Artificial Intelligence and Symbolic Computation: 7th by Markus Rosenkranz (auth.), Bruno Buchberger, John Campbell

By Markus Rosenkranz (auth.), Bruno Buchberger, John Campbell (eds.)

This ebook constitutes the refereed court cases of the seventh overseas convention on man made Intelligence and Symbolic Computation, AISC 2004, held in Linz, Austria in September 2004.

The 17 revised complete papers and four revised brief papers offered including four invited papers have been rigorously reviewed and chosen for inclusion within the ebook. The papers are dedicated to all present features within the region of symbolic computing and AI: mathematical foundations, implementations, and purposes in and academia.

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Extra resources for Artificial Intelligence and Symbolic Computation: 7th International Conference, AISC 2004, Linz, Austria, September 22-24, 2004. Proceedings

Sample text

Hence in addition to the determinate truth values ∆ = {•, ◦} we also consider the indeterminate truth values ∇ = { , , , . } to be used in case of inconsistencies. We refer to the determinate and indeterminate truth values ∆ ∪ ∇ as the truth codes. We can then use, say, (∆ ∪ ∇) \ {•} as substitutes for the natural numbers ω = {0, 1, 2, 3, . }. The second question is: 2. How are we going to define the connectives? One way to proceed is as follows. First we want De Morgan laws to holds; hence ϕ ∨ ψ ≡ ¬(¬ϕ ∧ ¬ψ).

E. programs for directing the proof search process. These tactics are then formally specified with methods using a metalanguage. Standard patterns of proof failure and appropriate patches to the failed proofs attempts are represented as critics. To form a proof plan for a conjecture the proof planner reasons with these methods and critics. The proof plan consists of a customized tactic for the conjecture, whose primitive actions are the general-purpose tactics. This customized tactic directs the search of a tactic-based theorem prover.

Rρϕ = sρϕ for (r = s) ∈ C. We must show that ϕ := (ρ ◦ ϕ ) Q∃ is an U-solution. For uy = t: We need to show (uρϕ )y = tρϕ . But (uρϕ )y = ((λyt)ϕ )y = tϕ = tρϕ since u does not appear in t. For (r = s) ∈ C: We need to show (r = s)ϕ. But this clearly follows from (r = s)ρϕ . 2. Definition of Φ : U-solutions → U -solutions, and proof of Φ (Φϕ) = ϕ. For a U-solution ϕ define Φϕ = ϕ Q∃ . Then uρϕ = λytϕ = λytϕ = uϕ, and clearly vρϕ = vϕ for all other flexible ϕ. For (r = s) ∈ C, from rϕ = sϕ we easily obtain rϕ = sϕ .

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