A Modality for Recursion
نویسنده
چکیده
We propose a modal logic that enables us to handle self-referential formulae, including ones with negative selfreferences, which on one hand, would introduce a logical contradiction, namely Russell’s paradox, in the conventional setting, while on the other hand, are necessary to capture a certain class of programs such as fixed point combinators and objects with so-called binary methods in object-oriented programming. Our logic provides a basis for axiomatic semantics of such a wider range of programs and a new framework for natural construction of recursive programs in the proofs-as-programs paradigm.
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