RETRACTED ARTICLE: A completeness theorem for continuous predicate modal logic

Modal Foundations for Predicate Logic

The complexity of any logical modeling reeects both the intrinsic structure of a topic described and the weight of the formal tools. Some of this weight seems inherent in even the most basic logical systems. Notably, standard predicate logic is undecidable. In this paper, we investigatèlighter' versions of this general purpose tool, by modally`deconstructing' the usual semantics, and locating i...

Dynamic Modal Predicate Logic

Completeness in modal logic

The Completeness Problem for Modal Logic

We examine the completeness problem for Modal Logic: given a formula, is it complete? We discover that for most cases, completeness and validity have the same complexity – with certain exceptions for which there are, in general, no complete formulas. To prove upper bounds, we give a game which combines bisimulation games and tableaux, and which determines whether a formula is complete. The game...

On the scope of the completeness theorem for first-order predicate logic∗

The problem of completeness of classical first-order predicate logic was formulated, for the first time in precise mathematical terms, in 1928 by Hilbert and Ackermann in [16] and solved positively by Gödel in his Ph.D. thesis one year later [8, 9]. In 1947 Henkin [14, 15] presented an alternative simpler proof that has become standard in logic textbooks. The main advantage of Henkin’s proof is...