Mathematical logics Spring 2010
 LOGICAL MODELING - SLIDE 01 LOGICAL MODELING - SLIDE 02 LOGICAL MODELING - SLIDE 03 LOGICAL MODELING - SLIDE 04 LOGICAL MODELING - SLIDE 05 LOGICAL MODELING - SLIDE 06 Looking at the slide someone could ask "is the Natural Language decidable"? Without any sort of restriction, the NL is NOT DECIDABLE and there are no ways to reach this property. Using the Godel numbering by which encodes any formal language in the set of naturals number, and the Godel's Theorem of Incompleteness, there is always at least one "True sentence" that cannot be stated True or False within the formal language itself nor in ITS NATURAL INTERPRETATION. References: http://en.wikipedia.org/wiki/Gödel%27s_incompleteness_theorem LOGICAL MODELING - SLIDE 07 LOGICAL MODELING - SLIDE 08 LOGICAL MODELING - SLIDE 09 LOGICAL MODELING - SLIDE 10 LOGICAL MODELING - SLIDE 11 LOGICAL MODELING - SLIDE 12 LOGICAL MODELING - SLIDE 13 The following is related to the previous slide: http://www.infitt.org/ti2003/papers/19_raman.pdf LOGICAL MODELING - SLIDE 14 LOGICAL MODELING - SLIDE 15 LOGICAL MODELING - SLIDE 16 LOGICAL MODELING - SLIDE 17 LOGICAL MODELING - SLIDE 18 LOGICAL MODELING - SLIDE 19 LOGICAL MODELING - SLIDE 20 LOGICAL MODELING - SLIDE 21 LOGICAL MODELING - SLIDE 22 LOGICAL MODELING - SLIDE 23 LOGICAL MODELING - SLIDE 24 The last interpretation function of the formal semantics box "I(MonkeyGetBanana) = F" should not be false. It should be true LOGICAL MODELING - SLIDE 25 LOGICAL MODELING - SLIDE 26 LOGICAL MODELING - SLIDE 27 LOGICAL MODELING - SLIDE 28 LOGICAL MODELING - SLIDE 29 LOGICAL MODELING - SLIDE 30 LOGICAL MODELING - SLIDE 31 LOGICAL MODELING - SLIDE 32 LOGICAL MODELING - SLIDE 33 LOGICAL MODELING - SLIDE 34 LOGICAL MODELING - SLIDE 35 LOGICAL MODELING - SLIDE 36 LOGICAL MODELING - SLIDE 37 LOGICAL MODELING - SLIDE 38 LOGICAL MODELING - SLIDE 39 LOGICAL MODELING - SLIDE 40 LOGICAL MODELING - SLIDE 41
University of Trento - Master in Computer Science