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The Talmudic Logic Project, Ongoing Since 2008 Gabbay, Dov M. ; ; in Logica Universalis (2019), 13(4), 425--442 We describe the state of the Talmudic Logic project as of end of 2019. The Talmud is the most comprehensive and fundamental work of Jewish religious law, employing a large number of logical components ... [more ▼] We describe the state of the Talmudic Logic project as of end of 2019. The Talmud is the most comprehensive and fundamental work of Jewish religious law, employing a large number of logical components centuries ahead of their time. In many cases the basic principles are not explicitly formulated, which makes it difficult to formalize and make available to the modern student of Logic. This project on Talmudic Logic, aims to present logical analysis of Talmudic reasoning using modern logical tools. We investigate principles of Talmudic Logic and publish a series of books, one book or more for each principle. http://www.collegepublications.co.uk/stl/ The series begins with the systematic analysis of Talmudic inference rules. The first book shows that we can present Talmudic reasoning intuitions as a systematic logical system basic to modern non-deductive reasoning, such as Argumentum A Fortiori, Abduction and Analogy. The second book offers a systematic common sense method for intuitively defining sets and claims that this method adequately models the Talmudic use of the rules Klal uPrat. These books also criticize modern Talmudic research methodology. Later books deal with additional topics like Deontic logic, and Temporal logic, Agency and processes in the Talmud and more. The aims of the project are two fold: 1. To import into the Talmudic study modern logical methods with a view to help understand complicated Talmudic passages, which otherwise cannot be addressed. 2. To export from the Talmud new logical principles which are innovative and useful to modern contemporary logic. [less ▲] Detailed reference viewed: 37 (0 UL)Computer-Assisted Analysis of the Anderson-Hájek Controversy Benzmüller, Christoph ; ; in Logica Universalis (2017), 11(1), 139-151 A universal reasoning approach based on shallow semantical embeddings of higher-order modal logics into classical higher-order logic is exemplarily employed to analyze several modern variants of the ... [more ▼] A universal reasoning approach based on shallow semantical embeddings of higher-order modal logics into classical higher-order logic is exemplarily employed to analyze several modern variants of the ontological argument on the computer. Several novel findings are reported which contribute to the clarification of a long-standing dispute between Anderson and Hájek. The technology employed in this work, which to some degree realizes Leibniz’s dream of a characteristica universalis and a calculus ratiocinator for solving philosophical controversies, is ready to be fruitfully adopted in larger scale by philosophers. [less ▲] Detailed reference viewed: 18 (0 UL)Theory of Semi-Instantiation in Abstract Argumentation Gabbay, Dov M. in Logica Universalis (2016), 10(4), 431--516 Detailed reference viewed: 96 (0 UL)Equilibrium States in Numerical Argumentation Networks Gabbay, Dov M. ; in Logica Universalis (2015), 9(4), 411--473 Detailed reference viewed: 68 (1 UL)Probabilistic Argumentation: An Equational Approach Gabbay, Dov M. ; in Logica Universalis (2015), 9(3), 345--382 There is a generic way to add any new feature to a system. It involves (1) identifying the basic units which build up the system and (2) introducing the new feature to each of these basic units. In the ... [more ▼] There is a generic way to add any new feature to a system. It involves (1) identifying the basic units which build up the system and (2) introducing the new feature to each of these basic units. In the case where the system is argumentation and the feature is probabilistic we have the following. The basic units are: (a) the nature of the arguments involved; (b) the membership relation in the set S of arguments; (c) the attack relation; and (d) the choice of extensions. Generically to add a new aspect (probabilistic, or fuzzy, or temporal, etc) to an argumentation network ⟨S,R⟩⟨S,R⟩ can be done by adding this feature to each component (a–d). This is a brute-force method and may yield a non-intuitive or meaningful result. A better way is to meaningfully translate the object system into another target system which does have the aspect required and then let the target system endow the aspect on the initial system. In our case we translate argumentation into classical propositional logic and get probabilistic argumentation from the translation. Of course what we get depends on how we translate. In fact, in this paper we introduce probabilistic semantics to abstract argumentation theory based on the equational approach to argumentation networks. We then compare our semantics with existing proposals in the literature including the approaches by M. Thimm and by A. Hunter. Our methodology in general is discussed in the conclusion. [less ▲] Detailed reference viewed: 99 (6 UL)Probabilistic Argumentation. An Equational Approach Gabbay, Dov M. ; in Logica Universalis (2015), abs/1503.05501 There is a generic way to add any new feature to a system. It involves 1) identifying the basic units which build up the system and 2) introducing the new feature to each of these basic units. In the case ... [more ▼] There is a generic way to add any new feature to a system. It involves 1) identifying the basic units which build up the system and 2) introducing the new feature to each of these basic units. In the case where the system is argumentation and the feature is probabilistic we have the following. The basic units are: a. the nature of the arguments involved; b. the membership relation in the set S of arguments; c. the attack relation; and d. the choice of extensions. Generically to add a new aspect (probabilistic, or fuzzy, or temporal, etc) to an argumentation network hS, R i can be done by adding this feature to each component a – d. This is a brute-force method and may yield a non-intuitive or meaningful result. A better way is to meaningfully translate the object system into another target system which does have the aspect required and then let the target system endow the aspect on the initial system. In our case we translate argumentation into classical propositional logic and get probabilistic argumentation from the translation. Of course what we get depends on how we translate. In fact, in this paper we introduce probabilistic semantics to abstract argumentation theory based on the equational approach to argumentation networks. We then compare our semantics with existing proposals in the literature including the approaches by M. Thimm and by A. Hunter. Our methodology in general is discussed in the conclusion. [less ▲] Detailed reference viewed: 63 (5 UL)Equilibrium States in Numerical Argumentation Networks Gabbay, Dov M. ; in Logica Universalis (2014), abs/1408.6706 Detailed reference viewed: 41 (6 UL)Dung’s Argumentation is Essentially Equivalent to Classical Propositional Logic with the Peirce-Quine Dagger Gabbay, Dov M. in Logica Universalis (2011), 5(2), 255-318 In this paper we show that some versions of Dung’s abstract argumentation frames are equivalent to classical propositional logic. In fact, Dung’s attack relation is none other than the generalised Peirce– ... [more ▼] In this paper we show that some versions of Dung’s abstract argumentation frames are equivalent to classical propositional logic. In fact, Dung’s attack relation is none other than the generalised Peirce– Quine dagger connective of classical logic which can generate the other connectives ¬,∧,∨,→ of classical logic. After establishing the above correspondence we offer variations of the Dung argumentation frames in parallel to variations of classical logic, such as resource logics, predicate logic, etc., etc., and create resource argumentation frames, predicate argumentation frames, etc., etc. We also offer the notion of logic proof as a geometrical walk along the nodes of a Dung network and thus we are able to offer a geometrical abstraction of the notion of inference based argumentation. Thus our paper is also a contribution to the question: “What is a logical system” in as much as it integrates logic with abstract argumentation networks [less ▲] Detailed reference viewed: 91 (0 UL) |
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