By Edmund M. Clarke (auth.), Franz Baader (eds.)
This quantity comprises the papers awarded 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 next different types: – four contributions by means of invited audio system: one complete paper and 3 brief abstracts; – 29 permitted technical papers; – 7 descriptions of automatic reasoning platforms. those complaints additionally include a quick description of the automatic theor- proving approach festival (CASC-19) geared up through Geo? Sutcli?e and Chr- tian Suttner. regardless of many competing smaller meetings and workshops overlaying di?- entaspectsofautomateddeduction,CADEisstillthemajorforumfordiscussing new effects on all elements of automatic deduction in addition to proposing new s- tems and enhancements of verified structures. not like the former 12 months, while CADE was once one of many meetings engaging within the 3rd Federated common sense convention (FLoC 2002), and subsequent 12 months, while CADE can be a part of the second one overseas Joint convention on computerized Reasoning (IJCAR 2004), CADE-19 was once geared up as a stand-alone event.
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Additional resources for Automated Deduction – CADE-19: 19th International Conference on Automated Deduction, Miami Beach, FL, USA, July 28 – August 2, 2003. Proceedings
The Pos-sets allow us to estimate which subterms of r1 and r2 with deﬁned symbols will occur after this simpliﬁcation without actually attempting an induction proof. Let M (α) denote the set of these subterms. ,ge (α) are in M (α). Moreover, the right-hand sides r2 [t∗1 ], . . , r2 [t∗n ] of induction hypotheses may also contain deﬁned symbols. Finally, if α ∈ Exc fd−1 ,fd , then compatibility does not hold for r1 . In this case, M (α) must include the whole simpliﬁed instantiated left-hand side r1 .
Using this information, we identify those subterms which might appear in subgoals during a proof attempt and we require that these terms satisfy the no-theory condition. Then all subgoals can be safely generalized to formulas over a decidable theory. Deciding Inductive Validity of Equations 31 Checking whether an equation belongs to DEC can be done eﬃciently, since it mainly depends on the deﬁnitions of functions. Therefore, the required information can be pre-compiled. Moreover, for every equation in DEC, a failed induction proof attempt refutes the conjecture.
Am · xm . Here, “a · x” denotes the term x + . . + x (a times) and “a0 ” denotes 1 + . . + 1 (a0 times). , without parentheses) since “+” is associative and commutative. For s =TP A b0 +b1 ·x1 +. +bm ·xm and t as above, we have s =TP A t iﬀ a0 = b0 , . . , am = bm . Instead of validity, we are usually interested in inductive validity. Deﬁnition 3 (Inductive Validity). A universal formula ∀x∗. , σ substitutes all variables of ϕ by ground terms of Terms(FT ). In general, validity implies inductive validity, but not vice versa.