RA³: Reasoning as Action Abstractions

• RA³ is a formal paradigm for modeling dynamic reasoning by replacing step-wise inferential operations with explicit, modular action abstractions.
• It unifies the handling of frame, qualification, and ramification problems using assumption-based and argumentation-theoretic mechanisms that ensure minimal, traceable state changes.
• The framework is applied to classic scenarios like the Yale Shooting Problem and Blocked Car scenario, enabling transparent commonsense and scientific reasoning.

Reasoning as Action Abstractions (RA³) is a formal paradigm for structuring, modeling, and mechanizing reasoning in dynamic domains by treating reasoning processes themselves as composed of modular, high-level “actions.” The central idea is to replace raw, step-wise inferential operations in reasoning about actions, change, and agency with explicit, manipulable abstractions—enabling declarative representation, non-monotonic inference, and uniform treatment of classic problems such as the frame, qualification, and ramification problems. This approach leverages an assumption-based, argumentation-theoretic foundation and provides a logical and model-theoretic account of actions and their indirect effects, allowing for transparent management of persistence, exceptions, and explanations in domains with complex dynamics.

1. Assumption-Based and Argumentation-Theoretic Foundation

RA³ builds on the explicit enumeration and manipulation of assumptions within a logical framework. The knowledge base is extended with an assumption base, whose members are typed according to the kinds of non-monotonic inferences required. Two primary classes of assumptions are fundamental:

• Frame Assumptions (FA): Capture the default persistence of fluents (state variables), formalizing the inertia law—if a fluent is true at time $t$, and nothing acts to change it, assume it remains true at $t+1$.
• Qualification Assumptions (AQ): Model the principle that an action is assumed to succeed in producing its effect unless explicitly “qualified” (prevented) by further information.

The framework defines a set of inference rules $R$, partitioned into classical logical rules, frame-based persistence axioms, action description (effect) rules, and qualification rules (for modeling failures/qualifications of actions).

A key innovation is the attack relation between assumptions and the notion of a leniently rejected assumption—an assumption may be rejected by virtue of leading to inconsistency, even if not directly challenged. This accounts for indirect conflicts and supports the dynamic management of default and exceptional cases.

2. Uniform Treatment of Frame, Qualification, and Ramification Problems

Traditional approaches often addressed the frame and qualification problems (the need to explicitly model persistence and the rare, exceptional failure of expected effects) in isolation, relying on implicit minimization or ad hoc default logic. In RA³, these are unified by:

• Explicit enumeration of assumptions controlling state changes, for both persistence and action qualifications.
• Coherent models: Every state change across a transition must be justified either by a basic (“known”) action or, if unaccounted for, by the introduction of a dummy action explaining unexpected change. This supports a uniform minimization strategy by prioritizing minimal, traceable changes (prioritised minimal models or PMMs).
• Canonical Prioritised Minimal Models (CPMM): These are models that maximize the set of accepted frame assumptions (and, in the presence of qualifications, qualification assumptions as well).

The interplay between frame and qualification assumptions is controlled by a fixed prioritization: when a conflict exists over the same fluent, qualification assumptions take precedence—reflecting the intuition that action execution trumps default persistence only when its effect is not qualified.

Formally, equivalence theorems connect plausible sets of assumptions (those that are “admissible” given minimality and maximality criteria) with the existence of corresponding CPMMs.

3. Handling Ramifications and Complex Dynamics

RA³ supports modeling of indirect effects (ramifications), concurrency, and non-determinism:

• Indirect effects: The framework distinguishes explicitly between external events (direct, intentional effects) and internal events (ramifications imposed by domain constraints). This enables the modeling of causation chains where multiple events may be triggered before a stable successor state is reached.
• Stable and unstable states: Temporal representations encode both stable timepoints (where all constraints are satisfied) and intermediate unstable states (where a chain of ramifications is in progress). The logic embodies definitions such as “instantwise state” and an explicit causation relation to manage these chains.

Qualification assumptions can be indexed not only by affected fluents but also by the specific action that brings about an effect, which is critical when multiple concurrent actions could independently trigger the same fluent (e.g., two independent actions both breaking a vase).

4. Concrete Applications and Comparative Advantages

The argumentation-theoretic RA³ approach is demonstrated in canonical domains:

• Yale Shooting Problem: The approach resolves the classic conflict between the inertia of “loaded” and the effect of “shooting” by explicit rejection of the relevant frame assumption.
• Blocked Car scenario: Competing qualification assumptions (e.g., “engine starts if turned” vs. “car does not start if tailpipe blocked”) yield alternative extensions; the minimality principle selects the more intuitive extension.
• Stolen Car Problem and Abduction: Introduction of dummy actions and competition between frame and qualification assumptions enables abductive explanations for surprising observations.

Relative to circumscription, default logic, and minimization-based nonmonotonic formalisms, key advantages include:

Feature	Circumscription/Defaults	RA³ Argumentation Framework
Reason trace transparency	Implicit	Explicit via assumptions
Handling of exceptions	Problematic/ad hoc	Systematic via assumption attacks
Modular extension	Difficult	Flexible via argumentation semantics

The explicit reasoning about which assumptions are accepted/rejected allows for modular analysis, efficient explanation, counterfactual reasoning, and adaptation of semantics (e.g., to stability, admissibility, preferable sets).

5. Formal Structure and Logical Properties

RA³ provides a precise semantic account, grounded in temporal propositional logic and formalized through:

• Assumption-based semantics: Acceptable (plausible) sets of assumptions correspond to CPMMs. Proofs show that for every plausible set $A$, the $A$-relativized model is a CPMM, and vice versa.
• Conflict resolution: Built-in mechanisms, such as lenient rejection and prioritization between FA and AQ, ensure that the framework is consistent with commonsense intuitions and robust to conflicting information.

A canonical model is constructed by achieving maximal acceptance of frame assumptions (in the absence of qualification attacks) and minimal deviation from expected action effects.

6. Integration with Commonsense Cognitive and Scientific Reasoning

By elevating reasoning steps—selection, rejection, and modification of assumptions—to explicit abstract actions, RA³ mirrors the reasoning patterns underlying both everyday cognitive processes and formal scientific inquiry.

• Commonsense reasoning: The explicit handling of defaults and exceptions mirrors human reasoning about “normality” and atypical failures or interventions.
• Explanation and belief revision: The modular structure allows transparent updates and explanations when new evidence arises.
• Bridging to scientific representation: RA³’s logical rigor and modular semantics provide a bridge between informal, qualitative explanations and formally tractable scientific modeling.

7. Summary and Impact

RA³ recasts the reasoning about action and change as reasoning over explicit action abstractions—implemented via an argumentation-theoretic mechanism that models persistence, exceptions, and indirect effects in a single expressive, nonmonotonic framework. Through explicit assumption management, minimality/maximality criteria, and flexible argumentation semantics, it enables robust, modular reasoning suitable for complex dynamic and multiagent domains. The framework’s logical definitions (e.g., coherent models, CPMM, Q-plausibility) and theorems provide a formal foundation for both explanation and efficient computation. By integrating abstract and concrete action reasoning, RA³ advances the rigorous representation of dynamic worlds and supports realistic, explainable AI reasoning about action and change (Foo et al., 2011).