Mathieu Beirlaen

An inconsistency-adaptive deontic logic for normative conflicts

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 Standard Deontic Logic (SDL). DPr interprets a given premise set ‘as normally as possible’ with respect to SDL. Whereas some SDL-rules are verified unconditionally by DPr, 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 DPr.

A conditional logic for abduction

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.

Two Adaptive Logics of Norm-Propositions

We present two defeasible logics of norm-propositions (statements about norms) that (i) consistently allow for the possibility of normative gaps and normative conicts, and (ii) map each premise set to a suciently rich consequence set.

Non-monotonic reasoning with normative conflicts in multi-agent deontic logic

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. Moreover, it is non-monotonic due to its definition within the adaptive logics framework for defeasible reasoning. The logic is equipped with a defeasible proof theory and semantics.

Adaptive Logic Characterizations of Input/Output Logic

We translate unconstrained and constrained input/output logics as introduced by Makinson and van der Torre to modal logics, using adaptive logics for the constrained case. The resulting reformulation has some additional benefits. First, we obtain a proof-theoretic (dynamic) characterization of input/output logics. Second, we demonstrate that our framework naturally gives rise to useful variants and allows to express important notions that go beyond the expressive means of input/output logics, such as violations and sanctions.

Inconsistency-Adaptive Dialogical Logic

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 Batens’ approach to extend the paraconsistent approach to dialogical logic as developed by Rahman and Carnielli. In bringing these frameworks closer together, we obtain a dynamic mechanism for the systematic study of dialogues in which two parties exchange arguments over a central claim, in the possible presence of inconsistencies.

A logic for the discovery of deterministic causal regularities

We present a logic,

Avoiding deontic explosion by contextually restricting aggregation

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