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Formal Language.docx

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Department
Philosophy
Course
Philosophy 2250
Professor
Lorne Falkenstein
Semester
Fall

Description
Formal Language 9/11/2013 11:39:00 AM The Vocabulary of SL consists of:  Sentence letters of SL: A,B,C,..A1, A2, A3  Connectives of SL: ~(not),&(and),v(or),,  Punctuation marks: (,) Syntax  Syntactic formation rules: o An expression of SL is any string of vocabulary elements. o A sentences of SL is a string of vocabulary elements assembled in accord with the following rules:  If P is a sentence of SL, then ~P is a sentence of SL  If P and Q are (not necessarily distinct) sentences of SL, then (P & Q), (P v Q), (P  Q), and (P  Q) are sentences of SL.  Nothing is a sentence of SL unless it can be formed by repeated applications of rules 1-3.  Informal notational conventions: o Allows [,] as substitutions for (,). o Allow omission of outer parentheses.  Named forms: o If P is a sentence letter of SL then it is an atomic sentence. o If P contains a connective, then it is a compound sentence. o ~ is a unary connective. o &, v, >, and  are binary connectives. o A sentences of the form ~P is a negation. Its main connective is “~” and its immediate component is P. o A sentence of the form (P & Q) is a conjunction. It’s main connective is “&” and P and Q are immedia
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