## Fine’s Theorem on First-Order Complete Modal Logics (2011)

### BibTeX

@MISC{Goldblatt11fine’stheorem,

author = {Robert Goldblatt},

title = {Fine’s Theorem on First-Order Complete Modal Logics},

year = {2011}

}

### OpenURL

### Abstract

Fine’s Canonicity Theorem states that if a modal logic is determined by a first-order definable class of Kripke frames, then it is valid in its canonical frames. This article reviews the background and context of this result, and the history of its influence on further research. It then develops a new characterisation of when a logic is canonically valid, providing a precise point of distinction with the property of firstorder completeness. 1 The Canonicity Theorem and Its Impact In his PhD research, completed in 1969, and over the next half-dozen years, Kit Fine made a series of fundamental contributions to the semantic analysis and metatheory of propositional modal logic, proving general theorems about notable classes of logics and providing examples of failure of some significant properties. This work included the following (in order of publication): • A study [6] of logics that have propositional quantifiers and are defined