Discrete Mathematics (II)
Spring 2015
Lecture 2: Lattice(II)
Lecturer: Yi Li
1
Introduction
In this lecture, we will introduce some special lattices. And a very special structure called a Boolean
algebra will be discussed in detail, which has a great many

Discrete Mathematics (II)
Spring 2015
Lecture 7: Tableau Proof System
Lecturer: Yi Li
1
Overview
In last lecture, we have defined consequence, the relationship between a proposition and a set of
propositions, on side of semantics. we prove the validity of

Discrete Mathematics (II)
Spring 2014
Lecture 1: Lattice(I)
Lecturer: Yi Li
1
Introduction
In the first half of the nineteenth century, George Booles attempt to formalize propositional logic
led to the concept of boolean algebras. While investigating the

Discrete Mathematics (II)
Spring 2015
Lecture 6: Truth Assignments and Valuations
Lecturer: Yi Li
1
Overview
In this lecture, we define truth assignments and valuations in order to get rid of truth
table, which is tedious. Finally, a truth valuation can b

Discrete Mathematics (II)
Spring 2015
Lecture 8: Deduction from Premises, Soundness and Completeness
Lecturer: Yi Li
1
Overview
In last lecture, we introduce a tableau proof system to prove the validity of a proposition.But we
should handle whether is a l

Discrete Mathematics (II)
Spring 2015
Lecture 9: Compactness Theorem and Application
Lecturer: Yi Li
1
Overview
Compactness is a very important property in mathematics. It has occurred in Calculus. It is also
a key role in logic.
Mathematical Logic is a c

Discrete Mathematics (II)
Spring 2015
Lecture 3: Introduction to Logic
Lecturer: Yi Li
1
Overview
What is a mathematical proof? How can proofs be justified? Are there limitations to provability?
To what extent can machines carry out mathematical proofs?
W

Discrete Mathematics (II)
Spring 2015
Lecture 11: Semantics of Predicated Language
Lecturer: Yi Li
1
Overview
In this lecture, we try to interpret the symbols of predicate language. In other words, we will assign
the meaning or semantics to symbols which

Discrete Mathematics (II)
Spring 2015
Lecture 10: Predicate Logic and Its Language
Lecturer: Yi Li
1
Predicates and Quantifiers
In this action, we show you why a richer language should be introduced than propositional language,
PL in brief.
1.1
Expressive

Discrete Mathematics (II)
Spring 2013
Lecture 5: Formation Tree and Parsing Algorithm
Lecturer: Yi Li
1
Overview
In this lecture, we completely focus on syntax of proposition. And the term proposition does
always mean well-defined proposition without expl

Discrete Mathematics (II)
Spring 2014
Lecture 4: Proposition, Connectives and Truth Tables
Lecturer: Yi Li
1
Overview
In last lecture, we give a brief introduction to mathematical logic and then redefine order and tree,
which has minor dierences with the

Discrete Mathematics (II)
Spring 2015
Lecture 12: Tableau Proof of Predicate Logic
Lecturer: Yi Li
1
Overview
In this lecture, we will show you how to prove the validity of sentences of predicate logic.
To handle quantifiers, we introduce new atomic table