Syllogistics reduces to only two rules of inference: monotonicity and symmetry, plus a third if one wants to take existential import into account. We give an implementation that uses only the monotonicity and symmetry rules, with an addendum for the treatment of existential import. Soundness follows from the monotonicity properties and symmetry properties of the Aristotelean quantifiers, while completeness for syllogistic theory is proved by direct inspection of the valid syllogisms. Next, the valid syllogisms are decomposed in terms of the (...) rules they involve. The implementation uses Haskell [8], and is given in ‘literate programming’ style [9]. (shrink)

One of the epistemological results emerging from this initial study is that the different forms of co-relational inference, known in the Islamic jurisprudence as qiyās, represent an innovative and sophisticated form of reasoning that not only provides new epistemological insights into legal reasoning in general 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 argumentation studied in contemporary (...) philosophy of science. However, in the present paper we will only discuss the case of so-called co-relational inferences of the occasioning factor and only in the context of Islamic jurisprudence. (shrink)

In its first meaning, a logic is a collection of closely related artificial languages. There are certain languages called first‐order languages, and together they form first‐order logic. In the same spirit, there are several closely related languages called modal languages, and together they form modal logic. Likewise second‐order logic, deontic logic and so forth.

This monograph proposes a new way of studying the different forms of correlational inference, known in the Islamic jurisprudence as qiyās. According to the authors’ view, qiyās represents an innovative and sophisticated form of dialectical reasoning that not only provides new epistemological insights into legal argumentation in general 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 qiyās and of the work of al-Shīrāzī penned by Soufi Youcef, the authors discuss al-Shīrāzī’s classification of correlational inferences of the occasioning factor. The second part of the volume deliberates on the system of correlational inferences by indication and resemblance. 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. (shrink)

We implement the extension of the logical consequence relation to a partial order ≤ on arbitary types built from e (entities) and t (Booleans) that was given in [1], and the definition of monotonicity preserving and monotonicity reversing functions in terms of ≤. Next, we present a new algorithm for polarity marking, and implement this for a particular fragment of syntax. Finally, we list the reseach agenda that these definitions and this algorithm suggest. The implementations use Haskell [8], and are (...) given in ‘literate programming’ style [9]. (shrink)

Given some links between Lyndon’s Interpolation Theorem, term distribution, and Sommers and Englebretsen’s logic, in this contribution we attempt to capture a sense of interpolation for Sommers and Englebretsen’s Term Functor Logic. In order to reach this goal we first expound the basics of Term Functor Logic, together with a sense of term distribution, and then we offer a proof of our main contribution.

This paper is a brief history of natural logic at the interface of logic, linguistics, and nowadays also other disciplines. It merely summarizes some facts that deserve to be common knowledge.

RésuméCette première étude permet notamment de dégager ce résultat épistémologique: les différentes formes d’“inférence co-relationnelle” connues dans la jurisprudence islamique sous le nom de qiyās représentent une forme innovante et sophistiquée de raisonnement qui permet non seulement d'avoir une conception épistémologique plus claire du raisonnement légal en général, mais aussi de produire une mécanique bien huilée pour le “raisonnement parallèle”; cette mécanique du “raisonnement parallèle” peut être déployée selon un large spectre dans différents cadres de résolution de problèmes et ne (...) semble pas se réduire aux formes standard de l'argumentation analogique étudiées en philosophie des sciences contemporaine. Nous n'aborderons cependant dans la présente étude que le cas de la dénommée “inférence co-relationnelle du facteur occasionnel”, et ce seulement dans le contexte de la jurisprudence islamique. (shrink)