Task
The task in this programming assignment is to implement, a knowledge base and an inference engine for the wumpus world. First of all, you have to create a knowledge base (stored as a text file) storing the rules of the wumpus world, i.e., what we know about pits, monsters, breeze, and stench. Second, you have to create an inference engine, that given a knowledge base and a statement determines if, based on the knowledge base, the statement is definitely true, definitely false, or of unknown truth value.
Command-line Arguments
The program should be invoked from the commandline as follows:
check_true_false wumpus_rules.txt [additional_knowledge_file] [statement_file]
For example:
check_true_false wumpus_rules.txt kb1.txt statement1.txt
- Argument wumpus_rules.txt specifies the location of a text file containing the wumpus rules, i.e., the rules that are true in any possible wumpus world, as specified above (once again, note that the specifications above are not identical to the ones in the book).
- Argument [additional_knowledge_file] specifies an input file that contains additional information, presumably collected by the agent as it moves from square to square. For example, see kb3.txt.
- Argument [statement_file] specifies an input file that contains a single logical statement. The program should check if, given the information in wumpus_rules.txt and [additional_knowledge_file], the statement in [statement_file] is definitely true, definitely false, or none of the above.
Output
Your program should create a text file called "result.txt". Depending on what your inference algorithm determined about the statement being true or false, the output file should contain one of the following four outputs:
- definitely true
- definitely false
- possibly true, possibly false
- both true and false
Notice that the sample code provided below stores the words "result unknown" to the result.txt file. Also, the "both true and false" output should be given when the knowledge base (i.e., the info stored in wumpus_rules.txt AND in the additional knowledge file) entails both the statement from statement_file AND the negation of that statement.
Syntax
The wumpus rules file and the additional knowledge file contain multiple lines. Each line contains a logical statement. The knowledge base constructed by the program should be a conjunction of all the statements contained in the two files. The sample code (as described later) already does that. The statement file contains a single line, with a single logical statement.
Statements are given in prefix notation. Some examples of prefix notation are:
(or M_1_1 B_1_2)
(and M_1_2 S_1_1 (not (or M_1_3 M_1_4)))
(if M_1_1 (and S_1_2 S_1_3))
(iff M_1_2 (and S_1_1 S_1_3 S_2_2))
(xor B_2_2 P_1_2)
P_1_1
B_3_4
(not P_1_1)
Statements can be nested, as shown in the above examples.
Note that:
- Any open parenthesis that is not the first character of a text line must be preceded by white space.
- Any open parenthesis must be immediately followed by a connective (without any white space in between).
- Any close parenthesis that is not the last character of a text line must be followed by white space.
- If the logical expression contains just a symbol (and no connectives), the symbol should NOT be enclosed in parentheses. For example, (P_1_1) is not legal, whereas (not P_1_1) is legal. See also the example statements given above.
- Each logical expression should be contained in a single line.
- The wumpus rules file and the additional knowledge file contain a set of logical expressions. The statement file should contain a single logical expression. If it contains more than one logical expression, only the first one is read.
- Lines starting with # are treated as comment lines, and ignored.
- You can have empty lines, but they must be totally empty. If a line has a single space on it (and nothing more) the program will complain and not read the file successfully.
There are six connectives: and, or, xor, not, if, iff. No other connectives are allowed to be used in the input files. Here is some additional information:
- A statement can consist of either a single symbol, or a connective connecting multiple (sub)statements. Notice
that this is a recursive definition. In other words, statements are symbols or more complicated statements that we can make by connecting simpler statements with one of the six connectives.
- Connectives "and", "or", and "xor" can connect any number of statements, including 0 statements. It is legal for a statement consisting of an "and", "or", or "xor" connective to have no substatements, e.g., (and). An "and" statement with zero substatements is true. An "or" or "xor" statement with zero substatements is false. An "xor" statement is true if exactly 1 substatement is true (no more, no fewer).
- Connectives "if" and "iff" require exactly two substatements.
- Connective "not" requires exactly one substatement.
The only symbols that are allowed to be used are:
- M_i_j (standing for "there is a monster at square (i, j)).
- S_i_j (standing for "there is a stench at square (i, j)).
- P_i_j (standing for "there is a pit at square (i, j)).
- B_i_j (standing for "there is a breeze at square (i, j)).
NO OTHER SYMBOLS ARE ALLOWED. Also, note that i and j can take values 1, 2, 3, and 4. In other words, there will be 16 unique symbols of the form M_i_j, 16 unique symbols of the form S_i_j, 16 unique symbols of the form P_i_j, and 16 unique symbols of the form B_i_j, for a total of 64 unique symbols.
The Wumpus Rules
Here is what we know to be true in any wumpus world, for the purposes of this assignment (NOTE THAT THESE RULES ARE NOT IDENTICAL TO THE ONES IN THE TEXTBOOK):
- If there is a monster at square (i,j), there is stench at all adjacent squares.
- If there is stench at square (i,j), there is a monster at one of the adjacent squares.
- If there is a pit at square (i,j), there is breeze at all adjacent squares.
- If there is breeze at square (i,j), there is a pit at one or more of the adjacent squares.
- There is one and only one monster (no more, no fewer).
- Squares (1,1), (1,2), (2,1), (2,2) have no monsters and no pits.
- The number of pits can be between 1 and 11.
- We don't care about gold, glitter, and arrows, there will be no information about them in the knowledge base, and no reference to them in the statement.
