منابع مشابه
The logic of proofs, semantically
A new semantics is presented for the logic of proofs (LP), [1, 2], based on the intuition that it is a logic of explicit knowledge. This semantics is used to give new proofs of several basic results concerning LP. In particular, the realization of S4 into LP is established in a way that carefully examines and explicates the role of the + operator. Finally connections are made with the conventio...
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 کاملHypothetical Logic of Proofs
The Logic of Proofs (LP) [2–5] is a refinement of modal logic introduced by Artemov in 1995 which has recently been proposed for explaining well-known paradoxes arising in the formalization of Epistemic Logic. Assertions of knowledge and belief are accompanied by justifications: the formula [[t]]A states that proof witness t is “reason” for knowing/believing A. Also, LP is capable of reflecting...
متن کاملSymmetric Logic of Proofs
The Logic of Proofs LP captures the invariant propositional properties of proof predicates t is a proof of F with a set of operations on proofs sufficient for realizing the whole modal logic S4 and hence the intuitionistic logic IPC. Some intuitive properties of proofs, however, are not invariant and hence not present in LP. For example, the choice function ‘+’ in LP, which is specified by the ...
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...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2005
ISSN: 0168-0072
DOI: 10.1016/j.apal.2004.04.009