Application( Cont. Example(Graphs) Let C=R) where R is a binary relation. We can characterize undirected irreflexive graphs with O VXR(x, x), oxvy(R(x,y)→R(y,x)
Application(Cont.) . Example (Graphs) . . Let L = {R} where R is a binary relation. We can characterize undirected irreflexive graphs with 1. ∀x¬R(x, x), 2. ∀x∀y(R(x, y) → R(y, x)). Yi Li (Fudan University) Discrete Mathematics June 9, 2013 6 / 15
Application( Cont. Example(Groups) Let C=f, el where is a binary relation and e is a constant symbol. The class of group is described as oVxe·x=x.e=x O VxVyVzx·(yz)=(x·y)·z, xyx:y=y·x=e
Application(Cont.) . Example (Groups) . . Let L = {·, e} where · is a binary relation and e is a constant symbol. The class of group is described as 1. ∀xe · x = x · e = x, 2. ∀x∀y∀zx · (y · z) = (x · y) · z, 3. ∀x∃yx · y = y · x = e. Yi Li (Fudan University) Discrete Mathematics June 9, 2013 7 / 15