Generalization in first-order logic.

Towards Inductive Generalization in Higher Order Logic

øncestor(X,Z),øncestor(Z,Y)' (1) Y XYY V Z .I e s s Jhøn(X,Y ) * less-than(X,Z),lest-than(Z,Y)' (2) which are the generalisation respectiveþ of the facts lesslhan(!,3\, Iesslhan(2,4), " ' and the facts an ce stor (i ohn, st eo e), ance st or (st ea e, mi k e),''' The clauses in (1) and (2) a,re very similarjn the sense that (1) can be obtained from (2) by exchanging the pt"¿iàiu symbol ancestot...

First Order Logic in Practice

There is a trend away from monolithic automated theorem provers towards using automation as a tool in support of interactive proof. We believe this is a fruitful drawing together of threads in automated reasoning. But it raises a number of issues that are often neglected in the classical rst order theorem proving literature such as the following. Is rst order automation actually useful, and if ...

First-Order Logic

Taming First-Order Logic

In this paper we define computationally well-behaved versions of classical first-order logic and prove that the validity problem is decidable1.

Extended First-Order Logic

We consider the EFO fragment of simple type theory, which restricts quantification and equality to base types but retains lambda abstractions and higher-order variables. We show that this fragment enjoys the characteristic properties of first-order logic: complete proof systems, compactness, and countable models. We obtain these results with an analytic tableau system and a concomitant model ex...