Provability logic

Provability logic is a modal logic, in which the box (or "necessity") operator is interpreted as 'it is provable that'. The point is to capture the…

Papers overview

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2014

For the Heyting Arithmetic HA, HA* is defined as the theory $\{A\mid {\sf HA}\vdash A^{\Box}\}$, where $A^{\Box}$ is called the…

2013

We introduce a first order extension of GL, called ML 3 , and develop its proof theory via a proxy cut-free sequent calculus GLTS…

2012

For any ordinal Λ, we can define a polymodal logic GLPΛ, with a modality [ξ] for each ξ < Λ. These represent provability…

2002

In this paper we study the method of refutation rules in the modal logic K4. We introduce refutation rules with certain normal…

2001

The core ideas of the dialogicalapproach to modal propositional logic are explainedby means of an elementary example…

1998

Besides the well-known principles K, K4 and L, the Leivant principle ⁪(AVВ)→ ⁪(AV⁪B) and the Formalized Markov scheme ⁪ ¬¬ (⁪A…

1993

We discuss the logics of the operators “p is a proof of A” and “p is a proof containing A” for the standard Godel proof predicate…

1992

In this paper are studied the properties of the proofs in PRA of provability logic sentences, i.e. of formulas which are Boolean…

1992

Propositional Provability Logic was axiomatized in [5]. This logic describes the behaviour of the arithmetical operator “y is…

1992

Abstract In this paper I give a characterization of the closed fragment of the provability logic of I Δ0 + EXP with a…