by Corry Shores

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[Logic and Semantics, entry directory]

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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 distracting mistakes, because I have not finished proofreading.]

Summary of

Graham Priest

*An Introduction to Non-Classical Logic: From If to Is*

8. First Degree Entailment

8.1. Introduction [to first degree entailment]

Brief summary:

In *first degree entailment *(*FDE*), interpretations are not formulated as functions that assign truth values, standard or not, to propositional parameters. Rather, in *FDE*, interpretations are formulated as relations between formulas and standard truth values. In this chapter we examine *FDE*, along with an alternate possible world semantics for it, and we discuss the issues of explosion and disjunctive syllogism.

Summary

8.1

[In *first degree entailment *(*FDE*), interpretations are not formulated as functions (assigning truth values, standard or not, to propositional parameters) but rather as as relations between formulas and standard truth values.]

[First recall from section 1.3.1 the notion of interpretation in classical logic:

An

interpretationof the language is a function,ν, which assigns to each propositional parameter either 1 (true), or 0 (false). Thus, we write things such as( andp) = 1ν(q) = 0.(5)

We also saw in section 7.3 examples of three-valued logics whose interpretation function assigns *i *in addition to 1 and 0.] We will examine *first degree entailment *(*FDE*), which “is formulated, first, as a logic where interpretations are *relations* between formulas and standard truth values, rather than as the more usual *functions*” (142). We well also see connections between *FDE* and many-valued logics (see section 7).

8.2

[We also examine alternate possible-world semantics for FDE. This will introduce a new kind of semantics for negation.]

Another thing we do in this chapter is examine “an alternate possible-world semantics for *FDE*, which will introduce us to a new kind of semantics for negation” (142).

8.3

[We also examine the issue of explosion and disjunctive syllogism.]

“Finally, we look at the relation of all this to the explosion of contradictions, and to the disjunctive syllogism” (142).

Priest, Graham. 2008 [2001]. *An Introduction to Non-Classical Logic: From If to Is*, 2nd edn. Cambridge: Cambridge University.

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