A general strategy for proving completeness theorems for quantified modal logics is provided. Starting from free quantified modal logic K, with or without identity, extensions obtained either by adding the principle of universal instantiation or the converse of the Barcan formula or the Barcan formula are considered and proved complete in a uniform way. Completeness theorems are also shown for systems with the extended Barcan rule as well as for some quantified extensions of the modal logic B. The incompleteness of (...) Q°.B + BF is also proved. (shrink)

Dummett's logic LC quantified, Q-LC, is shown to be characterized by the extended frame Q+, ,D, where Q+ is the set of non-negative rational numbers, is the numerical relation less or equal then and D is the domain function such that for all v, w Q+, Dv and if v w, then D v . D v D w . Moreover, simple completeness proofs of extensions of Q-LC are given.

Predicate extensions of the intermediate logic of the weak excluded middle and of the modal logic S4.2 are introduced and investigated. In particular it is shown that some of them are characterized by subclasses of the class of directed frames with either constant or nested domains.

The paper presents an epistemic logic with quantification over agents of knowledge and with a syntactical distinction between de re and de dicto occurrences of terms. Knowledge de dicto is characterized as ‘knowledge that’, and knowlegde de re as ‘knowledge of’. Transition semantics turns out to be an adequate tool to account for the distinctions introduced.

The main aim of this paper is to introduce the logic QE-LC whose language contains the existence predicate E and which is characterized by the class of connected (Kripke) E-models with nested domains.

The aim of this paper is to provide a decision procedure for Dummett's logic LC, such that with any given formula will be associated either a proof in a sequent calculus equivalent to LC or a finite linear Kripke countermodel.

The essays collected in this volume address such questions from different points of view and will interest students and scholars in several branches of scientific knowledge.

We show how to use diagrams in order to obtain straightforward completeness theorems for extensions of K4.3 and a very simple and constructive proof of Bull's theorem: every normal extension of S4.3 has the finite model property.

In this paper we present two calculi for intuitionistic logic. The first one, IG, is characterized by the fact that every proof-search terminates and termination is reached without jeopardizing the subformula property. As to the second one, SIC, proof-search terminates, the subformula property is preserved and moreover proof-search is performed without any recourse to metarules, in particular there is no need to back-track. As a consequence, proof-search in the calculus SIC is accomplished by a single tree as in classical logic.