Mathematical logics Spring 2010
 PROPOSITIONAL LOGIC - SLIDE 01 In this paper it is possible to find some interesting exercises. www.dif.unige.it/epi/hp/pal/ssis04/prop.pdf PROPOSITIONAL LOGIC - SLIDE 02 PROPOSITIONAL LOGIC - SLIDE 03 PROPOSITIONAL LOGIC - SLIDE 04 PROPOSITIONAL LOGIC - SLIDE 05 PROPOSITIONAL LOGIC - SLIDE 06 PROPOSITIONAL LOGIC - SLIDE 07 In this slide may be useful a paragraph that list the operator priorities. This defines a method/way to disambiguate formulas without parenthesis. The operator precedence is (from higher to lower): not, and, or, implication (left/right), equality (double implication). In other words: "the 'not' operator has higher precedence than 'and', 'and' has higher precedence than 'or', and 'or' has higher precedence than '-- >','<--', and '<-->'." PROPOSITIONAL LOGIC - SLIDE 08 The following is related to the previous slide: http://en.wikipedia.org/wiki/Backus-Naur_Form PROPOSITIONAL LOGIC - SLIDE 09 PROPOSITIONAL LOGIC - SLIDE 10 PROPOSITIONAL LOGIC - SLIDE 11 PROPOSITIONAL LOGIC - SLIDE 12 PROPOSITIONAL LOGIC - SLIDE 13 PROPOSITIONAL LOGIC - SLIDE 14 PROPOSITIONAL LOGIC - SLIDE 15 PROPOSITIONAL LOGIC - SLIDE 16 PROPOSITIONAL LOGIC - SLIDE 17 PROPOSITIONAL LOGIC - SLIDE 18 PROPOSITIONAL LOGIC - SLIDE 19 PROPOSITIONAL LOGIC - SLIDE 20 PROPOSITIONAL LOGIC - SLIDE 21 PROPOSITIONAL LOGIC - SLIDE 22 PROPOSITIONAL LOGIC - SLIDE 23 PROPOSITIONAL LOGIC - SLIDE 24 PROPOSITIONAL LOGIC - SLIDE 25 PROPOSITIONAL LOGIC - SLIDE 26 PROPOSITIONAL LOGIC - SLIDE 27 PROPOSITIONAL LOGIC - SLIDE 28 PROPOSITIONAL LOGIC - SLIDE 29 PROPOSITIONAL LOGIC - SLIDE 30 PROPOSITIONAL LOGIC - SLIDE 31 PROPOSITIONAL LOGIC - SLIDE 32 PROPOSITIONAL LOGIC - SLIDE 33 PROPOSITIONAL LOGIC - SLIDE 34 PROPOSITIONAL LOGIC - SLIDE 35 PROPOSITIONAL LOGIC - SLIDE 36 PROPOSITIONAL LOGIC - SLIDE 37 PROPOSITIONAL LOGIC - SLIDE 38 PROPOSITIONAL LOGIC - SLIDE 39 PROPOSITIONAL LOGIC - SLIDE 40 PROPOSITIONAL LOGIC - SLIDE 41 PROPOSITIONAL LOGIC - SLIDE 41 PROPOSITIONAL LOGIC - SLIDE 42 PROPOSITIONAL LOGIC - SLIDE 43 PROPOSITIONAL LOGIC - SLIDE 44 PROPOSITIONAL LOGIC - SLIDE 45 PROPOSITIONAL LOGIC - SLIDE 46 PROPOSITIONAL LOGIC - SLIDE 47 PROPOSITIONAL LOGIC - SLIDE 48 PROPOSITIONAL LOGIC - SLIDE 49 PROPOSITIONAL LOGIC - SLIDE 50 PROPOSITIONAL LOGIC - SLIDE 51 PROPOSITIONAL LOGIC - SLIDE 52 PROPOSITIONAL LOGIC - SLIDE 53 PROPOSITIONAL LOGIC - SLIDE 54 PROPOSITIONAL LOGIC - SLIDE 55 Some more exercises about conjunctive normal form (a) (P ∧Q)→ R (b) ¬((P ∧ ¬Q)∨(R ∧ ¬S)) (c) P ↔(Q ∧R) (d) P ∧¬(Q→ (P ∧ Q)) (e) ¬((p → q) ↔ (¬q → ¬p)) PROPOSITIONAL LOGIC - SLIDE 56 PROPOSITIONAL LOGIC - SLIDE 57
University of Trento - Master in Computer Science