interpolation property

A logic is said to have the interpolation property if whenever ϕ(R,S)ψ(R,T) holds, then there is a sentenceMathworldPlanetmath θ(R), so that both ϕ(R,S)θ(R) and θ(R)ψ(R,T) hold, where R,S and T are some sets of symbols that occur in the formulasMathworldPlanetmathPlanetmath, R being the set of symbols common to both ϕ and ψ.

The interpolation property holds for first order logic. The interpolation property is related to Beth definability property and Robinson’s consistency property. Also, a natural generalisation is the concept Δ-closed logic.

Title interpolation property
Canonical name InterpolationProperty
Date of creation 2013-03-22 13:49:36
Last modified on 2013-03-22 13:49:36
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 7
Author CWoo (3771)
Entry type Definition
Classification msc 03B99
Defines interpolation property