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Symbolic Logic Text

An Exposition of Symbolic Logic
The system of logic used here is essentially that of Kalish & Montague 1964 and Kalish, Montague and Mar, Harcourt Brace Jovanovich, 1992. The principle difference is that written justifications are required for boxing and canceling: 'dd' for a direct derivation, 'id' for an indirect derivation, etc. This text is written to be used along with the UCLA Logic 2010 software program, but that program is not mentioned, and the text can be used independently (although you would want to supplement the exercises).
The system of notation is almost the same as KK&M; major differences are that the signs '∀' and '∃' are used for the quantifiers, name and operation symbols are the small letters between ‘a’ and ‘h’, and variables are the small letters between ‘i’ and ‘z’.
The exercises are new.
Chapters 1-3 cover pretty much the same material as KM&M except that the rule allowing for the use of previously proved theorems is now in chapter 2, immediately following the section on theorems. (Previous versions of this text used the terminology ‘tautological implication’ in section 2.11. This has been changed to ‘tautological validity’ to agree with the logic program.)
Chapters 4-6 include invalidity problems with infinite universes, where one specifies the interpretation of notation "by description"; e.g. "R((1)(2)): (1)≤(2)". These are discussed in the final section of each chapter, so they may easily be avoided. (They are not currently implemented in the logic program.)
Chapter 4 covers material from KK&M chapter IV, but without operation symbols. Chapter 4 also includes material from KK&M chapter VII, namely interchange of equivalents, biconditional derivations, monadic sentences without quantifier overlay, and prenex form.
Chapter 5 covers identity and operation symbols.
Chapter 6 covers Fregean definite descriptions, as in KK&M chapter VI.

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Terence Parsons,
Mar 21, 2015, 2:47 PM
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Terence Parsons,
Mar 21, 2015, 2:47 PM
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Terence Parsons,
Mar 21, 2015, 2:47 PM
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Terence Parsons,
Mar 21, 2015, 2:47 PM
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Terence Parsons,
Mar 21, 2015, 2:47 PM
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Terence Parsons,
Mar 21, 2015, 2:47 PM
Ċ
Terence Parsons,
Mar 21, 2015, 2:47 PM
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