Logic of Intuitionistic Interactive Proofs (Formal Theory of Perfect Knowledge Transfer)
نویسندگان
چکیده
منابع مشابه
A Logic of Interactive Proofs (Formal Theory of Knowledge Transfer)
We propose a logic of interactive proofs as a framework for an intuitionistic foundation for interactive computation, which we construct via an interactive analog of the Gödel-McKinsey-Tarski-Artëmov definition of Intuitionistic Logic as embedded into a classical modal logic of proofs, and of the Curry-Howard isomorphism between intuitionistic proofs and typed programs. Our interactive proofs e...
متن کاملIntuitionistic Logic of Proofs
The logic of proofs LP was introduced in [3] and thoroughly studied in [1]. LP is a natural extension of the propositional calculus in the language representing proofs as formal objects. Proof expressing terms are constructed using constants, variables, and symbols of natural operations on derivations. Then formula t :F has the intended interpretation “t is a proof of F”. LP is complete with re...
متن کاملIntuitionistic Hypothetical Logic of Proofs
We study a term assignment for an intuitonistic fragment of the Logic of Proofs (LP). LP is a refinement of modal logic S4 in which the assertion 2A is replaced by [[s]]A whose intended reading is “s is a proof of A”. We first introduce a natural deduction presentation based on hypothetical judgements and then its term assignment, which yields a confluent and strongly normalising typed lambda c...
متن کاملLogic of Negation-Complete Interactive Proofs (Formal Theory of Epistemic Deciders)
We produce a decidable classical normal modal logic of internalised negation-complete or disjunctive non-monotonic interactive proofs (LDiiP) from an existing logical counterpart of non-monotonic or instant interactive proofs (LiiP). LDiiP internalises agent-centric proof theories that are negation-complete (maximal) and consistent (and hence strictly weaker than, for example, Peano Arithmetic)...
متن کاملThe basic intuitionistic logic of proofs
The language of the basic logic of proofs extends the usual propositional language by forming sentences of the sort x is a proof of F for any sentence F . In this paper a complete axiomatization for the basic logic of proofs in Heyting Arithmetic HA was found.
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ژورنال
عنوان ژورنال: ACM Transactions on Computational Logic
سال: 2015
ISSN: 1529-3785,1557-945X
DOI: 10.1145/2811263