David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Studia Logica 82 (2):271 - 291 (2006)
Algebraic approach to study of classical and non-classical logical calculi was developed and systematically presented by Helena Rasiowa in , . It is very fruitful in investigation of non-classical logics because it makes possible to study large families of logics in an uniform way. In such research one can replace logics with suitable classes of algebras and apply powerful machinery of universal algebra. In this paper we present an overview of results on interpolation and definability in modal and positive logics,and also in extensions of Johansson's minimal logic. All these logics are strongly complete under algebraic semantics. It allows to combine syntactic methods with studying varieties of algebras and to flnd algebraic equivalents for interpolation and related properties. Moreover, we give exhaustive solution to interpolation and some related problems for many families of propositional logics and calculi.
|Keywords||interpolation definability amalgamation modal logic intuitionistic logic non-classical logics|
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References found in this work BETA
Alexander Chagrov (1997). Modal Logic. Oxford University Press.
Helena Rasiowa (1974). An Algebraic Approach to Non-Classical Logics. Warszawa,Pwn - Polish Scientific Publishers.
Helena Rasiowa (1963). The Mathematics of Metamathematics. Warszawa, Państwowe Wydawn. Naukowe.
Dov M. Gabbay (1986). Semantical Investigations in Heyting's Intuitionistic Logic. Journal of Symbolic Logic 51 (3):824-824.
William Craig (1957). Three Uses of the Herbrand-Gentzen Theorem in Relating Model Theory and Proof Theory. Journal of Symbolic Logic 22 (3):269-285.
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