Modal logics, justification logics, and realization
نویسندگان
چکیده
منابع مشابه
Realization Theorems for Justification Logics: Full Modularity
Justification logics were introduced by Artemov in 1995 to provide intuitionistic logic with a classical provability semantics, a problem originally posed by Gödel. Justification logics are refinements of modal logics and formally connected to them by so-called realization theorems. A constructive proof of a realization theorem typically relies on a cut-free sequent-style proof system for the c...
متن کاملA Syntactic Realization Theorem for Justification Logics
Justification logics are refinements of modal logics where modalities are replaced by justification terms. They are connected to modal logics via so-called realization theorems. We present a syntactic proof of a single realization theorem that uniformly connects all the normal modal logics formed from the axioms d, t, b, 4, and 5 with their justification counterparts. The proof employs cut-free...
متن کاملJustification logics and hybrid logics
Hybrid logics internalize their own semantics. Members of the newer family of justification logics internalize their own proof methodology. It is an appealing goal to combine these two ideas into a single system, and in this paper we make a start. We present a hybrid/justification version of the modal logic T. We give a semantics, a proof theory, and prove a completeness theorem. In addition, w...
متن کاملProof Realization of Intuitionistic and Modal Logics
Logic of Proofs (LP) has been introduced in [2] as a collection of all valid formulas in the propositional language with labeled logical connectives [[t]]( ) where t is a proof term with the intended reading of [[t]]F as \t is a proof of F". LP is supplied with a natural axiom system, completeness and decidability theorems. LP may express some constructions of logic which have been formulated o...
متن کاملRealization for justification logics via nested sequents: Modularity through embedding
Justification logics are refinements of modal logics, where justification terms replace modalities. Modal and justification logics are connected via the so-called realization theorems. We develop a general constructive method of proving the realization of a modal logic in an appropriate justification logic by means of cut-free modal nested sequent systems. We prove a constructive realization th...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2016
ISSN: 0168-0072
DOI: 10.1016/j.apal.2016.03.005