By Nikolaj Bjørner (auth.), Bernhard Gramlich, Dale Miller, Uli Sattler (eds.)
This publication constitutes the refereed complaints of the sixth foreign Joint convention on computerized Reasoning, IJCAR 2012, held in Manchester, united kingdom, in June 2012. IJCAR 2012 is a merger of prime occasions in computerized reasoning, specifically CADE (International convention on automatic Deduction), FroCoS (International Symposium on Frontiers of mixing Systems), FTP (International Workshop on First-Order Theorem Proving), and TABLEAUX (International convention on automatic Reasoning with Analytic Tableaux and similar Methods). The 32 revised complete study papers and nine approach descriptions offered including three invited talks have been conscientiously reviewed and chosen from 116 submissions. The papers tackle all facets of computerized reasoning, together with foundations, implementations, and applications.
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Additional info for Automated Reasoning: 6th International Joint Conference, IJCAR 2012, Manchester, UK, June 26-29, 2012. Proceedings
Example text
Let Π ∈ {L, R}∗ and β ∈ {0, 1}∗ and q1 , q2 ∈ Q be two states in M , where q1 , q2 ∈ V ar(S). Then Πq1 ↔∗SM q2 β if and only if Πq1 ↔∗ST h q2 β. Proof. The “only if” part is obvious since ↔∗SM is subsumed by ↔∗ST h . Conversely, suppose Πq1 ↔∗SM q2 β holds. In this case note that the only applicable −−→ −−→ ∗ ∗ ∗ rules in CM ∪ ST h are the rules in CM . t. SM . Then the rules involving the non-state variables ut do not affect the derivation −−→ and hence ST h does not affect the rewrite steps. t.
D. This difference is, however, irrelevant since C ≡? D can be seen as a shorthand for the two subsumptions C ? D and D ? C, and C ? D has the same unifiers as C D ≡? C. Second, note that—as in [2]—we have restricted the background ontology O to be ground. This is not without loss of generality. In fact, if O contained variables, then we would need to apply the substitution also to its axioms, and instead of requiring σ(Ci ) O σ(Di ) we would thus need to require σ(Ci ) σ(O) σ(Di ), which would change the nature of the problem considerably.
The restriction to ground general TBoxes is, however, appropriate for the application scenario sketched in the introduction. In this scenario, there is a fixed background ontology, which is extended with definitions of new concepts by several knowledge engineers. t. , define the same intuitive concept. , they define new concepts rather than adding definitions SAT Encoding of Unification in ELHR+ 35 for concepts that already occur in the background ontology. , be found in [12], where different extensions of SNOMED CT are checked for overlaps, albeit not by using unification, but by simply testing for equivalence.