Semantics- Example -

Semantics – Example I

Logic for 'Flakey'

Constants Karen, John, Flakey, Hall, Kurt, f1, o1, o2Predicates R binary

S binaryFunctions F unary

Proper Axioms

x,y: R(x,y) F(x)=F(y)

Semantics – Example I

Domain 'Flakey'

Objects D = {Karen Meyers, John Bear, Flakey, Hall, Kurt Konolidge, the file, office-1, office-2}

Relations has = {(Karen Meyers, the file)}office = {(John Bear, office-1),

(Karen Meyers, office-2)}Functions f f(Karen Meyers)=office-2,

f(Flakey)=Hall, f(John Bear)=office-1,f(the file)=office-2

Semantics – Example I

Interpretation for Domain 'Flakey'

I (c) for Karen, John, Flakey, Hall, Kurt, f1, o1, o2 obvious mapping onto D with

Karen Meyers, John Bear, Flakey, Hall, Kurt Konolidge, the file, office-1, office-2I (R) has = {(Karen Meyers, the file)}I (S) office = {(John Bear, office-1),

(Karen Meyers, office-2)}I (F) f f(Karen Meyers)=office-2, f(Flakey)=Hall, f(John Bear)=office-1, f(the file)=office-2

Semantics – Example I

Is the 'Flakey' Domain a Model for the Proper Axiom?

x,y: R(x,y) F(x)=F(y)

D = {Karen Meyers, John Bear, Flakey, Hall, Kurt Konolidge, the file, office-1, office-2

I (R) has = {(Karen Meyers, the file)}I (S) office = {(John Bear, office-1),

(Karen Meyers, office-2)}I (F) f(Karen Meyers)=office-2, f(Flakey)=Hall, f(John Bear)=office-1, f(the file)=office-2