![]() Since any function can be turned into an argument of a higher-order function - this is called type-shifting, type-raising, and is essentially function composition, the analyst can - recursively - re-analyze functions as arguments, and viceversa, at will, depending on the type of the domains of the functions they may be interested in, in order to exhaustively analyze e into just two factors: a function F, and its argument a. The enormous advantage of lambda calculus over elementary logics as a metalanguage for LF comes from that, assuming the analyst accepts a very rich ontology such as Frege's, where entities are either functions or objects of any type one chooses to include, it is possible to consider any non-atomic expression e of any L as the product of two factors, a function F and its argument a, and say that F(a) = e. ![]() Lambda calculus is actually a meta-syntax for any type of logic That means that lambda calculus is a syntactic system for expressing various systems of logic, so it is up to the person at hand to decide what underlying system of logic they will be using it with. You can take 'lambda calculus' as a limit of expressivity for a formal language - it can acknowledge and interoperate with an infinite number of types of entities. Others acknowledged times, time intervals, modalities, propositions, possible worlds, and more. The most austere and restrictive ones acknowledge only elements and sets.īut Russell, Church, Reichembach and others, enriched it with higher types. Logics are ontologies, systems expressing what exists. Different logics acknowledge different logical entities They may vary in their suitability for denoting the semantics of natural languages because they acknowledge different logical entities, like events or time intervals, so they introduce new variables to be quantified over.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |