Modularity results for interpolation, amalgamation and superamalgamation

作者：Ghilardi Silvio; Gianola Alessandro^*

来源：Annals of Pure and Applied Logic, 2018, 169(8): 731-754.

DOI：10.1016/j.apal.2018.04.001

• Interpolation
• Fusion
• Modal logic
• Superamalgamability

Wolter in [38] proved that the Craig interpolation property transfers to fusion of normal modal logics. It is well-known [21] that for such logics Craig interpolation corresponds to an algebraic property called superamalgamability. In this paper, we develop model-theoretic techniques at the level of first-order theories in order to obtain general combination results transferring quantifier-free interpolation to unions of theories over non-disjoint signatures. Such results, once applied to equational theories sharing a common Boolean reduct, can be used to prove that superamalgamability is modular also in the non-normal case. We also state that, in this non-normal context, superamalgamability corresponds to a strong form of interpolation that we call "comprehensive interpolation property" (which consequently transfers to fusions).

• 出版日期2018-8