Sample code
The following code implements, in Java and C++, a system that reads text files containing information for the knowledge base and the statement whose truth we want to check. Feel free to use that code and build on top of it. Also feel free to ignore that code and start from scratch.
You can test this code, by compiling on omega, and running on input files a.txt, b.txt, and c.txt. For example, for the Java code you can run it as:
javac *.java
java CheckTrueFalse a.txt b.txt c.txt
and for C++, you can do:
g++ -o check_true_false check_true_false.cpp
./check_true_false a.txt b.txt c.txt
Extracting symbols and evaluating sets of assignments
Note that, as stated below in the grading specifications, you need to include, in your code, specific functions that perform the following:
- a function that extracts, and stores in a list, the set of all symbols used in the wumpus rule, the knowledge base, and the statement. The list should contain no repetitions.
- a function that, given as arguments the knowledge base (including the wumpus rules), the statement to be shown true or false, and a a set of boolean assigments (i.e., either true or false) for each symbol, determines whether, under that set of assignments, the knowledge base entails the statement.
Choices for Inference
You can implement any inference algorithm you want. Efficiency will not be considered for grading. You are also free to use first-order logic instead of propositional logic. However, you should note that the sample code uses propositional logic, and that in general it will probably be easier if you stick to propositional logic. Also, EVEN IF YOU DECIDE TO USE FIRST-ORDER LOGIC, YOUR PROGRAM STILL HAS TO WORK WITH INPUT FILES THAT USE PROPOSITIONAL LOGIC AS EXPLAINED ABOVE.
Efficiency
Brute-force enumeration of all possible assignments to the Boolean variables will be too inefficient to produce answers in a reasonable amount of time. You should look closely at question 3 of the third written assignment, and integrate the answer to that question into your implementation. If you do that correctly, your program should produce answers in a reasonable amount of time (like a few seconds) when the agent has already visited 10 or more squares (and has added the information collected from those squares to the knowledge base that you will use as input).
In your solution, you are allowed to make (and use) the assumptions stated at question 3 of the third written assignment, which are repeated here:
- Every time your agent visits a square, it adds four individual statements to the knowledge base.
- Each of those four statements is a literal (i.e., a symbol, or the negation of a symbol). These four literals describe the presence or absence of breeze, pit, stench, and wumpus in that square.
Just for the record, there is also a solution (for this specific version of the wumpus world and wumpus rules) that would achieve a reasonable runtime even when the agent has not visited any squares yet. You are not required to find this solution, but you are welcome to try.
Grading
The assignment will be graded out of 100 points.
- 40 points: submitting an appropriate wumpus_rules.txt file that can be used as the first command-line input to the program, according to the propositional logic syntax and symbols defined above. The file should contain logical statements corresponding to the wumpus rules stated above. For each of the 8 rules, you need to determine if you need to add any statements to wumpus_rules.txt because of that rule, and if so, what statements to add. Correct handling of any of the eight rules is worth 5 points.
- 10 points: designing a function that extracts, and stores in a list, the set of all symbols used in the wumpus rule, the knowledge base, and the statement. The list should contain no repetitions.
- 10 points: designing a function that, given as arguments the knowledge base (including the wumpus rules), the statement to be shown true or false, and a a set of boolean assigments (i.e., either true or false) for each symbol, determines whether, under that set of assignments, the knowledge base entails the statement.
- 6 points: integrating, in your implementation, the correct answer to question 3 of the third written assignment, so that your program is reasonably efficient when the knowledge base contains information obtained by the agent visiting 10 or more squares.
- 24 points: correctness of results. In particular, 4 points will be allocated for each of the following requirements that the program satisfies:
- In all cases where a statement is definitely true (and its negation is not definitely true) given the wumpus rules and knowledge base, the program outputs "definitely true".
- In all cases where the program outputs "definitely true", the statement is definitely true (and its negation is not definitely true) given the wumpus rules and knowledge base.
- In all cases where a statement is definitely false given the wumpus rules and knowledge base, the program outputs "definitely false".
- In all cases where the program outputs "definitely false", the statement is definitely false given the wumpus rules and knowledge base.
- In all cases where a statement is possibly true and possibly false given the wumpus rules and knowledge base, the program outputs "possibly true, possibly false".
- In all cases where the program outputs "possibly true, possibly false", the statement is possibly true and possibly false given the wumpus rules and knowledge base.
- 10 points: Elegance of the software implementation: modular design, good code organization, code that is easy to read and understand, proper comments.
winner.
How to submit
Submissions should be made using Blackboard.
Implementations in Python, C, C++, and Java will be accepted. If you would like
to use another language, please first check with the instructor via
e-mail. Points will be taken off for failure to comply with this
requirement.
Submit a ZIPPED directory called programming3.zip (no other
forms of compression accepted, contact the instructor or TA if you do
not know how to produce .zip files). The directory should
contain source code. Including binaries is optional. The submission should also contain a file called readme.txt,
which should specify precisely:
- Name and UTA ID of the student.
- What programming language is used.
- How the code is structured.
- How to run the code, including very specific compilation instructions. Instructions such as "compile using g++" are NOT considered specific. Providing all the command lines that are needed to complete the compilation on omega is specific.
Insufficient or unclear instructions will be penalized by up to 20 points.
Code that does not run on omega machines gets AT MOST half credit (50 points).
Submission checklist
- DID YOU INCLUDE THE wumpus_rules.txt file?
- Is the code running on omega?
- Is the submitted zipped file called programming3.zip?
- Does the attachment include a readme.txt file, as specified?