Combinations and completeness transfer for quantified modal logics

The Unrestricted Combination of Temporal Logic Systems

This paper generalises and complements the work on combining temporal logics started by Finger and Gabbay [11, 10]. We present proofs of transference of soundness, completeness and decidability for the temporalisation of logics T(L) for any flow of time, eliminating the original restriction that required linear time for the transference of those properties through logic combination. We also gen...

The Semantics of Modal Predicate Logic I. Counterpart-Frames

We introduce a new semantics for modal predicate logic, with respect to which a rich class of first-order modal logics is complete, namely all normal first-order modal logics that are extensions of free quantified K. This logic is defined by combining positive free logic with equality PFL . = and the propositional modal logic K. We then uniformly construct—for each modal predicate logic L—a can...

A General Proof of Kripke-completeness for Quantified Modal Logics

Constant Domain QuantifiedModal Logics Without Boolean Negation

: This paper provides a sound and complete axiomatisation for constant domain modal logics without Boolean negation. This is a simpler case of the difficult problem of providing a sound and complete axiomatisation for constant-domain quantified relevant logics, which can be seen as a kind of modal logic with a twoplace modal operator, the relevant conditional. The completeness proof is ...

How Not to Combine Modal Logics

This paper describes a failed attempt to decompose the fusion of two non-normal modal logics as a composition of iterated nonnormal modalisations. That strategy had already succeeded in the transfer of soundness, completeness and decidability for normal modal logics, but we show here why it fails for the transference of some of these properties in the fusion non-normal modal logics. The possibi...