TY  - JOUR
A1  - Denecke, Klaus-Dieter
T1  - The partial clone of linear formulas
T2  - Siberian mathematical journal
N2  - A term t is linear if no variable occurs more than once in t. An identity s ≈ t is said to be linear if s and t are linear terms. Identities are particular formulas. As for terms superposition operations can be defined for formulas too. We define the arbitrary linear formulas and seek for a condition for the set of all linear formulas to be closed under superposition. This will be used to define the partial superposition operations on the set of linear formulas and a partial many-sorted algebra Formclonelin(τ, τ′). This algebra has similar properties with the partial many-sorted clone of all linear terms. We extend the concept of a hypersubstitution of type τ to the linear hypersubstitutions of type (τ, τ′) for algebraic systems. The extensions of linear hypersubstitutions of type (τ, τ′) send linear formulas to linear formulas, presenting weak endomorphisms of Formclonelin(τ, τ′).
KW  - term
KW  - formula
KW  - superposition
KW  - linear term
KW  - linear formula
KW  - clone
KW  - partial clone
KW  - linear hypersubstitution
Y1  - 2019
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/48892
SN  - 0037-4466
SN  - 1573-9260
VL  - 60
IS  - 4
SP  - 572
EP  - 584
PB  - Pleiades Publ.
CY  - New York
ER  -