# Semantical Analysis of Modal Logic I Normal Modal Propositional Calculi

```@article{Kripke1963SemanticalAO,
title={Semantical Analysis of Modal Logic I Normal Modal Propositional Calculi},
author={Saul Kripke},
journal={Mathematical Logic Quarterly},
year={1963},
volume={9},
pages={67-96}
}```
• Saul Kripke
• Published 1963
• Philosophy
• Mathematical Logic Quarterly
Publisher Summary This chapter discusses semantical analysis of modal logic ii and non-normal modal propositional calculi. The proof of sufficiency, which is omitted by many, proceeds by constructing a normal characteristic matrix by Lindenbaum's method. The tableaux that leads to a decision procedure for the propositional calculi is considered.
1,174 Citations

### Infinitary propositional normal modal logic

• Philosophy, Mathematics
Stud Logica
• 1987
A Hilbert's style axiomatization is proved complete for this logic, as well as for countable sublogics and subtheories, and it is shown that the logic has the interpolation property.

### Proof Theory for Modal Logic

The axiomatic presentation of modal systems and the standard formulations of natural deduction and sequent calculus for modal logic are reviewed, together with the difficulties that emerge with these

### On modal logic with propositional quantifiers

I am interested in extending modal calculi by adding propositional quantifiers, given by the rules for quantifier introduction: provided that p does not occur free in A.

### First-order modal tableaux

• M. Fitting
• Computer Science
Journal of Automated Reasoning
• 2004
We describe simple semantic tableau based theorem provers for four standard modal logics, in both propositional and first-order versions. These theorem provers are easy to implement in Prolog, have a

### Towards Determining the Subset Relation between Propositional Modal Logics

A test suite shows that relatively simple strategies can lead to satisfactory results, but also that certain subproblems are hard for current automated theorem provers.

### Some Lectures on Modal Logic

An exposition of some modal logics useful for teaching and research in computer science, including classical concurrent dynamic logic, and nonmonotonic reasoning.

### Standard Approach to Basic Modal Logics

This group of non-axiomatic systems that are called standard in the sense of keeping intact all the machinery of suitable systems for classical logic, covers modal extensions of standard Gentzen SC, Hintikka-style modal TS, and some ND systems.

### The Complexity of Some Non-Classical Logics

Using a theorem of Cook's and well-known transformations from intuitionistic to classical and modal to intuitionistic logics, the validity problem for intuitionistic andmodal logics is shown to be polynomial equivalent to the validity problems for classical logic.