Ontology-based inference for causal explanation

We define an inference system to capture explanations based on causal statements, using an ontology in the form of an IS-A hierarchy. We first introduce a simple logical language which makes it possible to express that a fact causes another fact and that a fact explains another fact. We present a set of formal inference patterns from causal statements to explanation statements. We introduce an elementary ontology which gives greater expressiveness to the system while staying close to propositional reasoning. We provide an inference system that captures the patterns discussed, firstly in a purely propositional framework, then in a datalog (limited predicate) framework.

💡 Research Summary

The paper proposes a formal inference system that captures explanatory reasoning based on causal statements, enriched by an IS‑A ontology. The authors first introduce a minimal logical language in which facts can be expressed as causing other facts (α causes β) and as explaining other facts (α explains β). They then define a set of inference patterns that allow one to derive explanation statements from causal statements combined with ontological knowledge.

Four kinds of atoms are distinguished: (C) causal atoms, (O) ontological IS‑A atoms, (W) the set of all implications that can be derived from C and O, and explanation atoms of the form “α explains β because possible Φ”. The key insight is that causal information alone is insufficient for explanation; ontological generalizations (going up the hierarchy) or specializations (going down) are required to bridge gaps between cause and effect.

The authors present five core inference patterns:

1. Base case – If α causes β and α is not contradicted in W, then α explains β (Φ = {α}).
2. Upward generalization – If α causes β and β →IS‑A γ, then α explains γ (Φ = {α}).
3. Downward specialization – If α causes β and γ →IS‑A β, then α explains γ (Φ = {α, γ}).
4. Transitivity of explanations – Two causal chains can be linked via ontological links between intermediate terms, yielding an explanation from the original cause to the final effect. Two sub‑cases are distinguished depending on whether the ontological link goes upward or downward. The resulting explanation’s condition set Φ is the union of the conditions of the constituent explanations.
5. Condition simplification – When multiple explanations of the same α and β exist with different condition sets Φ₁,…,Φₙ, and W entails the disjunction of these condition sets, the explanation can be simplified to a single condition set that captures the logical consequence of all.

These patterns are formalized as inference rules that check for consistency against the background knowledge W (e.g., ensuring ¬α is not derivable). The authors emphasize that explanations are provisional: they hold only as long as the supporting conditions remain possible.

After presenting the propositional framework, the paper extends the approach to a restricted predicate logic resembling Datalog. In this setting, constants are linked by IS‑A relations, and predicates may have “existential” or “universal” arguments, allowing representation of more complex events (e.g., “ship sinks” or “fireworks launch”). Ontological links are also defined between predicates, enabling the same inference patterns to operate on multi‑arity facts. Because the resulting rules are Datalog‑compatible, they can be executed by standard Datalog engines, making the approach practical for knowledge‑base applications.

The discussion acknowledges several limitations. Causality is treated as deterministic and always true; probabilistic, temporal, or counterfactual aspects are omitted. The ontology is assumed to be reflexive (every term IS‑A itself), which simplifies the rule set but may be unrealistic for real‑world taxonomies. Moreover, the system relies on user‑provided causal and ontological facts; automatic extraction is left for future work.

In conclusion, the paper delivers a clear, formally grounded method for deriving explanations from causal statements enriched by an IS‑A hierarchy. By providing both a propositional and a Datalog‑style implementation, it bridges theoretical reasoning with executable knowledge‑base inference, opening avenues for applications in domains where explanatory reasoning is essential (e.g., diagnostics, legal reasoning, scientific discovery). Future research directions include integrating uncertainty, handling dynamic temporal information, and scaling the ontology to richer, multi‑inheritance structures.