
AutoToS prompt:

Logical deduction is performed by applying rules of the form if X then Y to our current knowledge about a world, extending our knowledge with each single rule application. 
A rule if X then Y is applicable if we know X. If a state is defined as our current knowledge of the world, how are successor states defined, given a collection of rules? Please think step by step. Then, provide only the Python implementation for the successor function that receives a state and rules and returns a list of successor states.

Example initial state: {"integer"}
Example rules: [("integer", "real number"), ("integer", "float")]

Model response:
To define the successor states given a collection of rules, we need to follow these steps:

Identify Applicable Rules: For each rule if X then Y, check if X is present in the current state.

Generate Successor States: For each applicable rule, create a new state by adding Y to the current state.

Ensure Uniqueness: Each successor state should be unique to avoid redundant states.

Let's break down the process step-by-step:

Identify Applicable Rules:

Iterate through the list of rules.

For each rule (X, Y), check if X is in the current state.

Generate Successor States:

If X is in the current state, create a new state by copying the current state and adding Y to it.

Ensure Uniqueness:

Use a set or a similar data structure to ensure that each successor state is unique.

Now, let's implement the successor function in Python:

python
Copy code
```
def successor(state, rules):
    successor_states = []
    for rule in rules:
        X, Y = rule
        if X in state:
            new_state = state.copy()
            new_state.add(Y)
            if new_state not in successor_states:
                successor_states.append(new_state)
    return successor_states

# Example usage:
initial_state = {"integer"}
rules = [("integer", "real number"), ("integer", "float")]
print(successor(initial_state, rules))
```
Explanation:
state: A set representing the current knowledge of the world.

rules: A list of tuples where each tuple (X, Y) represents a rule if X then Y.

successor_states: A list to store the unique successor states.

for rule in rules: Iterate through each rule.

if X in state: Check if X is in the current state.

new_state = state.copy(): Create a copy of the current state.

new_state.add(Y): Add Y to the new state.

if new_state not in successor_states: Ensure the new state is unique before adding it to the list of successor states.

This function will return a list of unique successor states based on the given rules and the current state

AutoToS prompt:

Provide only the Python function for the goal test function that tests, given a target fact, whether a state is a goal state. 

Model response:
Here is the Python function for the goal test function:

python
Copy code
```
def is_goal_state(state, target_fact):
    return target_fact in state

# Example usage:
# state = {"integer", "real number"}
# target_fact = "real number"
# print(is_goal_state(state, target_fact))  # Output: True
```
This function checks if the target_fact is present in the state and returns True if it is, indicating that the state is a goal state. Otherwise, it returns False

System message:
Goal Soundness Test Passed
Soundness test

System message:
Successor States Soundness Test Passed
Completeness test
Successor Completeness Test Passed
Success: 4000, failure: 0, total expansions 86963, total evaluations 248574
