Mathieu Beirlaen

Bio: Mathieu Beirlaen is an academic researcher from Ruhr University Bochum. The author has contributed to research in topics: Deontic logic & Non-monotonic logic. The author has an hindex of 10, co-authored 27 publications receiving 229 citations. Previous affiliations of Mathieu Beirlaen include Ghent University & National Autonomous University of Mexico.

An Inconsistency-Adaptive Deontic Logic for Normative Conflicts

Abstract: We present the inconsistency-adaptive deontic logic DP r , 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 O A ∧ O ∼A, O A ∧ P ∼A or even O A ∧ ∼O A. On the other hand, DP r still verifies all intuitively reliable inferences valid in Standard Deontic Logic (SDL). DP r interprets a given premise set ‘as normally as possible’ with respect to SDL. Whereas some SDL-rules are verified unconditionally by DP r , others are verified conditionally. The latter are applicable unless they rely on formulas that turn out to behave inconsistently in view of the premises. This dynamic process is mirrored by the proof theory of DP r .

Avoiding deontic explosion by contextually restricting aggregation

Abstract: In this paper, we present an adaptive logic for deontic conflicts, called P2.1r, that is based on Goble's logic SDLaPe--a bimodal extension of Goble's logic P that invalidates aggregation for all prima facie obligations. The logic P2.1r has several advantages with respect to SDLaPe. For consistent sets of obligations it yields the same results as Standard Deontic Logic and for inconsistent sets of obligations, it validates aggregation "as much as possible". It thus leads to a richer consequence set than SDLaPe. The logic P2.1r avoids Goble's criticisms against other non-adjunctive systems of deontic logic. Moreover, it can handle all the 'toy examples' from the literature as well as more complex ones.

A conditional logic for abduction

Abstract: 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.

Avoiding deontic explosion by contextually restricting aggregation

Abstract: In this paper, we present an adaptive logic for deontic conflicts, called P2.1(r), that is based on Goble's logic SDLaPe-a bimodal extension of Goble's logic P that invalidates aggregation for all prima facie obligations. The logic P2.1(r) has several advantages with respect to SDLaPe. For consistent sets of obligations it yields the same results as Standard Deontic Logic and for inconsistent sets of obligations, it validates aggregation "as much as possible". It thus leads to a richer consequence set than SDLaPe. The logic P2.1(r) avoids Goble's criticisms against other non-adjunctive systems of deontic logic. Moreover, it can handle all the 'toy examples' from the literature as well as more complex ones.

Tolerating deontic conflicts by adaptively restricting inheritance

Abstract: In order to deal with the possibility of deontic conflicts Lou Goble developed a group of logics (DPM) that are characterized by a restriction of the inheritance principle. While they approximate the deductive power of standard deontic logic, they do so only if the user adds certain statements to the premises. By adaptively strengthening the DPM logics, this paper presents logics that overcome this shortcoming. Furthermore, they are capable of modeling the dynamic and defeasible aspect of our normative reasoning by their dynamic proof theory. This way they enable us to have a better insight in the relations between obligations and thus to localize deontic conflicts.

The Right and the Good

Abstract: This is a chapter for a political philosophy handbook being edited by Antonella Besussi for Ashgate Publishing. The chapter aims to set out the conceptual and theoretical landscape regarding the right and the good in a manner useful to political philosophers unfamiliar with it.