Inductive generalization is a defeasible type of inference which we use to reason from the particular to the universal. First, a number of systems are presented that provide different ways of implementing this inference pattern within first-order logic. These systems are defined within the adaptive logics framework for modeling defeasible reasoning...
Published in Synthese
We present a logic, ELIr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {ELI^r}$$\end{document}, for the discovery of deterministic causal regularities starting...
Published in Journal of Philosophical Logic
The early calculus is a popular example of an inconsistent but fruitful scientific theory. This paper is concerned with the formalisation of reasoning processes based on this inconsistent theory. First it is shown how a formal reconstruction in terms of a sub-classical negation leads to triviality. This is followed by the evaluation of the chunk an...
Published in Logica Universalis
Even when inconsistencies are present in our premise set, we can sensibly distinguish between good and bad arguments relying on these premises. In making this distinction, the inconsistency-adaptive approach of Batens strikes a particularly nice balance between inconsistency-tolerance and inferential strength. In this paper, we use the machinery of...
We present two multi-agent deontic logics that consistently accommodate various types of normative conflicts. Its language features modal operators for obligation and permission, and for the realization of individual and collective actions. The logic is non-classical since it makes use of a paraconsistent and paracomplete negation connective. Moreo...
Published in Foundations of Science
In this paper I propose a new approach to the foundation of mathematics: non-monotonic set theory. I present two completely different methods to develop set theories based on adaptive logics. For both theories there is a finitistic non-triviality proof and both theories contain (a subtle version of) the comprehension axiom schema. The first theory ...
In this article, I present a non-trivial but inconsistent set theory based on unrestricted comprehension. The theory is provably non-trivial and strong enough for most of the applications of regular mathematics. This is realized by distinguishing between strong and weak set membership and allowing for the derivation of strong membership from weak m...
Published in Journal of Philosophical Logic
We present the inconsistency-adaptive deontic logic DPr, a nonmonotonic logic for dealing with conflicts between normative statements. On the one hand, this logic does not lead to explosion in view of normative conflicts such as OA ∧ O ∼A, OA ∧ P ∼A or even OA ∧ ∼OA. On the other hand, DPr still verifies all intuitively reliable inferences valid in...
Published in Studia Logica
Modal logics have in the past been used as a unifying framework for the minimality semantics used in defeasible inference, conditional logic, and belief revision. The main aim of the present paper is to add adaptive logics, a general framework for a wide range of defeasible reasoning forms developed by Diderik Batens and his co-workers, to the grow...
