By Renate Schmidt
This booklet constitutes the refereed lawsuits of the twenty second overseas convention on automatic Deduction, CADE-22, held in Montreal, Canada, in August 2009. The 27 revised complete papers and five procedure descriptions awarded have been conscientiously reviewed and chosen from seventy seven submissions. additionally, 3 invited lectures by way of exclusive specialists within the zone have been integrated. The papers are prepared in topical sections on mixtures and extensions, minimum unsatisfiability and automatic reasoning help, process descriptions, interpolation and predicate abstraction, resolution-based platforms for non-classical logics, termination research and constraint fixing, rewriting, termination and productiveness, types, modal tableaux with worldwide caching, mathematics.
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Additional info for Automated Deduction - Cade-22: 22nd International Conference on Automated Deduction, Montreal, Canada, August 2-7, 2009. Proceedings
Iii) In case of Sup-Neg or Sup-Pos, where C · Γ is the left premise, (C · Γ )γ is universally redundant wrt. Λ Φ. Split: C · Γ = · Γ and Λ does not produce Γ . Close: C · Γ = · ∅ ∈ Φ . It is not diﬃcult to show that actually carrying out an inference renders it universally redundant in the resulting sequent. With a view to implementation, this indicates that eﬀective proof procedures for ME+Sup indeed exist. Finally, a sequent Λ Φ is saturated iﬀ every ιME+Sup inference with premise Λ Φ is universally redundant wrt.
Therefore, it is desirable to have a theorem prover that terminates on satisﬁable instances. In general, this is not a realistic goal since pure ﬁrst-order logic is not decidable, and, even worse, there is no sound and complete procedure for ﬁrst-order logic formulæ of linear arithmetic with uninterpreted functions . Axioms such as transitivity (¬(x y) ∨ ¬(y z) ∨ x z) and monotonicity (¬(x y) ∨ f (x) f (y)) are problematic for any resolution-based Γ , since they tend to generate an unbounded number of clauses, even with a selection function that selects negative literals to prevent self-resolutions.
Split: C · Γ = · Γ and Λ does not produce Γ . Close: C · Γ = · ∅ ∈ Φ . It is not diﬃcult to show that actually carrying out an inference renders it universally redundant in the resulting sequent. With a view to implementation, this indicates that eﬀective proof procedures for ME+Sup indeed exist. Finally, a sequent Λ Φ is saturated iﬀ every ιME+Sup inference with premise Λ Φ is universally redundant wrt. Λ Φ. 4 (Static Completeness). If Λ Φ is a saturated sequent with a non-contradictory context Λ and ·∅ ∈ / Φ then the induced rewrite system RΛ Φ satisﬁes all relevant instances of all clauses in Φ wrt.