Lesson 8. Logic as a Modeling Language. Logics as frameworks for argument. Logics are used to describe the structure of arguments but do not tell us whether the argument we are making is realistic. Argument 1, although coherently structured, does not describe a real situation.
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Logic as a Modeling Language
from these we can establish ¬martian(dave) ¬martian(jaume) since each part of this conjunction is in the conclusion set.
in which case author is no longer primitive but we have introduced two new primitive concepts – book and name_on_cover.
Look fornegativeslike ‘doesn’t’, ‘no’ or ‘never’
Look forphraseslike ‘also’ or ‘as well as’
be careful to distinguish between the use of inclusive and exclusive or connectives.
Look forphraseslike ‘If X then Y’ or ‘Whenever X then Y’
By using the general principle that implies for any two statements a and b gives us the expression:
The universal quantifier ‘All politicians are devious’ becomes:
The existential quantifier ‘There is a politician who can be trusted’ might be represented using the formula:
It is quite common to have a mixture of universal and existential quantifiers in a statement. ‘If all politician are devious then none of them are trustworthy’:
which means that for any X, there is some Y such that X is devious because he/she is a politician then Y is not a trustworthy politician.
The normal convention is that, in the absence of explicit bracketing, a quantifier further to the left in a formula will dominate those quantifiers to its right.
where A is instantiated to the set of expressions in Argument 5, will permit only two results for X: start or visited(edinburgh,start).