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Propositional logic algorithms are computational methods or procedures designed to manipulate and reason about propositions within propositional logic. Propositional logic is a branch of formal logic that deals with propositions—statements that are either true or false. These algorithms are used in various applications, including artificial intelligence, computer science, and automated reasoning systems. 

Some key aspects and algorithms related to propositional logic are: 

     i) Semantic Tableaux (Truth Tree) Algorithm: 

Semantic tableaux is a method used to determine the satisfiability of a propositional logic formula. The algorithm constructs a tree structure (truth tree) to explore all possible truth value assignments to propositions and checks for consistency. 

     ii) Resolution Algorithm: 

Resolution is a rule of inference that can be used to infer new propositions from existing ones. The resolution algorithm is used to check the validity of a propositional logic formula or to derive new propositions based on a set of given propositions. 

     iii) Davis-Putnam-Logemann-Loveland (DPLL) Algorithm: 

DPLL is a complete and efficient algorithm for determining the satisfiability of a propositional logic formula. It employs a backtracking search combined with the resolution rule to explore the space of possible truth assignments. 

     iv) Model Checking Algorithms: 

Model checking is a technique used to verify whether a given model (system) satisfies a particular property expressed in temporal or propositional logic. Algorithms like the Symbolic Model Checking algorithm use efficient data structures to represent and check large state spaces. 

     v) Binary Decision Diagrams (BDDs): 

BDDs are a data structure used to represent boolean functions efficiently. Algorithms involving BDDs are used in symbolic model checking and formal verification of hardware and software systems. 

     vi) SAT Solvers:

SAT (Boolean satisfiability) solvers are algorithms designed to determine the satisfiability of a given propositional logic formula. Modern SAT solvers use sophisticated heuristics and efficient algorithms, such as conflict-driven clause learning, to explore the solution space. 

With an example discussed in Knowledge Base (Repository), the  script explained below is an example of using the sympy library in Python to work with propositional logic and evaluate the truth values of logical expressions:

Defining Propositions: These lines create symbolic variables (Symbol) to represent propositions.

P = Symbol("The sky is dark") 

Q = Symbol("It is daytime.") 

R = Symbol("The temperature is warm.")

Defining Logical Rules: These lines define logical rules or expressions using the symbolic variables.

kb1_expr = And(P, Q) 

kb2_expr = And(Q, R)  

Knowledge Base Formulation: 

knowledge_base = And( 

Implies(Not(P), Q), 

Or(Q, R), 

Not(And(Q, R)), 

Q 

)  

Checking Model Satisfaction:  The script below checks for models (assignments of truth values to propositions) that satisfy the knowledge base.

models = list(satisfiable(knowledge_base, all_models=True))  

Generating Truth Value Combinations: This generates all possible combinations of truth values for the propositions P, Q, and R.

truth_values = list(product([True, False], repeat=3))  

Displaying Truth Values in a Table: The script then evaluates and displays the truth values for each combination of P, Q, and R, along with the truth values of the logical expressions kb1 and kb2.

for values in truth_values:

Output:

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