the negative literal ¬ a is removed. This has the effect to loosen the constraints imposed on a query e.g., by omitting in the query an unwanted ingredient.

For example, the substitution ¬ peanut oil ∅ applied to tgt generates the query σ(tgt) = chinese∧soup∧leek, in which the condition on the ingredient peanut oil is omitted.

However, when O is the only source of adaptation knowledge, the system is only able to perform simple adaptations, in which the modifications made to Sol(srce) correspond to a sequence of substitutions that can be used to transform srce into tgt. Therefore, an additional adaptation knowledge base AKB is introduced. AKB contains a set of reformulations (σ, Σ) that capture more complex adaptation strategies.

## 3.2 The Cbr Process In Taaable

Retrieval. The retrieval algorithm is based on a *smooth classification* algorithm on an index hierarchy. Such an algorithm aims at determining a set of modifications to apply to tgt in order to obtain a modified query srce that matches at least one recipe Sol(srce) of the case base. The algorithm computes a *similarity path*,
which is a composition of substitutions SP = σq ◦ σq−1 **◦ · · · ◦** σ1 such that there exists at least one recipe Sol(srce) matching the modified query srce =
σq(σq−1(. . . σ1(tgt) . . .)), i.e., such that Sol(srce) O srce holds. Thus, a similarity path SP can be written:
Sol(srce) O srce σq ←−
σq−1 **←−− · · ·** ←−
σ1tgt For example, to solve the above query tgt, the system generates a similarity path SP = σ2 ◦ σ1, with:
tgt = chinese ∧ soup ∧ leek ∧ ¬ peanut oil σ1 = ¬ peanut oil ∅, σ2 = leek onions srce = chinese ∧ soup ∧ onions Sol(srce) = chinese ∧ soup ∧ green onion ∧ . . . ∧ peanut oil ∧ *Nothing else* In this similarity path, Sol(srce) is the propositional representation of the recipe Wonton Soup. Since the ontology O contains the axiom green onion ⇒ onions, the modified query srce = σ2 ◦ σ1 (tgt) verifies Sol(srce) O srce.

Adaptation. To a similarity path is associated an *adaptation path* AP, which is a composition of substitutions AP = Σ1 ◦ Σ2 **◦ · · · ◦** Σq such that the modified recipe Sol g(tgt) = Σ1(Σ2(. . . Σq(Sol(srce)) . . .)) solves the initial query tgt, i.e.,
verifies Sol g(tgt) O tgt. Thus, an adaptation path AP can be written The adaptation path AP is constructed from the similarity path SP by associating a substitution Σi to each substitution σi. To determine which substitution Sol(srce)
Σq
−→
Σq−1
−−−→ · · ·
Σ1
−→ Sol g(tgt) O tgt