In logic, a **modal companion** of a superintuitionistic (intermediate) logic *L* is a normal modal logic which interprets *L* by a certain canonical translation, described below. Modal companions share various properties of the original intermediate logic, which enables to study intermediate logics using tools developed for modal logic.

Read more about Modal Companion: Gödel–McKinsey–Tarski Translation, Modal Companions, Blok–Esakia Isomorphism, Semantic Description, Preservation Theorems, Other Properties

### Other articles related to "modal companion, modal companions":

**Modal Companion**- Other Properties

... Every intermediate logic L has an infinite number of

**modal companions**, and moreover, the set of

**modal companions**of L contains an infinite descending chain ... The set of

**modal companions**of any L is either countable, or it has the cardinality of the continuum ... that the lattice ExtL can be embedded in in particular, a logic has a continuum of

**modal companions**if it has a continuum of extensions (this holds ...

### Famous quotes containing the word companion:

“Guilt is perhaps the most painful *companion* of death.”

—Elisabeth Kübler-Ross (b. 1926)

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