Lecture 6 Flashcards
What does it mean for a sentence to be satisfiable?
A sentence is satisfiable if there exists at least one model where the sentence is true.
What does it mean for a sentence to be valid?
A sentence is valid if it is true in all possible models.
What is logical entailment?
A sentence is entailed if it is true in all models of the knowledge base.
What is the purpose of SAT solving?
To determine whether a given set of sentences has at least one model that satisfies them.
What is a model in propositional logic?
An interpretation that assigns truth values to propositions, making the knowledge base true.
What is clause normal form (CNF)?
A standardized way of writing logical formulas as a conjunction of disjunctions.
Why is CNF useful?
It simplifies checking satisfiability and can be used as input for algorithms like DPLL.
What is the DPLL algorithm used for?
To determine the satisfiability of a sentence in propositional logic.
What is a unit clause in DPLL?
A clause with only one literal, which can be directly assigned a truth value.
What is a pure literal in DPLL?
A literal that appears only positively or only negatively in the entire set of clauses.
What does the DPLL algorithm do if a partial assignment makes a sentence false?
It backtracks and tries a different assignment.
What happens when the DPLL algorithm encounters an empty clause?
It returns false, indicating the sentence is unsatisfiable.
What is the first step in the DPLL algorithm?
Make an initial partial assignment to one of the propositions.
What does backtracking mean in the context of DPLL?
Revisiting previous assignments to explore alternative truth values.
What are the three variations of DPLL discussed in the lecture?
1) Branching on the first variable, 2) Branching on the most frequent variable in smallest clauses, 3) Branching on the most frequent positive literal.
What does a satisfiable sentence indicate in SAT solving?
That there is at least one truth assignment that makes the sentence true.
What does an unsatisfiable sentence indicate?
That no truth assignment can make the sentence true.
What is the relationship between CNF and satisfiability?
CNF makes it easier to systematically check whether a sentence is satisfiable.
What is the difference between a valid sentence and a satisfiable sentence?
A valid sentence is always true, while a satisfiable sentence is true in at least one model.
How can truth tables help in SAT solving?
They systematically evaluate all possible truth value combinations to check satisfiability.
What is the difference between a model and an interpretation?
An interpretation assigns truth values to propositions, while a model satisfies all sentences in a knowledge base.
What does the notation P ⋁ ¬Q represent?
A disjunction meaning ‘P OR NOT Q’.
What is the purpose of logical operators in propositional logic?
To connect propositions and evaluate their combined truth values.
What is the significance of pure literals in DPLL?
They can be directly assigned truth values to simplify the clause set.
What happens when all clauses in a clause set are satisfied?
The DPLL algorithm returns true, indicating the sentence is satisfiable.
What is the purpose of backtracking in DPLL?
To explore alternative assignments when a current assignment leads to an unsatisfiable clause.
What is the difference between unit propagation and pure literal elimination?
Unit propagation assigns values to single-literal clauses, while pure literal elimination assigns values to literals appearing only positively or negatively.
What is the goal of the DPLL algorithm?
To determine whether a given CNF sentence is satisfiable and to find a satisfying assignment if it exists.
What is a partial assignment in DPLL?
A temporary assignment of truth values to some variables during the algorithm’s process.
How does branching improve the efficiency of the DPLL algorithm?
It reduces the search space by systematically exploring possible truth assignments.
Why is CNF preferred for SAT solving algorithms?
Its standardized structure makes it easier to apply logical rules and algorithms like DPLL.
