Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-xm8r8 Total loading time: 0 Render date: 2024-06-22T10:30:38.478Z Has data issue: false hasContentIssue false

11 - Semantical aspects of quantified modal logic

Published online by Cambridge University Press:  05 November 2011

Giovanna Corsi
Affiliation:
Dipartimento di Filosofia, Università di Firenze
Silvio Ghilardi
Affiliation:
Dipartimento di Matematica, Università di Milano
Cristina Bicchieri
Affiliation:
University of Pennsylvania
Get access

Summary

This chapter is designed to outline some techniques, results, and new trends in quantified modal logics. Since it is directed to readers not specialized in the field of modal logic, we will start “from the beginning” and so discuss some basic material; at the same time, we intend to offer an idea of some of the recent research in the area and of possible directions for future research.

Quantified modal logics contain – in addition to classical connectives and quantifiers – a unary operator, the “box” operator □, whose meaning can be variously interpreted depending on the context and on the applications. Here is a list of possible readings of □A (taken from [15]):

  1. It is necessarily true that A;

  2. It will always be true that A;

  3. It ought to be that A;

  4. It is known that A;

  5. It is believed that A;

  6. It is provable in Peano arithmetic that A;

  7. After the program terminates, A.

A natural semantic demand is that the truth value of a sentence such as □A be determined (according to some of the above readings) once the truth value of A is known in a suitable set of “instants of time” or “states of affairs” that are considered as alternative to the actual one. Consequently, a semantics for quantified modal logic should contain a mathematical formalization of the following entities: (a) the different “worlds”; (b) the relation of “being conceivable as an alternative”; and (c) the objects or individuals “existing” in them and the connections between these.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×