Infinitary first-order categorical logic

Conceptual Completeness for First-Order Intuitionistic Logic: An Application of Categorical Logic

This paper concerns properties of interpretations between first-order theories in intuitionistic logic, and in particular how certain syntactic properties of such interpretations can be characterised by their model-theoretic properties. We allow theories written in possibly many-sorted languages. Given two such theories 3 and 7, an interpretation of 3 in 3’ will here mean a model of 3 in the ‘f...

Categorical Logic Categorical 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...