In the Head of the Beholder: Comparing Different Proof Representations

Alrabbaa, Christian; Borgwardt, Stefan; Hirsch, Anke; Knieriemen, Nina; Kovtunova, Alisa; Rothermel, Anna Milena; Wiehr, Frederik

doi:10.1007/978-3-031-21541-4_14

Cited by 2 publications

(3 citation statements)

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“…The concrete domain D Q,diff has the set Q of rational numbers as domain and, in addition to ⊤ and ⊥, the concrete predicates x = q, x > q, and x + q = y, for constants q ∈ Q, with their natural semantics [7]. For example, 4 The concrete domain D Q,lin has the same domain as D Q,diff , but its predicates other than {⊤, ⊥} are given by linear equations n i=1 a i x i = b, for a i , b ∈ Q, with the natural semantics [11], e.g. the linear equation x + y − z = 0 is interpreted as the ternary addition predicate…”

Section: Concrete Domainsmentioning

confidence: 99%

“…In principle, such a consequence can be explained by producing a proof for it, which shows how the consequence can be derived from the axioms in the ontology by applying certain easy-to-understand inference rules. In recent work, we have investigated how proofs for consequences derived by DL reasoners can be computed [1,2] and displayed [27] in a user-friendly way [4]. However, like previous work [17,18], this was restricted to DLs without concrete domains.…”

Section: Introductionmentioning

confidence: 99%

“…Often, the classification is done only for concept names in O, but we use a variant that considers all subconcepts, as it is done by the EL ⊥ reasoner Elk 4. The index diff in its name is motivated by the fact that such a predicate fixes the difference between the values of two variables.…”

mentioning

confidence: 99%

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Finding Small Proofs for Description Logic Entailments: Theory and Practice

Alrabbaa¹,

Baader²,

Borgwardt³

et al.

EPiC Series in Computing

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Logic-based approaches to AI have the advantage that their behaviour can in principle be explained by providing their users with proofs for the derived consequences. However, if such proofs get very large, then it may be hard to understand a consequence even if the individual derivation steps are easy to comprehend. This motivates our interest in finding small proofs for Description Logic (DL) entailments. Instead of concentrating on a specific DL and proof calculus for this DL, we introduce a general framework in which proofs are represented as labeled, directed hypergraphs, where each hyperedge corresponds to a single sound derivation step. On the theoretical side, we investigate the complexity of deciding whether a certain consequence has a proof of size at most n along the following orthogonal dimensions: (i) the underlying proof system is polynomial or exponential; (ii) proofs may or may not reuse already derived consequences; and (iii) the number n is represented in unary or binary. We have determined the exact worst-case complexity of this decision problem for all but one of the possible combinations of these options. On the practical side, we have developed and implemented an approach for generating proofs for expressive DLs based on a non-standard reasoning task called forgetting. We have evaluated this approach on a set of realistic ontologies and compared the obtained proofs with proofs generated by the DL reasoner ELK, finding that forgetting-based proofs are often better w.r.t. different measures of proof complexity.

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Section: Concrete Domainsmentioning

confidence: 99%