Interactions Between Defaults and Roles in Defeasible Description Logics

Scientific Conference (2022, August 18)

On the Strength of Defeasible Inference Trees

Presentation (2021)

On the Nature of Nonmonotonic Reasoning - Some formal clarifications

Presentation (2019, February 12)

Conditional Inference Trees - Proxies for real-world arguments

Scientific Conference (2018)

What is an argument? Nature and necessity of generalized arguments.

Scientific Conference (2018)

A Multiverse Axiom Induction Framework

in Symposium on the Theoretical Foundations of Mathematics III (2015, September 23)

A MULTIVERSE AXIOM INDUCTION FRAMEWORK The multiverse paradigm in set theory does not only reflect philosophical preferences, or set up a new playground for mathematical investigation, but it also offers ... [more ▼]

A MULTIVERSE AXIOM INDUCTION FRAMEWORK The multiverse paradigm in set theory does not only reflect philosophical preferences, or set up a new playground for mathematical investigation, but it also offers a powerful methodological tool for investigating the conceptual foundations of set theory by guiding the search for and the evaluation of new set-theoretic axioms or facts. The prototypical example is Friedman's Hyperuniverse Program (HUP). Our goal is to develop an abstract inferential framework generalizing the HUP whose (defeasible, inductive) inference methods are meant to identify or validate new axioms. We consider nonmonotonic consequence relations |~, parametrized by specifications of the multiverse and set-theoretic desiderata, which associate with any suitable ZFC + X new - not necessarily classically derivable - candidate truths. The desiderata could, for instance, consist of consistency conditions or maximization demands w.r.t. preorders over universes. There are a number of possible inductive strategies, but it doesn't seem that conceptual considerations at the level of set theory are sufficient to decide among them. The idea is therefore to also assess the inferential level and to use rationality postulates for nonmonotonic inference, heavily investigated within AI for modeling commonsense reasoning, to classify and evaluate such procedures. This is however a non-trivial task because of the special characteristics of axiom induction. [less ▲]

On the plausibility of abstract arguments

in van der Gaag, Linda (Ed.) Symbolic and Quantitative Approaches to Reasoning with Uncertainty (2013)

On the Acceptability of Incompatible Arguments

in Symbolic and Quantitative Approaches to Reasoning with Uncertainty, 9th European Conference, ECSQARU 2007, Hammamet, Tunisia, October 31 – November 2, 2007, Proceedings (2007)

In this paper we study the acceptability of incompatible arguments within Dung’s abstract argumentation framework. As an example we introduce an instance of Dung’s framework where arguments are ... [more ▼]

In this paper we study the acceptability of incompatible arguments within Dung’s abstract argumentation framework. As an example we introduce an instance of Dung’s framework where arguments are represented by propositional formulas and an argument attacks another one when the conjunction of their representations is inconsistent, which we characterize as a kind of symmetric attack. Since symmetric attack is known to have the drawback to collapse the various argumentation semantics, we consider also two variations. First, we consider propositional arguments distinguishing support and conclusion. Second, we introduce a preference ordering over the arguments and we define the attack relation in terms of a symmetric incompatibility relation and the preference relation. We show how to characterize preference-based argumentation using a kind of acyclic attack relation. [less ▲]