Constructive Modalities with Provability Smack
نویسنده
چکیده
I overview the work of the Tbilisi school on intuitionistic modal logics of well-founded/scattered structures and its connections with contemporary theoretical computer science. Fixed-point theorems and their consequences are of particular interest.
منابع مشابه
A Note on Constructive Modalities for Information
Kurt Gödel (1933) proved the formal correspondence between the intuitionistic truth of a formula F and its classical provability via modal necessity: if F is derivable in a calculus for intuitionistic logic, a translation of F such that each of its subformulas is prefixed by a necessity operator can be derived in the modal language S4. The inverse implication was established few years later by ...
متن کاملConstructive Provability Logic 1
We present two variants of an intuitionistic sequent calculus that validates the Löb rule and permits logical reflection over provability. We explore properties of both variants of this logic, which we call constructive provability logic due to its close ties to Gödel-Löb provability logic.
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We present a novel formulation of CPL, a constructive logic of provability that is closely connected to the Gödel-Löb logic of provability. Our logical formulation allows modal operators to talk about both provability and non-provability of propositions at reachable worlds. We use this logic as a basis for a discussion of negation in logic programming.
متن کاملConstructive Provability Logic
We present constructive provability logic, an intuitionstic modal logic that validates the Löb rule of Gödel and Löb’s provability logic by permitting logical reflection over provability. Two distinct variants of this logic, CPL and CPL*, are presented in natural deduction and sequent calculus forms which are then shown to be equivalent. In addition, we discuss the use of constructive provabili...
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In this paper we give a new proof of the characterization of the closed fragment of the provability logic of Heyting’s Arithmetic. We also provide a characterization of the closed fragment of the provability logic of Heyting’s Arithmetic plus Markov’s Principle and Heyting’s Arithmetic plus Primitive Recursive Markov’s Principle.
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ورودعنوان ژورنال:
- CoRR
دوره abs/1708.05607 شماره
صفحات -
تاریخ انتشار 2014