LYCOS RETRIEVER 
First-Order Logic: Fol Ruleml
built 654 days ago
"The Language of First-order Logic [A]nd Tarski's World redress one of the main shortcomings of traditional beginning-level logic texts which emphasize the formal aspects of logic and pay scant attention to semantics. Tarski's World sets a high standard for those who follow." --Kevin Compton, Journal of Symbolic Logic.
Source:
Generic first-order logic (GFOL) is a first-order logic parameterized with terms defined axiomatically (rather than constructively), by requiring them to only provide generic notions of free variable and substitution satisfying reasonable properties. GFOL has a complete Gentzen system generalizing that of FOL. GFOL can conveniently define a wide variety of lambda-calculi as theories, by instanciating its syntax and stating the appropriate axioms. GFOL endows its theories with a default loose semantics, complete for the specified calculi.
Source:
While propositional logic deals with simple declarative propositions, first-order logic additionally covers predicates and quantification. Take for example the following sentences: "Socrates is a man", "Plato is a man". In propositional logic these will be two unrelated propositions, denoted for example by p and q. In first-order logic ... both sentences would be connected by the same property: Man(x), where Man(x) means that x is a man. When x=Socrates we get the first proposition - p, and when x=Plato we get the second proposition - q. Such a construction allows for a much more powerful logic when quantifiers are introduced, such as "for every x..." - for example, "for every x, if Man(x), then...". Without quantifiers, every valid argument in FOL is valid in propositional logic, and vice versa.
Source:
Propositional representations have some shortcomings which are solved when using first order logic(FOL). For an in depth introduction to first order logic, see for instance [Tru92, SA91, GGH89, RN95, NM94]. In propositional logic it is difficult to describe cases such as when a person has the same age as shoe-size. A rule for such a case would have to be like:
Source:
[O]rder logic in which no atomic sentence lies in the scope of more than three quantifiers, has the same expressive power as the relation algebra of Tarski and Givant (1987). They ... show that FOL with a primitive ordered pair, and a relation algebra including the two ordered pair
Source:
MORE ABOUT
Fol Ruleml