Shahid Rahman

This monograph proposes a new (dialogical) way of studying the different forms of correlational inference, known in the Islamic jurisprudence as qiyas. According to the authors’ view, qiyas represents an innovative and sophisticated form of dialectical reasoning that not only provides new epistemological insights into legal argumentation in general (including legal reasoning in Common and Civil Law) but also furnishes a fine-grained pattern for parallel reasoning which can be deployed in a wide range of problem-solving contexts and does not seem to reduce to the standard forms of analogical reasoning studied in contemporary philosophy of science and argumentation theory. After an overview of the emergence of qiyas and of the work of al-Shirazi penned by Soufi Youcef, the authors discuss al-Shirazi’s classification of correlational inferences of the occasioning factor (qiyas al-'illa). The second part of the volume deliberates on the system of correlational inferences by indication and resemblance (qiyas al-dalala, qiyas al-shabah). The third part develops the main theoretical background of the authors’ work, namely, the dialogical approach to Martin-Löf's Constructive Type Theory. The authors present this in a general form and independently of adaptations deployed in parts I and II. Part III also includes an appendix on the relevant notions of Constructive Type Theory, which has been extracted from an overview written by Ansten Klev. The book concludes with some brief remarks on contemporary approaches to analogy in Common and Civil Law and also to parallel reasoning in general.

This monograph proposes a new (dialogical) way of studying the different forms of correlational inference, known in the Islamic jurisprudence as qiyas. According to the authors’ view, qiyas represents an innovative and sophisticated form of dialectical reasoning that not only provides new epistemological insights into legal argumentation in general (including legal reasoning in Common and Civil Law) but also furnishes a fine-grained pattern for parallel reasoning which can be deployed in a wide range of problem-solving contexts and does not seem to reduce to the standard forms of analogical reasoning studied in contemporary philosophy of science and argumentation theory. After an overview of the emergence of qiyas and of the work of al-Shirazi penned by Soufi Youcef, the authors discuss al-Shirazi’s classification of correlational inferences of the occasioning factor (qiyas al-'illa). The second part of the volume deliberates on the system of correlational inferences by indication and resemblance (qiyas al-dalala, qiyas al-shabah). The third part develops the main theoretical background of the authors’ work, namely, the dialogical approach to Martin-Löf's Constructive Type Theory. The authors present this in a general form and independently of adaptations deployed in parts I and II. Part III also includes an appendix on the relevant notions of Constructive Type Theory, which has been extracted from an overview written by Ansten Klev. The book concludes with some brief remarks on contemporary approaches to analogy in Common and Civil Law and also to parallel reasoning in general.

This monograph proposes a new way of implementing interaction in logic. It also provides an elementary introduction to Constructive Type Theory (CTT). The authors equally emphasize basic ideas and finer technical details. In addition, many worked out exercises and examples will help readers to better understand the concepts under discussion. One of the chief ideas animating this study is that the dialogical understanding of definitional equality and its execution provide both a simple and a direct way of implementing the CTT approach within a game-theoretical conception of meaning. In addition, the importance of the play level over the strategy level is stressed, binding together the matter of execution with that of equality and the finitary perspective on games constituting meaning. According to this perspective the emergence of concepts are not only games of giving and asking for reasons (games involving Why-questions), they are also games that include moves establishing how it is that the reasons brought forward accomplish their explicative task. Thus, immanent reasoning games are dialogical games of Why and How.

This monograph proposes a new way of implementing interaction in logic. It also provides an elementary introduction to Constructive Type Theory (CTT). The authors equally emphasize basic ideas and finer technical details. In addition, many worked out exercises and examples will help readers to better understand the concepts under discussion. One of the chief ideas animating this study is that the dialogical understanding of definitional equality and its execution provide both a simple and a direct way of implementing the CTT approach within a game-theoretical conception of meaning. In addition, the importance of the play level over the strategy level is stressed, binding together the matter of execution with that of equality and the finitary perspective on games constituting meaning. According to this perspective the emergence of concepts are not only games of giving and asking for reasons (games involving Why-questions), they are also games that include moves establishing how it is that the reasons brought forward accomplish their explicative task. Thus, immanent reasoning games are dialogical games of Why and How.

This title links two of the most dominant research streams in philosophy of logic, namely game theory and proof theory. As the work’s subtitle expresses, the authors will build this link by means of the dialogical approach to logic. One important aspect of the present study is that the authors restrict themselves to the logically valid fragment of Constructive Type Theory (CTT). The reason is that, once that fragment is achieved the result can be extended to cover the whole CTT system. The first chapters in the brief offer overviews on the two frameworks discussed in the book with an emphasis on the dialogical framework. The third chapter demonstrates the left-to-right direction of the equivalence result. This is followed by a chapter that demonstrates the use of the algorithm in showing how to transform a specific winning strategy into a CCT-demonstration of the axiom of choice. The fifth chapter develops the algorithm from CTT-demonstrations to dialogical strategies. This brief concludes by introducing elements of discussion which are to be developed in subsequent work.

Der Verfasser hat sich die Aufgabe gestellt, die sehr verschiedenen Charakterisierungen der intuitionistischen Logik - die garbentheoretische, die kalkultheoretische, die verbandstheoretische, die operative, die spieltheoretische - unter einem einheitlichen Gesichtspunkt, namlich ihrer strukturellen Beschreibung mit Hilfe der Kategorientheorie und der dialogischen Logik, neu zu entwickeln. Er geht aus von dem immer wieder unterstellten ad-hoc-Charakter der gewahlten Spielregeln und fragt nach den Grunden fur die Wahl gerade der zur effektiven Logik fuhrenden Rahmenregeln. Die dialogische Logik lasst sich als operative dialogische Logik auszeichnen und so als der gemeinsame Kern der von jeder protologischen Kategorie jeweils induzierten Logik verstehen."