
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:
A successor state is a new state that can be reached by applying a single rule to the current state. Given a collection of rules, the successor states are defined as follows:
Initialize an empty list to store the successor states.
For each rule in the collection of rules:
a. Check if the condition (X) of the rule is present in the current state.
b. If the condition is present, create a new state by adding the conclusion (Y) of the rule to the current state.
c. Add the new state to the list of successor states.
Return the list of successor states.
Here is the Python implementation for the successor function:
Python
```
def successor_states(state, rules):
    successor_states = []
    for rule in rules:
        if rule[0] in state:
            new_state = state.copy()
            new_state.add(rule[1])
            successor_states.append(new_state)
    return successor_states
```
You can use this function like this:
Python
initial_state = {"integer"}
rules = [("integer", "real number"), ("integer", "float")]
print(successor_states(initial_state, rules))
This will output:
Python
[{'integer', 'real number'}, {'integer', 'float'}

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:
Python
```
def goal_test(state, target_fact):
    return target_fact in state
```
This function takes in a state and a target fact, and returns True if the target fact is in the state, 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 87490, total evaluations 523778
