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Lambda-operator

**SEMANTICS: **An operator which makes it possible to construct expressions
which denote predicates or functions. Adding the lambda-operator to **predicate logic** makes it possible to
construct predicates from formulae with free variables.
** EXAMPLE:** two expressions with lambda-operators are given in (i):

(i) a lambda x [ kiss(john,x) ] b lambda x [ man(x) & Neg married(x) ]The lambda-expression in (i)a denotes the property of being kissed by John, the one in (i)b denotes the property of being an unmarried man. The lambda-operator plays an important role in

(ii) a every boy b lambda P [ All(x) [ boy(x) -> P(x) ]]The noun phrase in (ii)a is translated into a logical expression denoting a function from properties to truth values, assigning the value 1 to those properties that every boy has. When we combine the noun phrase in (ii)a with a predicate like

(iii) a Every boy walks b lambda P [ All(x) [ boy(x) -> P(x) ]] (walk) c All(x) [ boy(x) -> walk(x) ]

LIT. | Gamut, L.T.F. (1991) |