by Corry Shores
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[Priest, Introduction to Non-Classical Logic, entry directory]
[The following is summary of Priest’s text, which is already written with maximum efficiency. Bracketed commentary and boldface are my own, unless otherwise noted. I do not have specialized training in this field, so please trust the original text over my summarization. I apologize for my typos and other unfortunate mistakes, because I have not finished proofreading, and I also have not finished learning all the basics of these logics.]
Summary of
Graham Priest
An Introduction to Non-Classical Logic: From If to Is
Part I:
Propositional Logic
11a
Appendix: Many-valued Modal Logics
11a.1
Introduction
Brief summary:
(11a.1.1) In this chapter we will examine many-valued modal logics. (11a.1.2) First we examine the general structure of a many-valued modal logic, illustrated with Łukasiewicz continuum-valued modal logic. (11a.1.3) We will also examine many-valued modal First Degree Entailment logics, including modal K3 and modal LP. (11a.1.4) We will end the chapter with a discussion of future contingents.
[Many-Valued Modal Logics]
[The General Structure]
[FDE Modal Logics]
[Future Contingents]
Summary
[Many-Valued Modal Logics]
[In this chapter we will examine many-valued modal logics.]
[Normally in modal logics, worlds are two-valued, meaning that a formula can take one of two values, true or false. However, we can also formulate modal logics where worlds are many-valued (also see ch.7 and ch.9).]
In standard modal logics, the worlds are two-valued, in the following sense: there are two values (true and false) that a sentence may take at a world. Technically, however, there is no reason why this has to be the case: the worlds could be many-valued. This chapter looks at many-valued modal logics.
(241)
[The General Structure]
[First we examine the general structure of a many-valued modal logic, illustrated with Łukasiewicz continuum-valued modal logic.]
[(ditto)]
We will start with the general structure of a many-valued modal logic. To illustrate the general structure, we will look briefly at modal logic based on Łukasiewicz continuum-valued logic.
(241)
[FDE Modal Logics]
[We will also examine many-valued modal First Degree Entailment logics, including modal K3 and modal LP.]
[(ditto)]
We will then look at one particular many-valued modal logic in more detail, modal First Degree Entailment (FDE), and its special cases, modal K3 and modal LP. In particular, tableau systems for these logics will be given.
(241)
[Future Contingents]
[We will end the chapter with a discussion of future contingents.]
[(ditto)]
Modal many-valued logics engage with a number of philosophical issues. The final part of the chapter will illustrate by returning to the issue of future contingents.
(241)
From:
Priest, Graham. 2008 [2001]. An Introduction to Non-Classical Logic: From If to Is, 2nd edn. Cambridge: Cambridge University.
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