FIT2014 Lecture Notes - Lecture 3: Logic Programming, First-Order Logic, Atomic Sentence
28 Jun 2018
School
Department
Course
Professor
Lecture 3: Predicate logic
Predicate Logic: Example:
All men are mortal
Socrates is a man
Therefore, Socrates is mortal
Object: Socrates, set of people
Properties: man, Mortal
Example: There is an app which is loved by every student
Therefore, every student loves some app
Object: set of people
properties: app student
relation: love
Objects:
- Constant Symbols
o Name which refer exactly one object
o Socrates, rumpus, 1,2,
- Function Symbols:
o Relates some object to exactly one object
o mother of, king of, plus, times
o complex name
- Individual variables
o A variable which can refer to any object
o X, Y
Term
A term is a logical expression which refers to an object
e.g.
- Constant symbols.
- Individual variables.
- Functions of constant symbols.
- Functions of other terms.
Predicates
- Predicate symbols:
o Is it being talk about an object
o Properties(1place)
o But if it is more than one place, it is a relation
- Equality symbol (=)
o Used to state that two objects are the same
Sentence
- Atomic sentence
o A predicate symbol followed by a list of term in brackets
o E.g. Taller (mother of(Clair), Mary)
- Complex sentences
o Atomic sentences joined together by logical connectives
Document Summary
Example: there is an app which is loved by every student. Object: set of people properties: app student relation: love. Constant symbols: name which refer exactly one object. Function symbols: relates some object to exactly one object, mother of, king of, plus, times complex name. Individual variables: a variable which can refer to any object, x, y. A term is a logical expression which refers to an object e. g. constant symbols. Is it being talk about an object: properties(1place, but if it is more than one place, it is a relation. Equality symbol (=: used to state that two objects are the same. Atomic sentence: a predicate symbol followed by a list of term in brackets, e. g. Complex sentences: atomic sentences joined together by logical connectives, e. g. man(socrates) => mortal(socrates) Used to make a statement about every object. For all x, the properties of x being a dog implies that x has a property is being happy.
