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...

This paper presents the case for the use of higher-order logic as a foundation for computational logic. A suitable polymorphicallytyped, higher-order logic is introduced and its syntax and proof theory briefly described. In addition, a metric space of closed terms suitable for knowledge representation purposes is presented. The approach to representing individuals is illustrated with some examp...

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...

Distributed First Order Logic (DFOL) is a formalism introduced more than 10 years ago with the purpose of formalising distributed knowledge-based systems. In these systems, knowledge is scattered in a set of heterogeneous and interconnected modules. The original version of DFOL defined a set of primitives for the specification of a restricted subset of interconnections between knowledge modules...

Abstract We characterize non-distributive positive logic as the fragment of a single-sorted first-order language that is preserved by new notion simulation called meet-simulation. Meet-simulations distinguish themselves from simulations because they relate pairs states one model to single another. En route this result, we use more traditional and prove Hennessy–Milner-style theorem for it, usin...

Message sequence charts (MSCs) naturally arise as executions of communicating finite-state machines (CFMs), in which processes exchange messages through unbounded FIFO channels. We study the first-order logic MSCs, featuring Lamport's happened-before relation. To this end, we introduce a star-free version propositional dynamic (PDL) with loop and converse. Our main results state that (i) every ...