Birkhoff completeness in institutions

Mihai Codescu; Daniel Gǎinǎ

doi:10.1007/s11787-008-0035-1

Birkhoff completeness in institutions

Mihai Codescu, Daniel Gǎinǎ

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

Abstract

We develop an abstract proof calculus for logics whose sentences are 'Horn sentences' of the form: (∀X)H ⇒ c and prove an institutional generalization of Birkhoff completeness theorem. This result is then applied to the particular cases of Horn clauses logic, the 'Horn fragment' of preorder algebras, order-sorted algebras and partial algebras and their infinitary variants.

Original language	English
Pages (from-to)	277-309
Number of pages	33
Journal	Logica Universalis
Volume	2
Issue number	2
DOIs	https://doi.org/10.1007/s11787-008-0035-1
Publication status	Published - 2008
Externally published	Yes

All Science Journal Classification (ASJC) codes

Logic
Applied Mathematics

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10.1007/s11787-008-0035-1

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abstract = "We develop an abstract proof calculus for logics whose sentences are 'Horn sentences' of the form: (∀X)H ⇒ c and prove an institutional generalization of Birkhoff completeness theorem. This result is then applied to the particular cases of Horn clauses logic, the 'Horn fragment' of preorder algebras, order-sorted algebras and partial algebras and their infinitary variants.",

author = "Mihai Codescu and Daniel Gǎinǎ",

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AU - Gǎinǎ, Daniel

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AB - We develop an abstract proof calculus for logics whose sentences are 'Horn sentences' of the form: (∀X)H ⇒ c and prove an institutional generalization of Birkhoff completeness theorem. This result is then applied to the particular cases of Horn clauses logic, the 'Horn fragment' of preorder algebras, order-sorted algebras and partial algebras and their infinitary variants.

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Birkhoff completeness in institutions

Abstract

All Science Journal Classification (ASJC) codes

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