The basic intuitionistic logic of proofs
نویسندگان
چکیده
منابع مشابه
The 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.
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 کاملThe Basic Logic of Proofs
Propositional Provability Logic was axiomatized in [7]. This logic describes the behaviour of the arithmetical operator \y is provable". The aim of the current paper is to provide propositional axiomatizations of the predicate \x is a proof of y" by means of modal logic, with the intention of meeting some of the needs of computer science.
متن کاملFunctionality in the Basic Logic of Proofs
This report describes the elimination of the injectivity restriction for functional arithmetical interpretations as used in the systems PF and PFM in the Basic Logic of Proofs. An appropriate axiom system PU in a language with operators \x is a proof of y" is de ned and proved to be sound and complete with respect to all arithmetical interpretations based on functional proof predicates. Uni cat...
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ژورنال
عنوان ژورنال: Journal of Symbolic Logic
سال: 2007
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1185803617