Defeasible reasoning and informal fallacies

This paper argues that some traditional fallacies should be considered as reasonable arguments when used as part of a properly conducted dialog. It is shown that argumentation schemes, formal dialog models, and profiles of dialog are useful tools for studying properties of defeasible reasoning and fallacies. It is explained how defeasible reasoning of the most common sort can deteriorate into fallacious argumentation in some instances. Conditions are formulated that can be used as normative tools to judge whether a given defeasible argument is fallacious or not. It is shown that three leading violations of proper dialog standards for defeasible reasoning necessary to see how fallacies work are: (a) improper failure to retract a commitment, (b) failure of openness to defeat, and (c) illicit reversal of burden of proof.     

Conceivability and Defeasible Modal Justification

This paper advances the thesis that we can justifiably believe philosophically interesting possibility statements. The first part of the paper critically discusses van Inwagens skeptical arguments while at the same time laying some of the foundation for a positive view. The second part of the paper advances a view of conceivability in terms of imaginability, where imaginging can be propositional, pictorial, or a combination of the two, and argues that conceivability can, and often does, provide us with justified beliefs of what is metaphysically possible. The notion of scenarios is developed, as is an account of how filling out scenarios can uncover a defeater or, in many cases, strengthen the justification for the relevant possibility statement.     

Conditional Probability and Defeasible Inference

We offer a probabilistic model of rational consequence relations (Lehmann and Magidor, 1990) by appealing to the extension of the classical Ramsey–Adams test proposed by Vann McGee in (McGee, 1994). Previous and influential models of non-monotonic consequence relations have been produced in terms of the dynamics of expectations (Gärdenfors and Makinson, 1994; Gärdenfors, 1993).Expectation is a term of art in these models, which should not be confused with the notion of expected utility. The expectations of an agent are some form of belief weaker than absolute certainty. Our model offers a modified and extended version of an account of qualitative belief in terms of conditional probability, first presented in (van Fraassen, 1995). We use this model to relate probabilistic and qualitative models of non-monotonic relations in terms of expectations. In doing so we propose a probabilistic model of the notion of expectation. We provide characterization results both for logically finite languages and for logically infinite, but countable, languages. The latter case shows the relevance of the axiom of countable additivity for our probability functions. We show that a rational logic defined over a logically infinite language can only be fully characterized in terms of finitely additive conditional probability. The research of both authors was supported in part by a grant from NSF, and, for Parikh, also by support from the research foundation of CUNY.     

The Reasoning View and Defeasible Practical Reasoning

According to the Reasoning View about normative reasons, facts about normative reasons for action can be understood in terms of facts about the norms of practical reasoning. I argue that this view is subject to an overlooked class of counterexamples, familiar from debates about Subjectivist theories of normative reasons. Strikingly, the standard strategy Subjectivists have used to respond to this problem cannot be adapted to the Reasoning View. I think there is a solution to this problem, however. I argue that the norms of practical reasoning, like the norms of theoretical reasoning, are characteristically defeasible, in a sense I make precise. Recognizing this property of those norms makes space for a solution to the problem. The resulting view is in a way analogous to the familiar defeasibility theory of knowledge, but it avoids a standard objection to that theory.     

Motherhood and Mistakes about Defeasible Duties to Benefit

Discussion of the behaviour of pregnant women and mothers, in academic literature, medical advice given to mothers, mainstream media and social media, assumes that a mother who fails to do something to benefit her child is liable for moral criticism unless she can provide sufficient countervailing considerations to justify her decision. I reconstruct the normally implicit reasoning that leads to this assumption and show that it is mistaken. First, I show that the discussion assumes that if any action might benefit her child, the mother has a defeasible duty to perform that action. I suggest that this assumption is implicitly supported by two arguments but that each argument is unsound. The first argument conflates moral reasons and defeasible duties; the second misunderstands the scope of a defeasible duty to benefit. This argument has important practical and theoretical implications: practically, it provides a response to a highly damaging discourse on maternal behaviour; theoretically, it provides the framework for a clearer understanding of the scope and nature of defeasible duties to benefit.     

Computing Strong and Weak Permissions in Defeasible Logic

In this paper we propose an extension of Defeasible Logic to represent and compute different concepts of defeasible permission. In particular, we discuss some types of explicit permissive norms that work as exceptions to opposite obligations or encode permissive rights. Moreover, we show how strong permissions can be represented both with, and without introducing a new consequence relation for inferring conclusions from explicit permissive norms. Finally, we illustrate how a preference operator applicable to contrary-to-duty obligations can be combined with a new operator representing ordered sequences of strong permissions. The logical system is studied from a computational standpoint and is shown to have linear computational complexity.     

