GEOMETRISATION OF FIRST-ORDER LOGIC

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...

First-order intensional logic

First-order modal logic is very much under current development, with many different semantics proposed. The use of rigid objects goes back to Saul Kripke. More recently several semantics based on counterparts have been examined, in a development that goes back to David Lewis. There is yet another line of research, using intensional objects, that traces back to Richard Montague. I have been invo...

First-Order Default Logic

We propose a model theory for full first-order default logic that allows both closed and non-closed default theories. Beginning with first-order languages without logical equality, we note how Henkin’s proof of the completeness theorem for first-order logic yields complete algebras; that is, algebras over which models of consistent theories may always be found. The uniformity is what is interes...