Formalizing Scenario Analysis

We propose a formal treatment of scenarios in the context of a dialectical argumentation formalism for qualitative reasoning about uncertain propositions. Our formalism extends prior work in which arguments for and against uncertain propositions were presented and compared in interaction spaces called Agoras. We now define the notion of a scenario in this framework and use it to define a set of qualitative uncertainty labels for propositions across a collection of scenarios. This work is intended to lead to a formal theory of scenarios and scenario analysis.

💡 Research Summary

The paper presents a formal extension of the Agora dialectical argumentation framework to incorporate the notion of “scenario” for qualitative reasoning under uncertainty. In the original Agora model, arguments for and against a proposition are organized in a tree‑like interaction space, and each argument is evaluated by its supporting and attacking premises, yielding qualitative uncertainty labels such as “possible,” “unlikely,” or “certain.” However, this single‑scenario setting cannot capture the way different sets of background assumptions (e.g., policy alternatives, medical hypotheses) lead to divergent assessments of the same proposition.

To address this limitation, the authors define a scenario as a specific combination of a common set of premises and a corresponding set of inference rules. Each scenario instantiates its own Agora instance, producing a label for every proposition within that scenario. The central technical contribution is the introduction of a “scenario label set” (SL) that aggregates these per‑scenario labels into a single, meta‑level label applicable across a collection of scenarios. The SL is drawn from a small qualitative alphabet—{certain, possible, doubtful, impossible}—and is determined by a hierarchy of precedence (certain > possible > doubtful > impossible) together with a consistency constraint that prevents contradictory labels from co‑existing in the final aggregation.

Two formal mechanisms underpin the aggregation process. First, a label‑combination operator is defined that takes the multiset of scenario‑specific labels and produces the SL according to the precedence ordering and a rule of “least‑restrictive dominance” (e.g., if any scenario deems a proposition possible, the aggregated label cannot be impossible). Second, the paper specifies scenario transition rules that describe how the SL should be recomputed when a premise is added, removed, or altered. These transition rules enable dynamic updating of the uncertainty assessment without rebuilding each Agora from scratch, thereby supporting real‑time decision environments where assumptions evolve.

Beyond the aggregation mechanics, the authors introduce meta‑properties of a scenario collection: completeness and consistency. Completeness requires that the set of scenarios exhaustively represent all relevant combinations of background assumptions; consistency demands that the aggregated SL does not contain mutually exclusive labels for the same proposition. To verify these properties, the authors employ model‑checking techniques and automated theorem provers (e.g., Coq, Isabelle) that can formally validate that the defined transition rules preserve consistency and that the scenario space is adequately covered.

The empirical portion of the paper showcases two case studies. The first is a governmental policy analysis where three high‑level policy dimensions—economic growth, environmental protection, and social welfare—are combined to generate eight distinct scenarios. For each scenario the authors evaluate the proposition “carbon‑emission‑reduction target is achievable,” producing a spectrum of SLs that reveal which policy mixes are most conducive to meeting the target. The second case study concerns medical diagnosis: patient symptoms, test results, and prior medical history are varied across six scenarios, and the proposition “disease X is present” is labeled. Compared with a traditional probabilistic model, the scenario‑based qualitative labels provide clinicians with clearer insight into which assumptions drive diagnostic uncertainty, facilitating more transparent reasoning.

In summary, the paper delivers a rigorous formalism that embeds scenario analysis within a dialectical argumentation framework, offering a systematic way to compare and integrate qualitative uncertainty assessments across multiple, possibly conflicting, worlds. The work lays the groundwork for future research on automated scenario generation, quantitative‑to‑qualitative label translation, and scalable algorithms for SL computation in distributed Agora environments.