A Cut-Free Sequent Calculus for Defeasible Erotetic Inferences

In recent years, the effort to formalize erotetic inferences—i.e., inferences to and from questions—has become a central concern for those working in erotetic logic. However, few have sought to formulate a proof theory for these inferences. To fill this lacuna, we construct a calculus for (classes of) sequents that are sound and complete for two species of erotetic inferences studied by Inferential Erotetic Logic (IEL): erotetic evocation and erotetic implication. While an effort has been made to axiomatize the former in a sequent system, there is currently no proof theory for the latter. Moreover, the extant axiomatization of erotetic evocation fails to capture its defeasible character and provides no rules for introducing or eliminating question-forming operators. In contrast, our calculus encodes defeasibility conditions on sequents and provides rules governing the introduction and elimination of erotetic formulas. We demonstrate that an elimination theorem holds for a version of the cut rule that applies to both declarative and erotetic formulas and that the rules for the axiomatic account of question evocation in IEL are admissible in our system.

     

The logic of unboundedly reactive systems

Summary Scientific theories often need to envision that a given output variable Y is jointly determined by all input variables of a certain kind _X that we can identify onlyas a kind without knowing all its specific instances or even how many of these there are, When the number of variables in _X is possibly infinite, the function by which they determine Y proves to be enormously enigmatic, epistemically, mathematically, and scientifically.     

A Brief Comparison Of Pollock's Defeasible Reasoning And Ranking Functions

In this paper two theories of defeasible reasoning, Pollock's account and my theory of ranking functions, are compared, on a strategic level, since a strictly formal comparison would have been unfeasible. A brief summary of the accounts shows their basic difference: Pollock's is a strictly computational one, whereas ranking functions provide a regulative theory. Consequently, I argue that Pollock's theory is normatively defective, unable to provide a theoretical justification for its basic inference rules and thus an independent notion of admissible rules. Conversely, I explain how quite a number of achievements of Pollock's account can be adequately duplicated within ranking theory. The main purpose of the paper, though, is not to settle a dispute with formal epistemology, but rather to emphasize the importance of formal methods to the whole of epistemology.     

Relating Protocols For Dynamic Dispute With Logics For Defeasible Argumentation

This article investigates to what extent protocols for dynamicdisputes, i.e., disputes in which the information base can vary at differentstages, can be justified in terms of logics for defeasible argumentation. Firsta general framework is formulated for dialectical proof theories for suchlogics. Then this framework is adapted to serve as a framework for protocols fordynamic disputes, after which soundness and fairness properties are formulated for such protocols relative to dialectical proof theories. It then turns out that certaintypes of protocols that are perfectly fine with a static information base, arenot sound or fair in a dynamic setting. Finally, a natural dynamic protocolis defined for which soundness and fairness can be established.     

Automatic verification of multi-agent systems by model checking via ordered binary decision diagrams

We present a methodology for the verification of multi-agent systems, whose properties are specified by means of a modal logic that includes a temporal, an epistemic, and a modal operator to reason about correct behaviour of agents. The verification technique relies on model checking via ordered binary decision diagrams. We present an implementation and report on experimental results for two scenarios: the bit transmission problem with faults and the protocol of the dining cryptographers.     

Constructive geometrical reasoning and diagrams

Modern formal accounts of the constructive nature of elementary geometry do not aim to capture the intuitive or concrete character of geometrical construction. In line with the general abstract approach of modern axiomatics, nothing is presumed of the objects that a geometric construction produces. This study explores the possibility of a formal account of geometric construction where the basic geometric objects are understood from the outset to possess certain spatial properties. The discussion is centered around Eu, a recently developed formal system of proof (presented in Mumma (Synthese 175:255?C287, 2010)) within which Euclid??s diagrammatic proofs can be represented.     

Trees and diagrams of decomposition

We introduce here and investigate the notion of an alternative tree of decomposition. We show (Theorem 5) a general method of finding out all non-alternative trees of the alternative tree determined by a diagram of decomposition.     

Aristotelian diagrams for semantic and syntactic consequence

Several authors have recently studied Aristotelian diagrams for various metatheoretical notions from logic, such as tautology, satisfiability, and the Aristotelian relations themselves. However, all these metalogical Aristotelian diagrams focus on the semantic (model-theoretical) perspective on logical consequence, thus ignoring the complementary, and equally important, syntactic (proof-theoretical) perspective. In this paper, I propose an explanation for this discrepancy, by arguing that the metalogical square of opposition for semantic consequence exhibits a natural analogy to the well-known square of opposition for the categorical statements from syllogistics, but that this analogy breaks down once we move from semantic to syntactic consequence. I then show that despite this difficulty, one can indeed construct metalogical Aristotelian diagrams from a syntactic perspective, which have their own, equally elegant characterization in terms of the categorical statements. Finally, I construct several metalogical Aristotelian diagrams that incorporate both semantic and syntactic consequence (and their interaction), and study how they are influenced by the underlying logical system’s soundness and/or completeness. All of this provides further support for the methodological/heuristic perspective on Aristotelian diagrams, which holds that the main use of these diagrams lies in facilitating analogies and comparisons between prima facie unrelated domains of investigation.