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).
Modularity results for interpolation, amalgamation and superamalgamation / S. Ghilardi, A. Gianola. - In: ANNALS OF PURE AND APPLIED LOGIC. - ISSN 0168-0072. - 169:8(2018 Aug), pp. 731-754.
Modularity results for interpolation, amalgamation and superamalgamation
S. Ghilardi;
2018
Abstract
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).File | Dimensione | Formato | |
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