Discrete mathematics Yi Li Software School Fudan University June5,2012
Discrete Mathematics Yi Li Software School Fudan University June 5, 2012 Yi Li (Fudan University) Discrete Mathematics June 5, 2012 1 / 25
Review Semantics: Meaning and Truth Structure o Relation between Predicate Logic and Propositional OgIC Some Application
Review Semantics: Meaning and Truth Structure Relation between Predicate Logic and Propositional Logic Some Application Yi Li (Fudan University) Discrete Mathematics June 5, 2012 2 / 25
utline Atomic tableaux Tableau proof o Property of cst
Outline Atomic tableaux Tableau proof Property of CST Yi Li (Fudan University) Discrete Mathematics June 5, 2012 3 / 25
Tableaux Signed sentence o Entries of a tableaux o How to deal with quantifiers?
Tableaux Signed sentence Entries of a tableaux How to deal with quantifiers? Yi Li (Fudan University) Discrete Mathematics June 5, 2012 4 / 25
Truth efinition(Truth The truth of a sentence yp of L in a structure A in which every a E A is named by a ground term of L is defined by induction ●AF3vg(v)兮 for some ground term t,Ag(t) O AHVvp(v)+ for all ground term t, AFp(t)
Truth Definition (Truth) The truth of a sentence ϕ of L in a structure A in which every a ∈ A is named by a ground term of L is defined by induction. 7 A |= ∃vϕ(v ) ⇔ for some ground term t, A |= ϕ(t). 8 A |= ∀vϕ(v ) ⇔ for all ground term t, A |= ϕ(t). Yi Li (Fudan University) Discrete Mathematics June 5, 2012 5 / 25