David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 71 (3):1002 - 1028 (2006)
This paper studies definability within the theory of institutions, a version of abstract model theory that emerged in computing science studies of software specification and semantics. We generalise the concept of definability to arbitrary logics, formalised as institutions, and we develop three general definability results. One generalises the classical Beth theorem by relying on the interpolation properties of the institution. Another relies on a meta Birkhoff axiomatizability property of the institution and constitutes a source for many new actual definability results, including definability in (fragments of) classical model theory. The third one gives a set of sufficient conditions for 'borrowing' definability properties from another institution via an 'adequate' encoding between institutions. The power of our general definability results is illustrated with several applications to (many-sorted) classical model theory and partial algebra, leading for example to definability results for (quasi-)varieties of models or partial algebras. Many other applications are expected for the multitude of logical systems formalised as institutions from computing science and logic.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
M. Aiguier & F. Barbier (2007). An Institution-Independent Proof of the Beth Definability Theorem. Studia Logica 85 (3):333 - 359.
Mihai Prunescu (2002). An Isomorphism Between Monoids of External Embeddings About Definability in Arithmetic. Journal of Symbolic Logic 67 (2):598-620.
Finn V. Jensen (1974). Interpolation and Definability in Abstract Logics. Synthese 27 (1-2):251 - 257.
Eva Hoogland (2000). Algebraic Characterizations of Various Beth Definability Properties. Studia Logica 65 (1):91-112.
George Weaver (1994). A Note on Definability in Equational Logic. History and Philosophy of Logic 15 (2):189-199.
Eva Hoogland & Maarten Marx (2002). Interpolation and Definability in Guarded Fragments. Studia Logica 70 (3):373 - 409.
Anand Pillay (1998). Definability and Definable Groups in Simple Theories. Journal of Symbolic Logic 63 (3):788-796.
Răzvan Diaconescu (2004). An Institution-Independent Proof of Craig Interpolation Theorem. Studia Logica 77 (1):59 - 79.
Larisa Maksimova (2006). Definability and Interpolation in Non-Classical Logics. Studia Logica 82 (2):271 - 291.
Ernst Zimmermann (2003). Elementary Definability and Completeness in General and Positive Modal Logic. Journal of Logic, Language and Information 12 (1):99-117.
Kentaro Fujimoto (2010). Relative Truth Definability of Axiomatic Truth Theories. Bulletin of Symbolic Logic 16 (3):305-344.
Elias H. Alves (1984). Paraconsistent Logic and Model Theory. Studia Logica 43 (1-2):17 - 32.
Added to index2010-08-24
Total downloads11 ( #252,022 of 1,780,606 )
Recent downloads (6 months)1 ( #290,888 of 1,780,606 )
How can I increase my downloads?