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

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

ISBN-10: 3540405593

ISBN-13: 9783540405597

This quantity comprises the papers provided on the nineteenth foreign convention on automatic Deduction (CADE-19) held 28 July–2 August 2003 in Miami seashore, Florida, united states. they're divided into the subsequent different types: – four contributions by means of invited audio system: one complete paper and 3 brief abstracts; – 29 permitted technical papers; – 7 descriptions of computerized reasoning platforms. those lawsuits additionally include a brief description of the automatic theor- proving process festival (CASC-19) prepared through Geo? Sutcli?e and Chr- tian Suttner. regardless of many competing smaller meetings and workshops masking di?- entaspectsofautomateddeduction,CADEisstillthemajorforumfordiscussing new effects on all points of automatic deduction in addition to offering new s- tems and enhancements of demonstrated platforms. unlike the former yr, while CADE was once one of many meetings partaking within the 3rd Federated common sense convention (FLoC 2002), and subsequent 12 months, while CADE might be a part of the second one foreign Joint convention on automatic Reasoning (IJCAR 2004), CADE-19 used to be prepared as a stand-alone event.

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Extra resources for Automated Deduction – CADE-19: 19th International Conference on Automated Deduction, Miami Beach, FL, USA, July 28 – August 2, 2003. Proceedings

Example text

Now we check whether “+” is compatible with itself on argument 1. , D = s(✷), Rule +,+ (α2+ ) = {α2+ }, Var +,+ (α2+ ) = ∅. For α1+ : 0 + y → y, we have C = y, but y + x2 does not rewrite to a term D over FT . In general, for compatibility of g with f on argument j, we now permit that the compatibility requirement may be violated for some non-recursive rules Exc g,f of f (“exceptions”). However, a rule α should only be in Exc g,f if (14) does not rewrite to (15). Then, “+” is compatible with itself on argument 1 and Exc +,+ = {α1+ }.

The function f satisfies the no-theory condition iff for every q ∈ Q(f ), there is an f -rule l → r with l ↓f (x∗ )→q = r↓f (x∗ )→q . t. the rule f (x∗ ) → q. For “+” in Ex. 1, from the non-recursive rule 0 + y → y we obtain Q(+) = Q0,y (y) = {x2 }. However, the choice of q = x2 contradicts the second rule s(x) + y → s(x + y): normalizing by x1 + x2 → x2 produces non-identical terms y and s(y). Indeed, “+” (and also min, dbl, len, app) satisfy the no-theory condition. For the theory of Presburger Arithmetic, if f (x1 , .

F3 (t∗n , y ∗ )]. For any term r as above, it should be guaranteed that r[s∗ ] reduces to a term of the form E[r[t∗i1 ], . . , r[t∗ik ]] for some context E. For an instantiation C of C, we clearly have r[s∗ ] = →R/T f1 (p∗1 , f2 (p∗2 , f3 (s∗ , q3∗ ), q2∗ ), q1∗ ) f1 (p∗1 , f2 (p∗2 , C [f3 (t∗1 , q3∗ ), . . , f3 (t∗n , q3∗ )], q2∗ ), q1∗ ). Since f2 is compatible with f3 , C can be moved outside and turned into a new context D by rewriting f2 . But this is only possible if no f3 -rule α from Exc f2 ,f3 was used to create the context C .

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Automated Deduction – CADE-19: 19th International Conference on Automated Deduction, Miami Beach, FL, USA, July 28 – August 2, 2003. Proceedings by Edmund M. Clarke (auth.), Franz Baader (eds.)

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