
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:
Let's break it down step by step:
Current State: Our current knowledge about the world, represented as a set of facts. (e.g., {"integer"})
Rules: A collection of if-then rules, where each rule is a pair of facts (e.g., [("integer", "real number"), ("integer", "float")])
Applicable Rules: A rule is applicable if its "if" part (antecedent) is present in the current state.
Successor States: For each applicable rule, we create a new state by adding the "then" part (consequent) of the rule to the current state.
Here's the Python implementation for the successor function:
Python
```
def get_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

# Example usage:
initial_state = {"integer"}
rules = [("integer", "real number"), ("integer", "float")]
successor_states = get_successor_states(initial_state, rules)
print(successor_states)  # Output: [{'integer', 'real number'}, {'integer', 'float'}]
```
This function iterates over each rule, checks if the antecedent is in the current state, and if so, creates a new state by adding the consequent to the current state. The resulting list of successor states is then returned

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 is_goal_state(state, target_fact):
    return target_fact in state
```
This function checks if the target fact is present in the given state, returning True if it is, and False otherwise

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 87058, total evaluations 520385
