Interpolation, Amalgamation and Combination (The Non-disjoint Signatures Case)

Ghilardi, Silvio; Gianola, Alessandro

doi:10.1007/978-3-319-66167-4_18

Cited by 13 publications

(11 citation statements)

References 24 publications

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“…Despite its abstract formulation, Theorem 3.1 is powerful enough to imply the main disjoint signatures result of [5] and also to work out interesting examples arising from software verification: in [12] it is shown how to use Theorem 3.1 to prove that suitable unions of theories describing data structures (like lists and binary trees) are quantifier-free interpolating. We explain in more detail how to derive the disjoint signatures result of [5] from Theorem 3.1:…”

Section: Sub-amalgamation Schematamentioning

confidence: 99%

Modularity results for interpolation, amalgamation and superamalgamation

Ghilardi

Gianola

2018

Annals of Pure and Applied Logic

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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 such non-normal context, superamalgamability corresponds to a strong form of interpolation that we call "comprehensive interpolation property" (which consequently transfers to fusions).

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Section: Sub-amalgamation Schematamentioning

confidence: 99%

Modularity results for interpolation, amalgamation and superamalgamation

Ghilardi

Gianola

2018

Annals of Pure and Applied Logic

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“…There exist results which relate ground interpolation to amalgamation [17,1,39,2,8] and thus allow us to recognize many theories with ground interpolation. For instance, Bacsich [1] shows that every universal theory with the amalgamation property has ground interpolation.…”

Section: Amalgamation and Ground Interpolationmentioning

confidence: 99%

“…8 Definition 6.7 ( [35]). Let M be a model of T 0 ∪ K and let T be a finite set of ground terms such that st(K) ⊆ T .…”

Section: There Exists a Model M D Of T And Weak Embeddings Hmentioning

confidence: 99%

“…Then the following hold: (1) M |T ∈ PMod w,f (Σ, T ). 8 The partial W -amalgamation property for models with the same Π0-reduct can also be regarded as an embeddability property for partial algebras in which the set of terms which are defined can be seen as the union of two sets TM A and TM B which are closed under the application of W . We decided to use the notion "partial W -amalgamation property for models with the same Π0-reduct" in this paper for the sake of consistency with the terminology introduced in [33].…”

Section: There Exists a Model M D Of T And Weak Embeddings Hmentioning

confidence: 99%

“…There also exist results which relate ground interpolation to amalgamation or the injection transfer property [17,1,39,2,8]. We use such results for obtaining criteria which allow us to recognize theories with ground interpolation.…”

Section: Introductionmentioning

confidence: 99%

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On Interpolation and Symbol Elimination in Theory Extensions

Sofronie-Stokkermans

2016

Automated Reasoning

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Abstract. In this paper we study possibilities of interpolation and symbol elimination in extensions of a theory T0 with additional function symbols whose properties are axiomatised using a set of clauses. We analyze situations in which we can perform such tasks in a hierarchical way, relying on existing mechanisms for symbol elimination in T0. This is for instance possible if the base theory allows quantifier elimination. We analyze possibilities of extending such methods to situations in which the base theory does not allow quantifier elimination but has a model completion which does. We illustrate the method on various examples.

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