The Correspondence Between Monotonic Many Sorted Signatures and Well-Founded Graphs. Part II

Czeslaw Bylinski

Warsaw University, Bialystok

Piotr Rudnicki

University of Alberta, Edmonton

Summary.

The graph induced by a many sorted signature is defined as follows: the vertices are the symbols of sorts, and if a sort $s$ is an argument of an operation with result sort $t$, then a directed edge $[s, t]$ is in the graph. The key lemma states relationship between the depth of elements of a free many sorted algebra over a signature and the length of directed chains in the graph induced by the signature. Then we prove that a monotonic many sorted signature (every finitely-generated algebra over it is locally-finite) induces a {\em well-founded} graph. The converse holds with an additional assumption that the signature is finitely operated, i.e. there is only a finite number of operations with the given result sort.

This work was partially supported by NSERC Grant OGP9207.

MML Identifier: MSSCYC_2

Contents (PDF format)

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