Modal logic / Herman Ruge Jervell.

Format:

Book

Author/Creator:

Jervell, Herman Ruge, author.

Series:

Compact Companion ; 2

Language:

English

Subjects (All):

Modality (Logic).

Physical Description:

1 online resource (105 pages).

Edition:

1st ed.

Place of Publication:

Berlin : Logos Verlag Berlin, [2012]

Summary:

Long description: In modal logic we discuss multiple perspectives on truth - perspectives as given by time, by provability, by knowledge, by agents or by processes. We develop the theory of modal logic and emphasize the connections with and applications within computer science and mathematics. Among other things we develop Kurt Gödels incompleteness theorem and show memoryless determinacy of infinite games on finite arenas.

Contents:

Intro

1 Frege systems

1.1 Language of modal logic

1.2 The calculi of modal logic

1.3 Kripke models

1.4 Completeness

1.5 Finiteness

2 Gentzen systems

2.1 Strategies in and-or-trees

2.2 The language of modal logic

2.3 The basic modal system K

2.4 Many worlds semantics

2.5 Other systems

3 Interpolation and diagonalization

3.1 Classical logic

3.2 Modal logic

3.3 Fixpoint theorem

3.4 Cantors diagonal argument

3.5 Russells paradox

3.6 Fixed point of functions

3.7 Coding

3.8 The halting problem

3.9 The fix point theorem

3.10 Diagonal lemma

4 Provability

4.1 Expressing syntax

4.2 Calculi of syntax

4.3 G¨odel - L¨ob modal logic

5 Incompleteness

5.1 G¨odels zeroth incompleteness theorem

5.2 G¨odels first incompleteness theorem

5.3 G¨odels second incompleteness theorem

5.4 Tarskis theorem

6 Provability logic

6.1 Solovays first completeness theorem

6.2 Solovays second completeness teorem

7 Multi modal logic

7.1 Many modal operators

7.2 Temporal logic

7.3 Description logic

7.4 Epistemic logic

7.5 The Byzantine generals

8 Games on finite arenas

8.1 Arena

8.2 Game trees

8.3 Choices

8.4 Infinite positional strategies

9 Decision problems

9.1 Games using input

9.2 Second order monadic theory - S2S

9.3 Decidability of arithmetic

9.4 Processes.

Notes:

PublicationDate: 20130116

Description based on print version record.

ISBN:

3-8325-9000-5

9783832590000

OCLC:

1089524711