We present a generic method for establishing interpolation properties by ‘borrowing’ across logical systems. The framework used is that of the so-caled ‘institution theory’ which is a categorical abstract model theory providing a formal definition for the informal concept of ‘logical system’ and a mathematical concept of ‘homomorphism’ between logical systems. We develop three different styles ...

An event, as opposed to an atemporal property, has its own time and location and occurs once. Although the notion of events has been found in researches on ontology, logic, linguistics, artificial intelligence and deductive databases, the different approaches to this notion do not seem to capture the various logical aspects of events. This paper proposes an event logic with expressions such as ...

The introduction of sorts to rst-order automated deduction has brought greater conciseness of representation and a considerable gain in eeciency by reducing search spaces. This suggests that sort information can be employed in higher-order theorem proving with similar results. This paper develops a sorted-calculus suitable for automatic theorem proving applications. It extends the simply typed-...

In this paper definitions of many sorted closure system and many sorted closure operator are introduced. These notations are also introduced in [9], but in another meaning. In this article closure system is absolutely multiplicative subset family of many sorted sets and in [9] is many sorted absolutely multiplicative subset family of many sorted sets. Analogously, closure operator is function b...