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Detachment in Normative Systems: Examples, inference Patterns, Properties Parent, Xavier ; van der Torre, Leon in The IfCoLog Journal of Logics and their Applications (2017), 4(9), 2295-3039 There is a variety of ways to reason with normative systems. This partly reflects a variety of semantics developed for deontic logic, such as traditional semantics based on possible worlds, or alternative ... [more ▼] There is a variety of ways to reason with normative systems. This partly reflects a variety of semantics developed for deontic logic, such as traditional semantics based on possible worlds, or alternative semantics based on algebraic methods, explicit norms or techniques from non-monotonic logic. This diversity raises the question how these reasoning methods are related, and which reasoning method should be chosen for a particular application. In this paper we discuss the use of examples, inference patterns, and more abstract properties. First, benchmark examples can be used to compare ways to reason with normative systems. We give an overview of several benchmark examples of normative reasoning and deontic logic: van Fraassen’s paradox, Forrester’s paradox, Prakken and Sergot’s cottage regulations, Jeffrey’s disarmament example, Chisholm’s paradox, Makinson’s Möbius strip, and Horty’s priority examples. Moreover, we distinguish various interpretations that can be given to these benchmark examples, such as consistent interpretations, dilemma interpretations, and violability interpretations. Second, inference patterns can be used to compare different ways to reason with normative systems. Instead of analysing the benchmark examples semantically, as it is usually done, in this paper we use inference patterns to analyse them at a higher level of abstraction. We discuss inference patterns reflecting typical logical properties such as strengthening of the antecedent or weakening of the consequent. Third, more abstract properties can be defined to compare different ways to reason with normative systems. To define these more abstract properties, we first present a formal framework around the notion of detachment. Some of the ten properties we introduce are derived from the inference patterns, but others are more abstract: factual detachment, violation detection, substitution, replacements of equivalents, implication, para-consistency, conjunction, factual monotony, norm monotony, and norm induction. We consider these ten properties as desirable for a reasoning method for normative systems. [less ▲] Detailed reference viewed: 21 (6 UL)Reasoning under the Influence of Universal Distortion. Sex Offenders Case Study Gabbay, Dov M. ; ; in The IfCoLog Journal of Logics and their Applications (2017) We define and study the phenomenon of a universal distortion into a reasoning system or an argumentation network. Such distortions can happen for various reasons, for instance under the influence of ... [more ▼] We define and study the phenomenon of a universal distortion into a reasoning system or an argumentation network. Such distortions can happen for various reasons, for instance under the influence of alcohol or a fundamentalist religion, or as the result of a behavioural disorder such as paedophilia. We define the notion theoretically in the framework of abstract argumentation and present an actual case study of a sex offender. We then present a formal logical model. [less ▲] Detailed reference viewed: 3 (0 UL)Reasoning Schemes, Expert Opinions and Critical Questions. Sex Offenders Case Study Gabbay, Dov M. ; in The IfCoLog Journal of Logics and their Applications (2017) This paper examines in detail the argumentation features in the domain of sex offender with some applications to the scheme of “Argument from Expert Opinion". We build a model for reasoning schemes ... [more ▼] This paper examines in detail the argumentation features in the domain of sex offender with some applications to the scheme of “Argument from Expert Opinion". We build a model for reasoning schemes, critical questions and expert opinion on the question of “the degree of risk of a sex offender". We discover that in order to properly model expert practice in this area we need to use numerical argumentation as well as the new notion of “Attack as Information Input". The model is generic and we believe is not restricted to the sex offence area of expertise. Our paper also offers a more detailed example for Walton’s argumentation scheme of Expert Opinion as well as a bridge between the argumentation community and the community dealing with sex offenders. We offer an introduction to the student on the subject of determining the degree of risk of sex offenders. We also look at standard international tools for determining the risk of sex offenders and see how the argumentation community can integrate these tools. [less ▲] Detailed reference viewed: 3 (0 UL)HEAL2100: Human Effective Argumentation and Logic for the 21st Century. The next Step in the Evolution of Logic Gabbay, Dov M. ; in The IfCoLog Journal of Logics and their Applications (2017) This editorial is about weaponising the Fallacies, and offering them as active additional components to modern formal logic, thus forming the new evolutionary logic for the 21st Century. Logicians since ... [more ▼] This editorial is about weaponising the Fallacies, and offering them as active additional components to modern formal logic, thus forming the new evolutionary logic for the 21st Century. Logicians since Aristotle considered the fallacies as wrong arguments which look correct but are not. They classified them into groups, discussed them and left them by the sidelines of logic as failures. Modern society, with the rise of the internet, Twitter, Facebook and YouTube showed the fallacies as most used and most effective in argumentation and debate. If this is the way humans reason and think then we need to develop the logical theory of the the use of the fallacies and legitimise them as a significant component of modern reasoning. This manifesto outlines our approach to the new logic of the 21st century which allows for the systematic use of the fallacies in argumentation and debate as practiced by people in the mass media. [less ▲] Detailed reference viewed: 5 (0 UL)Implicit dynamic function introduction and Ackermann-like Function Theory Cramer, Marcos in The IfCoLog Journal of Logics and their Applications (2017) We discuss a feature of the natural language of mathematics – the implicit dynamic introduction of functions – that has, to our knowledge, not been captured in any formal system so far. If this feature is ... [more ▼] We discuss a feature of the natural language of mathematics – the implicit dynamic introduction of functions – that has, to our knowledge, not been captured in any formal system so far. If this feature is used without limitations, it yields a paradox analogous to Russell’s paradox. Hence any formalism capturing it has to impose some limitations on it. We sketch two formalisms, both extensions of Dynamic Predicate Logic, that innovatively do capture this feature, and that differ only in the limitations they impose onto it. One of these systems is based on Ackermann-like Function Theory, a novel foundational theory of functions that is inspired by Ackermann Set Theory and that interprets ZFC. [less ▲] Detailed reference viewed: 25 (1 UL) |
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