David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 70 (3):353-372 (2002)
The idea of interpretability logics arose in Visser [Vis90]. He introduced the logics as extensions of the provability logic GLwith a binary modality . The arithmetic realization of A B in a theory T will be that T plus the realization of B is interpretable in T plus the realization of A (T + A interprets T + B). More precisely, there exists a function f (the relative interpretation) on the formulas of the language of T such that T + B C implies T + A f(C).The interpretability logics were considered in several papers. An arithmetic completeness of the interpretability logic ILM, obtained by adding Montagna''s axiom to the smallest interpretability logic IL, was proved in Berarducci [Ber90] and Shavrukov [Sha88] (see also Hájek and Montagna [HM90] and Hájek and Montagna [HM92]). [Vis90] proved that the interpretability logic ILP, an extension of IL, is also complete for another arithmetic interpretation. The completeness with respect to Kripke semantics due to Veltman was, for IL, ILMand ILP, proved in de Jongh and Veltman [JV90]. The fixed point theorem of GLcan be extended to ILand hence ILMand ILP(cf. de Jongh and Visser [JV91]). The unary pendant "T interprets T + A" is much less expressive and was studied in de Rijke [Rij92]. For an overview of interpretability logic, see Visser [Vis97], and Japaridze and de Jongh [JJ98].
|Keywords||Philosophy Logic Mathematical Logic and Foundations Computational Linguistics|
|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
Petr Hájek & Vítězslav Švejdar (1991). A Note on the Normal Form of Closed Formulas of Interpretability Logic. Studia Logica 50 (1):25 - 28.
Joost J. Joosten & Albert Visser (2000). The Interpretability Logic of All Reasonable Arithmetical Theories. Erkenntnis 53 (1-2):3-26.
Albert Visser (1991). The Formalization of Interpretability. Studia Logica 50 (1):81 - 105.
Dick Jongh & Albert Visser (1991). Explicit Fixed Points in Interpretability Logic. Studia Logica 50 (1):39 - 49.
Vítězslav Švejdar (1991). Some Independence Results in Interpretability Logic. Studia Logica 50 (1):29 - 38.
Alessandro Berarducci (1990). The Interpretability Logic of Peano Arithmetic. Journal of Symbolic Logic 55 (3):1059-1089.
Claes Strannegård (1999). Interpretability Over Peano Arithmetic. Journal of Symbolic Logic 64 (4):1407-1425.
Maarten Rijke (1991). A Note on the Interpretability Logic of Finitely Axiomatized Theories. Studia Logica 50 (2):241 - 250.
Added to index2009-01-28
Total downloads6 ( #230,646 of 1,410,540 )
Recent downloads (6 months)1 ( #178,988 of 1,410,540 )
How can I increase my downloads?