Next Week's Homework

Read Loaden through 12.4 OR Read Tucker + Noonan through 9.5.3 except 9.4

Install gPrologue

Review of Propositional Logic's Structure:

Statements are simple combinations of variables and operators.

• AND : ^ OR : \vee NOT : ¬

  Implies : =>

p: it is raining

Predicate Logic

Statements are made from operators and Predicates that have arguments.

raining(10:20am, Needham) <- Raining is a predicate, 10:20am and Needham are arguments

raining(10:21am, Needham) <- Put together, they make an assertion.

sad_students(FOCS)

First Order Predicate Calculus(FOPC or FOL)

Only quantifies over the arguments, not over the predicates.

• \forall t raining(t,loc) => raining(t+1,loc) <- Rule

course(FOCS,ENGR3520,TuesFri,10,12,Stein) <- Predicate with 6 args

Ex 1

• \forall CN₁ , CN₂ course( _ , CN₁ ,date,tstart, tend, _ , R₁ )

course( _ , CN₂ ,date,tstart,tend, _ , R₂ )

• => CN₁ = CN₂ OR R₁ \neq R₂

Ex 2

course(C)

roomof(C,318) <- Accessors for object

nameof(C,FOCS)

etc...

• \forall C₁ ,C₂ course( C₁ ) , course( C₂ )

roomof( C₁ ,R₁ ) , roomof( C₂,R₁ )

starttime( C₁ ,t₁ ) , starttime( C₂,t₁ ) <- Related but not function

• => C₁=C₂

starttime( C₁y ) = starttime( C₂) <- Function returning value

Ex 4: RDF

<description about=FOCS>

<course-name> Foundations of Computer Science</course-name>

<course-instructor> LAS </course-instructor>

</description>

Ex 5

<class about="prof">

<rdf:subclassOf> http://location of def of person</rdf:subclassOf>

</class>

All of this means: \forall x prof (x) => person (x)