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PREDICATE LOGIC

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					PREDICATE LOGIC I English Singular Terms: any word or phrase that designates or purports to designate some one thing. E.g., “Janice”, “the shortest spy”. Predicates: parts of English sentences that can be obtained by deleting one or more singular terms from an English sentence. An n-place predicate has n blanks or holes in it. E.g., “ is taller than the shortest spy.” “ loves ” Quantity Terms: serve to indicate how many of the things under discussion are thus and so, not to designate some single entity. E.g., “Someone”, “Everyone” Sentential Connectives: terms or expressions used to generate sentences from other sentences E.g., “and”, “or”, “it is not the case that” Compound Sentences: sentences generated from other sentences using sentential connectives E.g., “It is raining and it is cold” Atomic Sentences: sentences that are not compound and which contain no quantity terms. E.g., “Mary is tall” Simple Sentences: atomic sentences which contain no singular terms. E.g., “It is raining.” Predicate Logic Singular Terms: Proper names/ indexicals/ demonstratives: lower case letters English: “Mary” Predicate Logic: “m” Definite descriptions: ???? Variables: lowercase Roman letters „w‟ though „z‟ Predicates: uppercase Roman letters „A‟ through „Z‟ (with or without numerical subscripts) followed by one or more variables of PL. An n-place predicate contains n variables. English: “___ is Tall”

Predicate Logic: “Tx” Simple Sentences: upper case letters English: “It is raining” Predicate Logic: “R” Atomic Sentences: an n-place predicate letter followed by n lower case letters. English: “Mary is tall” Predicate Logic: “Tm” Sentential Connectives: English Predicate Logic “and” “or” “&” “v” “if … then” “” “if and only if “” “not” “~”

Compound Sentences: a sentence on either side of a binary connective or a single sentence following a unary connective English: “If Mary is tall then it is not raining.” Predicate Logic: “Tm  ~R” Quantifiers: Universal Quantifier English: “All” Predicate Logic: “(x)” Existential Quantifier English: “Some” (= “at least one”) Predicate Logic: “(x)”

Quantified Sentences: a quantifier followed by an open sentence (a sentence with a variable rather than a name). English: “Everyone is tall”/ “Someone is not all” Predicate Logic: “(x)Tx”/ “(x)~Tx”


				
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