Results 1  10
of
32
Explicit Provability And Constructive Semantics
 Bulletin of Symbolic Logic
, 2001
"... In 1933 G odel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. In this paper we give a solution to this problem. We find the logic LP of propositions and proofs and show that G odel's provability calculus is noth ..."
Abstract

Cited by 139 (25 self)
 Add to MetaCart
In 1933 G odel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. In this paper we give a solution to this problem. We find the logic LP of propositions and proofs and show that G odel's provability calculus
QUANTUM LOGIC AND NONCLASSICAL LOGICS
"... Classical logic is sometimes described as “the logic of an omniscient mind in a deterministic universe”. From an intuitive point of view the basic features of classical semantics can be summarized as follows: 1) any problem is semantically decided: for any sentence α, either α ..."
Abstract
 Add to MetaCart
Classical logic is sometimes described as “the logic of an omniscient mind in a deterministic universe”. From an intuitive point of view the basic features of classical semantics can be summarized as follows: 1) any problem is semantically decided: for any sentence α, either α
The Logic of Provability
, 1997
"... Contents 1. Introduction, Solovay's theorems . . . . . . . . . . . . . . . . . . . . . . . . . . 360 2. Modal logic preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 3. Proof of Solovay's theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 4. ..."
Abstract

Cited by 26 (3 self)
 Add to MetaCart
Contents 1. Introduction, Solovay's theorems . . . . . . . . . . . . . . . . . . . . . . . . . . 360 2. Modal logic preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 3. Proof of Solovay's theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 4
ON PROVABILITY LOGIC
, 2000
"... This is an introductory paper about provability logic, a modal propositional logic in which necessity is interpreted as formal provability. I discuss the ideas that led to establishing this logic, I survey its history and the most important results, and I emphasize its applications in metamathematic ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
This is an introductory paper about provability logic, a modal propositional logic in which necessity is interpreted as formal provability. I discuss the ideas that led to establishing this logic, I survey its history and the most important results, and I emphasize its applications
On Modal µCalculus and GödelLöb Logic
"... Abstract. We show that the modal µcalculus over GL collapses to the modal fragment by showing that the fixpoint formula is reached after two iterations and answer to a question posed by van Benthem in [vBe06]. Further, we introduce the modal µ ∼calculus by allowing fixpoint constructors for any fo ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
formula where the fixpoint variable appears guarded but not necessarily positive and show that this calculus over GL collapses to the modal fragment, too. The latter result allows us a new proof of the de Jongh, Sambin Theorem and provides a simple algorithm to construct the fixpoint formula. Keywords
Problems in the Logic of Provability
, 2005
"... In the first part of the paper we discuss some conceptual problems related to the notion of proof. In the second part we survey five major open problems in Provability Logic as well as possible directions for future research in this area. 1 ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
In the first part of the paper we discuss some conceptual problems related to the notion of proof. In the second part we survey five major open problems in Provability Logic as well as possible directions for future research in this area. 1
Results 1  10
of
32