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I am reading the book Mathematical Logic by Ian Chiswell and Wilfred Hodges ... and am currently focused on Chapter 2: Informal Natural Deduction ...
I need help with interpreting the notation of an aspect of Exercise 2.1.3 which reads as follows:View attachment 4996In the above text after the text: "Possible sequent rule B:" we read the following:
"If the sequent \(\displaystyle ( \{ \phi \} \vdash \psi )\) ... ... "How do I interpret \(\displaystyle ( \{ \phi \} \vdash \psi )\) ... Chiswell and Hodges point out that \(\displaystyle ( \phi \vdash \psi )\) means "there is a proof whose conclusion is \(\displaystyle \psi\) and whose undischarged assumptions are all in the set \(\displaystyle \phi\)" ... or ... "\(\displaystyle \phi\) entails \(\displaystyle \psi\)" ... ...
... BUT ... what is meant by a sequent like \(\displaystyle ( \{ \phi \} \vdash \psi )\) where the assumptions are a set \{ \phi \} ... that is a set of a set of assumptions ... ...
Can someone clarify this notation ... what does it mean exactly ..
Peter
I need help with interpreting the notation of an aspect of Exercise 2.1.3 which reads as follows:View attachment 4996In the above text after the text: "Possible sequent rule B:" we read the following:
"If the sequent \(\displaystyle ( \{ \phi \} \vdash \psi )\) ... ... "How do I interpret \(\displaystyle ( \{ \phi \} \vdash \psi )\) ... Chiswell and Hodges point out that \(\displaystyle ( \phi \vdash \psi )\) means "there is a proof whose conclusion is \(\displaystyle \psi\) and whose undischarged assumptions are all in the set \(\displaystyle \phi\)" ... or ... "\(\displaystyle \phi\) entails \(\displaystyle \psi\)" ... ...
... BUT ... what is meant by a sequent like \(\displaystyle ( \{ \phi \} \vdash \psi )\) where the assumptions are a set \{ \phi \} ... that is a set of a set of assumptions ... ...
Can someone clarify this notation ... what does it mean exactly ..
Peter
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