We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 01 June 2011
In our final chapter we briefly discuss two topics we feel deserve to be mentioned in spite of space constraints that prevent us from giving them fuller treatment. In the first half of the chapter, we address the debate concerning the possibility of giving a compositional semantics for IF logic. In the second half, we investigate the effect of introducing imperfect information to modal logic.
Compositionality
The original game-theoretic semantics for IF logic assigned meanings only to IF sentences [30]. Thus IF logic was immune to a common complaint lodged against Tarski's semantics for first-order logic, namely that truth is defined in terms of satisfaction, rather than truth alone. However, it also meant that one was not able to analyze IF sentences by looking at the meanings of their subformulas. Furthermore, Hintikka famously claimed that there could be no compositional semantics for IF logic:
… there is no realistic hope of formulating compositional truth-conditions for [IF sentences], even though I have not given a strict impossibility proof to that effect.
[28, pp. 110ff]Hintikka's assertion inspired Hodges to develop his trump semantics, which gives meanings to all IF formulas [32, 33]. In Chapter 4, we defined two other semantics for IF formulas: game-theoretic semantics and Skolem semantics. In order to emphasize the similarities between IF logic and first-order logic, we introduced both semantics in terms of single assignments.
To save this book to your Kindle, first ensure no-reply@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.
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.
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.
