Discrete mathematics Software school Fudan University May28,2013
. . Discrete Mathematics Yi Li Software School Fudan University May 28, 2013 Yi Li (Fudan University) Discrete Mathematics May 28, 2013 1 / 24
Review o Semantics: Meaning and Truth Structure o Relation between Predicate Logic and Propositional Logic o Some Application
Review Semantics: Meaning and Truth Structure Relation between Predicate Logic and Propositional Logic Some Application Yi Li (Fudan University) Discrete Mathematics May 28, 2013 2 / 24
utline o Atomic tableaux Tableau proof ● Property of CsT
Outline Atomic tableaux Tableau proof Property of CST Yi Li (Fudan University) Discrete Mathematics May 28, 2013 3 / 24
T ableaux o Signed sentence Entries of a tableaux How to deal with quantifiers?
Tableaux Signed sentence Entries of a tableaux How to deal with quantifiers? Yi Li (Fudan University) Discrete Mathematics May 28, 2013 4 / 24
Truth Definition(Truth The truth of a sentence p of L in a structure A in which every a E A is named by a ground term of l is defined by induction
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 May 28, 2013 5 / 24