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Defeasible Normative Reasoning: A Proof-Theoretic Integration of Logical Argumentation
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Proposes annotated deontic argumentation calculi (ADAC) that add acceptance/rejection annotations to sequents, and proves they coincide with grounded semantics of induced argumentation frameworks and with free consequences of constrained I/O logics.
Problem
Resolving conflicts among norms via nonmonotonic (skeptical) normative reasoning in a proof-theoretic way that is transparent and linked to formal argumentation and I/O logics.
Approach
Annotate sequents with derivation statuses (introduced, accepted, rejected) and add acceptance/rejection rules mirroring Caminada's 3-valued grounded labeling, so that accepted sequents coincide with grounded-extension arguments and free consequences of constrained I/O logics.
Key results
- Theorem 1: ADAC-derived acceptance coincides with grounded entailment of DAC-induced argumentation frameworks (K |~[a] phi_o iff K |~grd phi_o).
- Theorem 2: ADAC acceptance entailments coincide with free consequences of constrained I/O logic (K |~[a] phi_o iff K| |~free I/O phi).
- Theorem 3: grounded DAC entailment coincides with free I/O consequences, giving a threefold characterization.
Surprising findings
- The obligation x is inferred under I/O logic R4 but not R3 for the running example, showing the choice of meta-rules (OR, CT) matters for free consequences.
Limitations
- Results are shown only via a running example and theorems; no implementation or empirical evaluation is reported.
- Base logics are assumed classical for simplicity.
- Skeptical (grounded) semantics only; credulous reasoning is not characterized by the calculus.
Experimental setup
Baselines: adaptive logic proof theory for I/O logic (Straßer, Beirlaen, and Van De Putte 2
Builds on: Dung abstract argumentation DAC calculi (van Berkel and Straßer 2022) constrained I/O logic sequent-based argumentation frameworks (Arieli and Straßer 2015) ADAC (Arieli, van Berkel, and Straßer 2022)
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