Logical Agents and Game Theory

Vocabulary flashcards covering Propositional Logic, Logical Agents, Truth Tables, Game Theory, Adversarial Search, and Zero-Sum Games.

Logic-Based Agent

A classic type of AI agent that relies on formal logic to represent information, reason systematically, make decisions, and infer new knowledge.

Knowledge Base (KB)

A component of a logic-based agent that stores facts about the world, often represented using propositional or first-order logic.

Inference Engine

A component of a logic-based agent that applies logical rules to the Knowledge Base to deduce new facts or determine actions.

Propositional Logic

A foundational system in AI and computer science (also called Boolean logic) that deals with declarative statements that are either true or false.

First-Order Logic

A formal logic system (also called Predicate Logic) that can handle complex relationships and quantifiers, such as 'All birds can fly'.

Proposition

A declarative sentence that can be characterized as either true or false.

Atomic Proposition

The simplest fact statement in propositional logic whose logical status is characterized by the truth values $T$ or $F$.

Negation

A logical operator represented by $\neg$ (meaning NOT) that negates the truth or false value of a proposition.

Conjunction

A logical connective represented by $\wedge$ (meaning AND) that evaluates to true only when both connected propositions are true.

Disjunction

A logical connective represented by $\vee$ (meaning OR) that evaluates to true when at least one of the connected propositions is true.

Implication

A logical connective represented by $\rightarrow$ (meaning IF…THEN) where if the first proposition is true, the second proposition must be true for the overall statement to be true.

Biconditional

A logical connective represented by $\leftrightarrow$ (meaning IF AND ONLY IF) where $P \leftrightarrow Q$ means $P$ is true when $Q$ is true and vice versa.

Logical Connectives

Operators that allow the formation of compound propositions from atomic ones.

Tautology

A logical statement that is incontestably correct and always evaluates to true regardless of the values of its constituent propositions, such as $P \vee \neg P$.

Contradiction

A logical statement that cannot be true in any logically possible world because a proposition and its negation cannot both be true simultaneously, such as $P \wedge \neg P$.

Propositional Logic Semantics Truth Table

A truth table showing all possible truth values for propositional symbols $P$ and $Q$ alongside the derived truth values for $\neg P$, $P \wedge Q$, $P \vee Q$, $P \Rightarrow Q$, and $P \Leftrightarrow Q$.

Game Theory

A branch of AI and mathematics studying strategic decision-making between two or more intelligent, rational players.

Strategy

In game theory, the set of possible actions available to a player during a game.

Payoff

The reward, utility, points, or profit received by a player after choosing a strategy.

Adversarial Search

A search technique in AI used for competitive games where one player's gain is another player's loss and the environment changes due to opponent moves.

MAX Player

In adversarial search, the player representing the AI or computer that attempts to maximize the utility score.

MIN Player

In adversarial search, the player representing the opponent that attempts to minimize the utility score.

Zero-Sum Game

A competitive game where one player's gain equals another player's loss, resulting in a constant total payoff sum of $0$.

Tic-Tac-Toe Payoff Matrix

A table outlining the zero-sum payoffs in Tic-Tac-Toe, where Player X winning yields $+1$ for X and $-1$ for O, Player O winning yields $-1$ for X and $+1$ for O, and a draw yields $0$ for both.

Matching Pennies Game

A zero-sum game example where Player A wins when both players pick matching sides (Head/Head or Tail/Tail) and Player B wins when the picks differ (Head/Tail or Tail/Head).