Automated Deduction – CADE-19: 19th International Conference by Edmund M. Clarke (auth.), Franz Baader (eds.)

By Edmund M. Clarke (auth.), Franz Baader (eds.)

This quantity comprises the papers provided on the nineteenth foreign convention on computerized Deduction (CADE-19) held 28 July–2 August 2003 in Miami seashore, Florida, united states. they're divided into the next different types: – four contributions by way of invited audio system: one complete paper and 3 brief abstracts; – 29 approved technical papers; – 7 descriptions of computerized reasoning structures. those court cases additionally include a quick description of the automatic theor- proving procedure festival (CASC-19) equipped through Geo? Sutcli?e and Chr- tian Suttner. regardless of many competing smaller meetings and workshops masking di?- entaspectsofautomateddeduction,CADEisstillthemajorforumfordiscussing new effects on all elements of computerized deduction in addition to providing new s- tems and enhancements of confirmed platforms. not like the former yr, while CADE was once one of many meetings engaging within the 3rd Federated good judgment convention (FLoC 2002), and subsequent 12 months, whilst CADE could be a part of the second one overseas Joint convention on automatic Reasoning (IJCAR 2004), CADE-19 was once equipped as a stand-alone event.

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Sample text

Thus, Rule min,(+,+) (α2+ ) = {α3min }, Pos min,(+,+) (α2+ ) = ∅, Exc min,(+,+) = {α1+ }. Moreover, in Ex. 2 the constructor “+” is simultaneously compatible with “∗” and “∗” on the arguments 1 and 2. To simplify the presentation, in the remainder we use a formulation with non-simultaneous compatibility in the definitions and theorems. To guarantee2 that the induction proof attempt for r1 = r2 transforms the equation into equivalent proof obligations over the theory T , both r1 and r2 must have a compatibility sequence f1 , .

But this is only possible if no f3 -rule α from Exc f2 ,f3 was used to create the context C . Then, the above term rewrites to f1 (p∗1 , D[ f2 (p∗2 , f3 (t∗j1 , q3∗ ), q2∗ ), . . , f2 (p∗2 , f3 (t∗jl , q3∗ ), q2∗ ) ], q1∗ ). As f1 is compatible with f2 , f1 -rules can move D outside into a new context E. But again, this is only possible if no f2 -rules from Exc f1 ,f2 were used to produce the context D. For every f3 -rule α ∈ / Exc f2 ,f3 , the set Rule f2 ,f3 (α) contains those f2 -rules which were used to create context D.

As mentioned in Sect. 3, compatibility may be extended to simultaneous compatibility and thus, this leads to a more general definition of DEC. Then, the equations (4) and (8) are also in DEC. For the distributivity equation u ∗ (v + w) = u ∗ v + u ∗ w, the left-hand side has the compatibility sequence ∗ and the right-hand side has the (simultaneous) sequence +, (∗, ∗) . Since Pos ∗ (α1∗ ) = Pos +,(∗,∗) (α1∗ ) = ∅, Pos ∗ (α2∗ ) = {2}, Pos +,(∗,∗) (α2∗ ) = {1 2, 2 2}, we obtain M (α1∗ ) = ∅, M1 (α2∗ ) = {v + w}, and M2 (α2∗ ) = {v, w}.

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