Truth Table Double Negation

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1/5/2011 PROPOSITION A proposition makes a claim (either an assertion or denial) that may be either true or false. It must Unit 1B have the structure of a complete sentence. Propositions and Truth Values NOTE: A proposition has one of two possible truth values: T = true or F = false NOTATION: Propositions are sometimes denoted by lower-case letters: p, q, r, s, t, . NEGATION (OPPOSITES) TRUTH TABLE The negation of a proposition p is another A truth table is a table with a row for each proposition that makes the opposite claim of p. possible set of truth values for the propositions being considered. NOTATION: The negation of p is written as not p or ~ p. TRUTH TABLE FOR p AND not p DOUBLE NEGATION not p The double negation not not p (~ ~ p) and p p ~ p have the same truth value. T F not p nottt not p p ~ p ~ ~ p FT TFT FTF 1 1/5/2011 LOGICAL CONNECTORS CONJUNCTIONS When we join two propositions, say p and q, We will consider three logical connectors. with the logical connector and , the resulting •And compound proposition p and q is called a conjunction. •Or • If . then . LOGIC OF A CONJUNCTION DISJUNCTION The conjunction of p and q [ p and q ] is true When we join two propositions, say p and q, only if both p and q are true. with the logical connector or , the resulting compound proposition p or q is called a p q pandqp and q ddsjuctoisjunction. TTT TFF FTF FFF TWO TYPES OF “OR” THE LOGIC OF DISJUNCTIONS There are two types of “or”: The disjunction of p and q [ p or q ] is false only if both p and q are false. •An inclusive or means “either or both.” p q porqp or q •An exclusive or means “one or the other, TTT but not both.” TFT FTT NOTE: In logic we always use the inclusive or, FFF unless told otherwise. 2 1/5/2011 LOGIC OF A CONDITIONAL CONDITIONAL PROPOSITION PROPOSITION A statement of the form if p, then q is called a The conditional if p, then q is true in all cases conditional proposition (or implication). except when p is true and q is false. p q If p, then q . Proposition p is called the hypothesis (or TTT antecedent). TFF Proposition q is called the conclusion (or FTT consequent). FFT ALTERNATIVE PHRASINGS OF VARIATIONS ON THE CONDITIONALS CONDITIONAL Name Form Example The following are common alternative ways of Conditional if p, then q If you are sleeping, then stating if p, then q: you are breathing. p is su ffici ent p will l ead t o q p iliimplies q Converse if q, then p If you are breathing, then for q you are sleeping Inverse if not p, If you are not sleeping, q is necessary q if p q whenever p then not q then you are not breathing. for p Contrapositive if not q, If you are not breathing, then not p then you are not sleeping LOGICALLY EQUIVALENT STATEMENTS Exercise: Make a truth table for the variations Two statements are logically equivalent if they on the conditional. share the same truth values: if one is true, so is that other; and if one is false, so is the other. NOTE: A conditional statement: if p, then q and its contrapositive: if not q, then not p are logically equivalent. 3.

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Chapter 18 Negation
Chapter 18 Negation Jong-Bok Kim Kyung Hee University, Seoul Each language has a way to express (sentential) negation that reverses the truth value of a certain sentence, but employs language-particular expressions and gram- matical strategies. There are four main types of negatives in expressing sentential negation: the adverbial negative, the morphological negative, the negative auxil- iary verb, and the preverbal negative. This chapter discusses HPSG analyses for these four strategies in marking sentential negation. 1 Modes of expressing negation There are four main types of negative markers in expressing negation in lan- guages: the morphological negative, the negative auxiliary verb, the adverbial negative, and the clitic-like preverbal negative (see Dahl 1979; Payne 1985; Zanut- tini 2001; Dryer 2005).1 Each of these types is illustrated in the following: (1) a. Ali elmalar-i ser-me-di-;. (Turkish) Ali apples-ACC like-NEG-PST-3SG ‘Ali didn’t like apples.’ b. sensayng-nim-i o-ci anh-usi-ess-ta. (Korean) teacher-HON-NOM come-CONN NEG-HON-PST-DECL ‘The teacher didn’t come.’ c. Dominique (n’) écrivait pas de lettre. (French) Dominique NEG wrote NEG of letter ‘Dominique did not write a letter.’ 1The term negator or negative marker is a cover term for any linguistic expression functioning as sentential negation. Jong-Bok Kim. 2021. Negation. In Stefan Müller, Anne Abeillé, Robert D. Borsley & Jean- Pierre Koenig (eds.), Head-Driven Phrase Structure Grammar: The handbook. Prepublished version. Berlin: Language Science Press. [Pre- liminary page numbering] Jong-Bok Kim d. Gianni non legge articoli di sintassi. (Italian) Gianni NEG reads articles of syntax ‘Gianni doesn’t read syntax articles.’ As shown in (1a), languages like Turkish have typical examples of morphological negatives where negation is expressed by an inflectional category realized on the verb by affixation.
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Journal of Linguistics Negation, 'Presupposition'
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