Logical and Knowledge-Based Agents

A sentence that is always true; a fact that is universally acknowledged. It is the opposite of a contradiction.

A sentence that is always false, regardless of the truth values of its components. Examples include 'this sentence is false' or '2+2=5'.

This symbol (⇔) connects two sentences, forming a statement that is only true if both component sentences have the same truth value. This means it's true if both are true or both are false.

A specific combination of truth values assigned to propositional variables. Each model represents a possible scenario for the truth values of the variables in a logical statement.

A symbol representing a statement or proposition that can be either true or false, but not both. Examples include 'It's raining' or 'The Earth is flat'.

A symbol representing a single proposition. Each atomic proposition can be assigned a truth value of 'true' or 'false'.

A method for determining the truth value of a logical sentence by systematically evaluating the truth values of its components. It involves evaluating the truth values of connectives (AND, OR, NOT, etc.) and simplifying the expression.

A type of logic that deals with propositions, or statements that can be either true or false. It uses connectives (AND, OR, NOT, etc.) to combine propositions and create more complex statements.

A sentence is valid if it is true in all possible scenarios, regardless of the truth values assigned to its components.

A sentence is satisfiable if there's at least one scenario where it is true. There might be other scenarios where it's false, but at least one must prove it true.

A sentence is unsatisfiable if it is always false, no matter what truth values are assigned to its components.

The process of deriving new information from a set of existing information or premises.

A proof method that systematically builds new sentences from existing ones using logical rules.

A method for checking if a sentence is true or false by systematically evaluating all possible truth value assignments.

A knowledge base where all statements are represented in a specific format called Horn clauses.

A rule of inference that allows deriving a conclusion from a set of premises. It states: If we know 'A' is true and we also know that 'if A then B' is true, then we can conclude that 'B' is true.

A propositional logic sentence is logically equivalent to another propositional logic sentence if they are true in the same models. It means they have the same truth value for every assignment of truth values to the propositional symbols.

A model is a possible assignment of truth values (true or false) to the propositional symbols in a knowledge base. It represents one possible state of the world.

A knowledge base (KB) is a set of propositional logic sentences that represent our knowledge about the world.

Inference by enumeration involves checking all possible truth assignments (models) to see if a particular sentence (query) is true in every model where the knowledge base (KB) is also true.

A valid model for a knowledge base (KB) is a model where all the sentences in the KB are true.

The TT-ENTAILS? function is a function in propositional logic that determines whether a knowledge base (KB) entails (logically implies) a query (α). It uses truth table enumeration to check.

TT-CHECK-ALL is a recursive function that checks all possible truth assignments (models) given a knowledge base (KB), a query (α), a list of propositional symbols, and an existing model.

PL-TRUE? function takes a sentence (e.g., a rule or a query) and a model, and returns true if the sentence is true in that model.

EXTEND function takes a proposition symbol (P), its truth value (true or false), and a current model, and returns a new model with the truth value for the proposition symbol added.

Depth-first enumeration of models is a method for checking entailment in propositional logic. It systematically explores all possible models, starting with the first symbol and going deeper.

A reasoning method that starts with a desired goal (conclusion) and works backward, attempting to find evidence that supports it. It involves checking if the goal can be inferred from known facts or rules, and if not, it breaks down the goal into subgoals until a known fact is reached.

A logical rule in backward chaining where the goal (conclusion) is reached if all its preconditions (premises) are true.

A logic problem where the goal is to infer a specific conclusion, often represented by a symbol like 'Q', by finding evidence that logically leads to it.

In backward chaining, repeatedly breaking down a complex goal into smaller, more manageable subgoals until a known fact is reached.

A reasoning approach that starts with known facts and rules and aims to derive new knowledge or reach a specific conclusion. It is data-driven and often used for tasks like object recognition or routine decisions.

A way to represent logical statements as a combination of clauses, where each clause is a disjunction (OR) of literals (propositions or their negations).

A rule used in CNF to derive new clauses from existing ones. It involves combining two clauses that share a complementary literal (one literal is negated, the other is not).

A method for proving the validity of CNF sentences by repeatedly applying the resolution rule until no new clauses can be derived. If the empty clause is derived, the original set of clauses is unsatisfiable.

A set of rules that describe the relationships between facts and actions in a specific domain. For example, 'If there's a breeze, then there's a pit adjacent.'

The process of converting logical statements into Conjunctive Normal Form (CNF). This transformation allows for using resolution inference and other techniques for knowledge representation and reasoning.

A type of logical reasoning that uses a set of rules to derive new knowledge from existing information. It's essential for solving problems and making decisions in AI systems.

The ability of a knowledge representation system to express complex concepts and relations efficiently. A representation with low complexity allows for faster reasoning and easier manipulation.

The process of determining the truth value of a proposition or sentence by systematically evaluating the truth values of its components. It involves using rules about truth values of logical connectives (AND, OR, NOT, etc.).

A logical inference rule that combines two clauses containing complementary literals, removing them and creating a new clause with all other literals.

A logical agent for Wumpus world explores actions like observing glitter, planning routes, and shooting arrows based on logical inferences about the world's state.