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Uniqueness of minimal coverings of maximal partial clones Schölzel, Karsten in Algebra Universalis (2011), 65(4), 393-420 A partial function f on a k-element set Ek is a partial Sheffer function if every partial function on Ek is definable in terms of f. Since this holds if and only if f belongs to no maximal partial clone ... [more ▼] A partial function f on a k-element set Ek is a partial Sheffer function if every partial function on Ek is definable in terms of f. Since this holds if and only if f belongs to no maximal partial clone on Ek, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on Ek. We show that for each k ≥ 2, there exists a unique minimal covering. [less ▲] Detailed reference viewed: 86 (0 UL)A classification of partial Boolean clones ; Schölzel, Karsten in Proceedings of The International Symposium on Multiple-Valued Logic (2010) We study intervals I(A) of partial clones whose total functions constitute a (total) clone A. In the Boolean case, we provide a complete classification of such intervals (according to whether the interval ... [more ▼] We study intervals I(A) of partial clones whose total functions constitute a (total) clone A. In the Boolean case, we provide a complete classification of such intervals (according to whether the interval is finite or infinite), and determine the size of each finite interval I(A). [less ▲] Detailed reference viewed: 92 (0 UL)Number of maximal partial clones Schölzel, Karsten in Proceedings of The International Symposium on Multiple-Valued Logic (2010) All maximal partial clones on 4-element, 5-element, and 6-element sets have been found and are compared to the case of maximal clones of all total functions. Due to the large numbers of maximal partial ... [more ▼] All maximal partial clones on 4-element, 5-element, and 6-element sets have been found and are compared to the case of maximal clones of all total functions. Due to the large numbers of maximal partial clones other criteria to check for generating systems of all partial functions are analyzed. [less ▲] Detailed reference viewed: 83 (0 UL)Minimal coverings of maximal partial clones Schölzel, Karsten in Proceedings of The International Symposium on Multiple-Valued Logic (2009) A partial function f on a κ-element set Eκ is a partial Sheffer function if every partial function on Eκ is definable in terms of f. Since this holds if and only if f belongs to no maximal partial clone ... [more ▼] A partial function f on a κ-element set Eκ is a partial Sheffer function if every partial function on Eκ is definable in terms of f. Since this holds if and only if f belongs to no maximal partial clone on Eκ, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on Eκ. We show that for each κ ≥ 3 there exists a unique minimal covering. [less ▲] Detailed reference viewed: 80 (0 UL)The minimal covering of maximal partial clones in 4-valued logic Schölzel, Karsten in Proceedings of The International Symposium on Multiple-Valued Logic (2009) A partial function f on a κ-element set Eκ is a partial Sheffer function if every partial function on Eκ is definable in terms of f. Since this holds if and only if f belongs to no maximal partial clone ... [more ▼] A partial function f on a κ-element set Eκ is a partial Sheffer function if every partial function on Eκ is definable in terms of f. Since this holds if and only if f belongs to no maximal partial clone on Eκ, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on Eκ. It is shown that. [less ▲] Detailed reference viewed: 93 (1 UL) |
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