searches for equivalence classes plays a vital role, and is implemented on the basis of proposed modifications of BDD diagrams. The results obtained were compared with synthesis results from competitive methods. [ABSTRACT FROM AUTHOR]

Marken and Shaffer (Exp Brain Res 235:1835-1842, 2017) have argued that the power law of movement, which is generally thought to reflect the mechanisms that produce movement, is actually an example of what Powers (Psychol Rev 85:417-435, 1978) dubbed a behavioral illusion, where an observed relationship between variables is seen as revealing something about the mechanisms that produce a behavior when, in fact, it does not. Zago et al. (Exp Brain Res. 10.1007/s0022-017-5108-z, 2017) and Taylor (Exp Brain Res, 10.1007/s00221-018-5192-8, 2018) have “reappraised” this argument, claiming that it is based on logical, mathematical, statistical and theoretical errors. In the present paper we answer these claims and show that the power law of movement is, indeed, an example of a behavioral illusion. However, we also explain how this apparently negative finding can point the study of movement in a new and more productive direction, with research aimed at understanding movement in terms of its purposes rather than its causes. [ABSTRACT FROM AUTHOR]

From the mid-1600s to the beginning of the eighteenth century, there were two main circles of German scholars which focused extensively on diagrammatic reasoning and representation in logic. The first circle was formed around Erhard Weigel in Jena and consists primarily of Johann Christoph Sturm and Gottfried Wilhelm Leibniz; the second circle developed around Christian Weise in Zittau, with the support of his students, particularly Samuel Grosser and Johann Christian Lange. Each of these scholars developed an original form of using geometric diagrams in logic. In this paper, I will trace the historical notes of John Venn and other modern logicians back to the original works published in the Weigel and Weise circles and describe the development of using geometric figures for logical reasoning and representation in that period of time. [ABSTRACT FROM PUBLISHER]

Background: Practical experience suggests that usage and understanding of UML diagrams is greatly affected by the quality of their layout. While existing research failed to provide conclusive and comprehensive evidence in support of this hypothesis, our own previous work provided substantial evidence to this effect, also suggesting diagram size as a relevant factor, for a range of diagram types and layouts.Aims: Since there is no generally accepted precise notion of “diagram size,” we first need to operationalize this concept, analyze its impact on diagram understanding, and derive practical advice from our findings.Method: We define three alternative, plausible metrics. Since they are all highly correlated on a large sample of UML diagrams, we opt for the simplest one. We use it to re-analyze existing experimental data on diagram understanding.Results: We find a strong negative correlation between diagram size and modeler performance. Our results are statistically highly significant and exhibit a very large degree of validity. We utilize these results to derive a recommendation on diagram sizes that are, on average, optimal for model understanding. These recommendations are implemented in a plug-in to a widely used modeling tool, providing continuous feedback about diagram size to modelers.Conclusions: The effect sizes are varying, but generally suggest that the impact of size matches or exceeds that of other factors in diagram understanding. With the guideline and tool, modelers are steered toward avoiding too large diagrams. [ABSTRACT FROM AUTHOR]

A seminal article by Margaret Baron, published in 1969, explored the history of set diagrams (Venn diagrams). However, Baron did not look beyond the evidence of European sources. This article presents evidence of a literary simile from ancient India that exemplifies the idea of a larger circle including within it many smaller circles, each circle standing for an ethical concept. The simile - an elephant's footprint enclosing the footprints of smaller animals - first appears in the Buddhist Canon, and it was used occasionally in South Asian literature through the following millennia until the eighteenth century. I argue that the Elephant's Foot simile can be added to Baron's catalogue of historical cases where ancient authors were using language that implied a simple concept of logical sets. [ABSTRACT FROM AUTHOR]