Reasoning With and About Norms in Logical Argumentation

Abstract

Normative reasoning is inherently defeasible. Formal argumentation has proven to be a unifying framework for representing nonmonotonic logics. In this work, we provide an argumentative characterization of a large class of Input/Output logics, a prominent defeasible formalism for normative reasoning. In many normative reasoning contexts, one is not merely interested in knowing whether a specific obligation holds, but also in why it holds despite other norms to the contrary. We propose sequent-style argumentation systems called Deontic Argument Calculi (DAC), which serve transparency and bring meta-reasoning about the inapplicability of norms to the object language level. We prove soundness and completeness between DAC-instantiated argumentation frameworks and constrained Input/Output logics. We illustrate our approach in view of two deontic paradoxes.

Defeasible Normative Reasoning: A Proof-Theoretic Integration of Logical Argumentation

“…2 We avoid overburdening the language with modalities by using labels. This suffices to represent the roles propositional formulas play in normative reasoning (van Berkel and Straßer 2022). Modal representations of deontic (I/O) logics are available, e.g., in (Makinson and van der Torre 2000;Lellmann 2021).…”

“…are jointly inapplicable." The latter is an extension of the language in (van Berkel and Straßer 2022), where only expressions of the form ¬(φ, ψ) were allowed. In what follows, we demonstrate the benefits of generalizing the language to referring to joint inapplicability of sets of norms.…”

Arguing About Choosing a Normative System: Conflict of Laws

“…We develop a general formalism for CoL reasoning by extending the deontic argumentation calculi (DAC) from [5]. We extend the calculi by reasoning about multiple national legal systems and develop various rules for restricted CoL reasoning such as reasoning with renvoi.…”

“…where p, q,... are used to denote propositional atoms and ϕ, ψ,... for arbitrary formulas. In particular, we adopt labellings of L to differentiate between formulas that denote facts, obligations, and constraints [5]. Since we aim at reasoning with legal systems of various nations, we index obligations with nation labels i ∈ nations = {i,..., n} (where n ∈ N):…”

“…To reach these aims, we develop a class of Conflict of Laws Calculi (CoLC) that extends the proof theoretic approach to Input/Output Logic [4] by [5], using formal argumentation [6] (Sect. 2).…”