Assignment 2: Logic

Goal

To understand representation of knowledge bases using first order logic, and the resolution inference technique.

Procedure

Formalize the blocks world using the situation calculus. The objects in the domain are blocks, tables, and situations. The predicates are:

On(x, y, s) ClearTop(x, s) Block(x) Table(x)

The only action is Puton(x, y), where x must be a block whose top is clear of other blocks, and y cab be either a table or another block whose top is also clear. The initial situation S0 has block A on B on C on the table.

  1. Write an axiom or axioms defining PutOn.
  2. Write facts describing S0 in which block A is on B which is on C which is on the table T.
  3. Write facts for a situtation Sf in which C is on top of B and B is on top of A, and Sf results from the shortest sequence of actions that produces the new arrangement of blocks.
  4. Show that the facts (as a conjunction) can be derived from the initial knowledge base. Use the resolution technique by transforming the knowledge base into conjunctive normal form, adding the negated goal and proving an inconsistency,.

Teams

Work in groups of 2 or 3, but no more. Let me know as soon as you can what your group is. You may work alone if you wish, but this assignment (and subsequent ones) will go faster if you work together.

Deliverables

The initial knowledge base (parts a and b). The goal (part c). The resolution proof

Due Date

Monday 15th. March, in class.