A Practical Comparison of Qualitative Inferences with Preferred Ranking Models

Ranking kinematics for revising by contextual information

“…The proof of Proposition 1 is a direct consequence of the propositions presented in [14]. The constraints given by (5) ensure that a c-revision κ * of κ by Δ as given by (4) accepts Δ, and κ 0 given by ( 6) is a normalization factor ensuring that κ * (ω) = 0 for at least one world ω. Since (4) and (5) provide a general schema for revision operators, many c-revisions are possible.…”

“…Also the set of c-representations can be characterized as the solutions of a CSP; furthermore, for skeptical c-inference, taking all c-representations of a set of conditionals into account, that was introduced in [2] and further elaborated in [4], this observation also holds. Solving these CSPs has been achieved by a constraint logic programming approach [5], employing the contraint solver provided by SICStus prolog [6]. An extension of these implementations to Hansson's descriptor revision [10] instantiated to a conditional logic is presented in [20], underlying the feasibility of implementing c-revsions by using a solver for CSPs because revisions can be simulated straightforwardly within the framework of descriptor revision.…”

“…Let σ be a selection strategy that chooses Pareto-minimal impact factors with respect to (5). From (IP-ESP σ ) it follows that 4 The prior OCF κ and the conditionalized OCFs κ|A i with i = 1, 2, 3 displayed in one column as if they were merged together.…”

“…For Δ = Δ 0 ∪ Δ 1 and Δ = Δ 0 ∪ Δ 1 with Δ 1 = {(B m |X m )} and Δ 1 = {(B m |X m )} we have to show σ (κ, Δ) = σ (κ, Δ ). Let us compare cr(κ, Δ) i and cr(κ, Δ ) i .According to(5), the only difference in the construction of the two constraints is that whenever ω |= X m B m (or ω |= X m B m , respectively) is used as a condition in the minimization or in the sum expressions in cr(κ, Δ) i , then ω |= X m B m (or ω |= X m B m , respectively) is used in cr(κ, Δ ) i . Thus, because X m B m ≡ X m B m and X m B m ≡ X m B m , we get cr(κ, Δ)…”

Normal forms of conditional knowledge bases respecting system P-entailments and signature renamings

“…Furthermore, we will study the normalizing systems Θ ρ , Θ ra , Θ ρra , and the generating algorithm KB ρra with respect to efficiency and complexity. Using implementations of these methods and the InfOCF system [25,26], we will empirically evaluate properties of given and of systematically generated conditional knowledge bases; some first results of this emperical evaluation are given in [27]. Another open question to be investigated is how the normal forms introduced in this article can be applied or extended to defeasible logics where conditionals occur in the form of defeasible concept subsumptions as in, e.g., [28].…”