The applicability of Bayesian conditionalization in setting one’s posterior probability for a proposition, α, is limited to cases where the value of a corresponding prior probability, PPRI(α|∧E), is available, where ∧E represents one’s complete body of evidence. In order to extend probability updating to cases where the prior probabilities needed for Bayesian conditionalization are unavailable, I introduce an inference schema, defeasible conditionalization, which allows one to update one’s personal probability in a proposition by conditioning on a proposition that represents a (...) proper subset of one’s complete body of evidence. While defeasible conditionalization has wider applicability than standard Bayesian conditionalization (since it may be used when the value of a relevant prior probability, PPRI(α|∧E), is unavailable), there are circumstances under which some instances of defeasible conditionalization are unreasonable. To address this difficulty, I outline the conditions under which instances of defeasible conditionalization are defeated. To conclude the article, I suggest that the prescriptions of direct inference and statistical induction can be encoded within the proposed system of probability updating, by the selection of intuitively reasonable prior probabilities. (shrink)

This paper presents an adaptive logic enhancement of conditional logics of normality that allows for defeasible applications of Modus Ponens to conditionals. In addition to the possibilities these logics already offer in terms of reasoning about conditionals, this way they are enriched by the ability to perform default inferencing. The idea is to apply Modus Ponens defeasibly to a conditional and a fact on the condition that it is ‘safe' to do so concerning the factual and conditional knowledge at hand. (...) It is for instance not safe if the given information describes exceptional circumstances: although birds usually fly, penguins are exceptional to this rule. The two adaptive standard strategies are shown to correspond to different intuitions, a skeptical and a credulous reasoning type, which manifest themselves in the handling of so-called floating conclusions. (shrink)

Argumentation is a very fertile area of research in Artificial Intelligence, and various semantics have been developed to predict when an argument can be accepted, depending on the abstract structure of its defeaters and defenders. When these semantics make conflicting predictions, theoretical arbitration typically relies on ad hoc examples and normative intuition about what prediction ought to be the correct one. We advocate a complementary, descriptive-experimental method, based on the collection of behavioral data about the way human reasoners handle these (...) critical cases. We report two studies applying this method to the case of reinstatement (both in its simple and floating forms). Results speak for the cognitive plausibility of reinstatement and yet show that it does not yield the full expected recovery of the attacked argument. Furthermore, results show that floating reinstatement yields comparable effects to that of simple reinstatement, thus arguing in favor of preferred argumentation semantics, rather than grounded argumentation semantics. Besides their theoretical value for validating and inspiring argumentation semantics, these results have applied value for developing artificial agents meant to argue with human users. (shrink)

In this paper we will analyse the issue of defeasibility in the law, taking into account research carried out in philosophy, artificial intelligence and legal theory. We will adopt a very general idea of legal defeasibility, in which we will include all different ways in which certain legal conclusions may need to be abandoned, though no mistake was made in deriving them. We will argue that defeasibility in the law involves three different aspects, which we will call inference‐based defeasibility, process‐based (...) defeasibility, and theory‐based defeasibility. Only the integration of these three perspectives allows us to provide a satisfactory account of the role of defeasibility in legal reasoning. (shrink)

The Ostrogorski paradox and the discursive dilemma are seemingly unrelated paradoxes of aggregation. The former is discussed in traditional social choice theory, while the latter is at the core of the new literature on judgment aggregation. Both paradoxes arise when, in a group, each individual consistently makes a judgment, or expresses a preference, (in the form of yes or no) over specific propositions, and the collective outcome is in some respect inconsistent. While the result is logically inconsistent in the case (...) of the discursive paradox, it is not stable with respect to the level of aggregation in the case of the Ostrogorski paradox. In the following I argue that, despite these differences, the two problems have a similar structure. My conclusion will be twofold: on the one hand, the similarities between the paradoxes support the claim that these problems should be tackled using the same aggregation procedure; on the other hand, applying the same procedure to these paradoxes will help clarify the strengths and weaknesses of the aggregation method itself. More specifically, I will show that an operator defined in artificial intelligence to merge belief bases can deal with both paradoxes. (shrink)

Fixpoint semantics are provided for ambiguity blocking and propagating variants of Nute's defeasible logic. The semantics are based upon the well-founded semantics for logic programs. It is shown that the logics are sound with respect to their counterpart semantics and complete for locally finite theories. Unlike some other nonmonotonic reasoning formalisms such as Reiter's default logic, the two defeasible logics are directly skeptical and so reject floating conclusions. For defeasible theories with transitive priorities on defeasible rules, the logics are shown (...) to satisfy versions of Cut and Cautious Monotony. For theories with either conflict sets closed under strict rules or strict rules closed under transposition, a form of Consistency Preservation is shown to hold. The differences between the two logics and other variants of defeasible logic—specifically those presented by Billington, Antoniou, Governatori, and Maher—are discussed. (shrink)

Judgment aggregation is naturally applied to the modeling of collective attitudes. In the individual case, we represent agents as having not just beliefs, but also as supporting them with reasons. Can the Judgment Aggregation help model a concept of collective reason? I argue that the resources of the standard judgment aggregation framework are insufficiently general. I develop a generalization of the framework that improves along this dimension. In the new framework, new aggregation rules become available, as well as a natural (...) account of collective reasons. (shrink)

We propose a logic of abduction that (i) provides an appropriate formalization of the explanatory conditional, and that (ii) captures the defeasible nature of abductive inference. For (i), we argue that explanatory conditionals are non-classical, and rely on Brian Chellas’s work on conditional logics for providing an alternative formalization of the explanatory conditional. For (ii), we make use of the adaptive logics framework for modeling defeasible reasoning. We show how our proposal allows for a more natural reading of explanatory relations, (...) and how it overcomes problems faced by other systems in the literature. (shrink)

When there are two lines of argument that contradict each other but still end up with the same conclusion, this conclusion is called a floating conclusion. It is an open topic in skeptical defeasible reasoning if floating conclusions ought to be accepted. Inter- estingly, the answer seems to be changing for different examples. In this paper, we propose a solution for explaining the different treatments of the floating conclusion in the various examples from the literature. We collect the examples from (...) the literature, extend them with additional examples and test various hypotheses for explaining the difference by means of the examples. We will argue for a framework that accepts a floating conclusion by default but allows for reasons to deviate from the default in order to reject it. These reasons nicely explain the different underlying patterns of our intuitions. (shrink)

This text is expository. We explain Gödel’s ‘Master Argument’ for incompleteness as distinguished from the 'official' proof of his 1931 paper, highlight its attractions and limitations, and explain how some of the limitations may be transcended by putting it in a more abstract form that makes no reference to truth.