CPSC 312 Functional and Logic Programming January-April 2021
Assignment Four: Logic Programming Introduction
Due: 11:59pm, Thursday 11 March 2021. Submit solution online using Canvas
These questions should be done with SWI Prolog. See the web page for how to download, install and run SWI Prolog.
Submit your answers using Canvas. The file for question 2 must run in Prolog (any text answers should be in comments). Use proper sentences in your answers. Make sure you name(s), student number(s) is at the top of each file. In your submission, use only non-proproatary formats (e.g., text, pdf, jpeg but not Word or Excel or Pages). You may work is a group of size one or two. Ask questions on Piazza.
Question One
Consider the facts in http://cs.ubc.ca/~poole/cs312/2021/as4/cs312_2021.pl.
The queries that you provide should work for any knowledge base with the same predicates.
You are not allowed to use any built-in predicates. For each question (a) to (d):
i) Give a (conjunctive) query to answer the question or explain why there cannot be a conjunc- tive query. (Prolog’s answer may provide more information than is asked for, but it should not be wrong.)
ii) If the query is possible, give all of the answers from the facts in cs312_2021.pl.
iii) If there are no answers, suggest some fact(s) that could be added so that the answer is not
“false”, and give the answer for the query given the new facts. Make sure you test it!
(a) “What dates in March are assignments due?”
(b) “What is the email of a TA of cs312 in 2021?” [Note that not all of the emails are for TAs.]
(c) “What are the first names of people that have office hours on consecutive days?”
(d) “Is there a TA who is not holding office hours?”
(e) What information would be required to compute number of classes before from exam? (You do not need to write any Prolog for this. Hint: try to compute it yourself and take notice of any information you required.)
Question Two
Consider the domain of house plumbing represented in Figure 1. In this figure, p1, p2 and p3 are water pipes. p1 is the pipe coming in from the main water supply. t1, t2 and t3 are taps and d1, d2 and d3 are drainage pipes. The other labels should be obvious.
Suppose we have the following atoms:
• pressurized pi , is true if pipe pi has mains pressure in it. Pipe p1 is always pressurized. Other
pipes are pressurized if they are connected to a pressurized pipe through an open tap.
• on ti istrueiftapti ison.
• off ti istrueiftapti isoff.
• wet b is true if b is wet.
1
p3 t3
sink
shower floor
t2 p2
bath
d3
d2
t1
p1 d1
Figure 1: The Plumbing Domain
• flow c is true if water is flowing through component c.
• plugged c is true if component c has the plug in.
• unplugged c is true if component c doesn’t have the plug in.
Assume the taps and plugs have been in the same positions for one hour; you don’t need to consider the dynamics of turning on taps and inserting and removing plugs.
The file http://www.cs.ubc.ca/~poole/cs312/2021/as4/plumbing.pl
contains a Prolog axiomatization for how water can flow down drain d1 if taps t1 and t2 are on and the bath is unplugged.
(a) Finish the axiomatization for the sink in the same manner as the axiomatization for the bath. Give the intended interpretation (using Prolog comments) for all atoms you introduce.
Test it with various configurations of taps on and off, and the plug in and out.
(b) Axiomatize how the floor is wet if the sink overflows or the bath overflows. Each will overflow if the plug is in and water is flowing in. You may invent new atoms as long as you give their intended interpretation.
(c) Suppose a hot water system is installed to the left of tap t1. There is another tap in the pipe leading into the how water system, and it supplies hot water to the shower and the sink (there are separate hot and cold water taps for each). Add this to your axiomatization. You don’t need to model water temperature. Give the intended interpretation for all atoms you invent.
You need to hand in a complete listing of your program (including the intended interpretation for all symbols) and a trace of a session to show it runs for various setting of taps on and off, and plugs in and out.
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Question Three
Given the Prolog program in
http://www.cs.ubc.ca/~poole/cs312/2021/as4/sillyeg.pl
(a) Show how the bottom-up proof procedure works for this example. In particular show a sequence of atoms added to the consequence set together with the corresponding clauses selected.
(b) Give a failing derivation for query: ?- slithy.
(c) Give a succeeding derivation for query: ?- slithy.
(d) Give the box model for slithy. Use this model to explain a trace of the Prolog’s proof. In particular, explain one instance of each of {call, exit, redo, fail} when you use Prolog’s “trace.” command, for the query ?- slithy.
(e) How many answers does Prolog give for this query? Explain why there are this many answers.
Question Four
For each question, specify how long you spend on it, and what you learned. Was the question reasonable? (This question is part of the assignment, so please do it!)
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