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

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

This ebook constitutes the refereed court cases of the seventh foreign 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 provided including four invited papers have been conscientiously reviewed and chosen for inclusion within the publication. The papers are dedicated to all present points within the sector of symbolic computing and AI: mathematical foundations, implementations, and purposes in and academia.

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

Example text

N instead of the term ((ϕψ1 ) . )ψn . Note that the relational types are τ1 . . τn o (also called predicates). If we add a sort of individuals ι to the propositional higher order logic ∇ we obtain the higher order logic ∇ι (further sorts can be added, but for our purposes they are not needed). 2 Semantics As usual Y X is the set of functions from X to Y . A universe U is an indexed set of type universes Uτ = ∅ such that Uαβ ⊆ UβUα . The universe is full if ⊆ is replaced by =. A basic interpretation I on a universe U is a function I : Cτ → Uτ such that Iκτ ∈ Uτ for κτ ∈ Cτ .

Where Do the Wave Annotations in Wave-Rules and in Induction Rules Come from? Wave annotation can be inserted in expressions by a family of difference unification algorithms invented by Basin and Walsh (see [Basin & Walsh, 1993]). These algorithms are like unification but with the additional ability to hide non-matching structure in wave-fronts. Ground difference matching can be used to insert wave annotation into induction rules and ground difference unification for wave-rules. ‘Ground’ means that no instantiation of variables occurs.

We use the following abbreviations: ϕ ≡ ¬ϕ ϕ˙ ≡ ∂ ϕ ϕ¨ ≡ ∂ ϕ˙ ... The indeterminacy generation operator is injective and we can use it for the natural numbers. We say much more about it later. The truth tables in case of four truth values are the following. | • ◦ • ◦ ◦ • | || • • • • | • | • || • • || | || | || = • ◦ • ◦ | || • ◦ ◦ ◦ ◦ • ◦ ◦ | || ∂ ◦ ◦ • ◦ ◦ ◦ ◦ • • ◦ • | || || ◦ | The truth table only displays equality = between formulas (the biimplication operator ⇔), but it is applicable to any type.

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