"It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic."
Propositional logic deals with propositions, which can either be true or false. This type of logic focuses on the relationship between these propositions.
Propositions: Statements that can be either true or false, used as basic units in logic.
Connectives: Symbols used to link propositions together, such as "and", "or", "not", "implies", etc.
Truth tables: Charts used to show the resulting truth values of compound propositions for all possible combinations of truth values for their component propositions.
Logical equivalence: The relationship between two propositions that have the same truth value for every combination of truth values for their component propositions.
Logical implication: A relationship between two propositions where the truth of one implies the truth of the other.
Tautologies: Propositions that are always true, regardless of the truth values of the component propositions.
Contradictions: Propositions that are always false, regardless of the truth values of the component propositions.
Consistency: A group of propositions that can all be true at the same time.
Validity: An argument in which the conclusion necessarily follows from the premises, based on the rules of logic.
Inference rules: Procedures used to derive new propositions from existing propositions, such as modus ponens, modus tollens, etc.
Classical logic: The most commonly used type of propositional logic is classical logic, which is also referred to as Boolean logic. It uses basic logical connectives such as AND, OR, and NOT to help infer logical relationships between truth values.
Fuzzy logic: Fuzzy logic is a type of propositional logic that allows partial truths and degrees of certainty. It uses fuzzy sets and fuzzy logic operations that allow the degree of validity and falsity of a statement to be expressed.
Modal logic: Modal logic is used to study the relationship between statements and the world. It uses modal operators such as "necessarily" and "possibly" to express different levels of certainty and possibility.
Intuitionistic logic: Intuitionistic logic is a type of propositional logic that adds a new operator known as "intuitionistic implication." It is used to express the idea that a statement is true if there is a constructive proof for it.
Deontic logic: Deontic logic is a type of modal logic that studies the logic of obligation, permission, and prohibition. It tries to identify the rules that govern ethical and moral reasoning.
Linear logic: Linear logic is a type of multiplicative logic that is designed to handle resources and their interactions. It is used in computer science and programming to analyze and model resource usage.
Relevance logic: Relevance logic is a type of propositional logic that introduces the notion of relevance as a criteria for logical inference. It is used to study the rules of implication that are relevant to a given context.
"It deals with propositions (which can be true or false) and relations between propositions, including the construction of arguments based on them."
"Compound propositions are formed by connecting propositions by logical connectives."
"Propositions that contain no logical connectives are called atomic propositions."
"Unlike first-order logic, propositional logic does not deal with non-logical objects, predicates about them, or quantifiers."
"Yes, all the machinery of propositional logic is included in first-order logic and higher-order logics."
"In this sense, propositional logic is the foundation of first-order logic and higher-order logic."
"It is also called statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic."
"It deals with propositions (which can be true or false) and relations between propositions."
"The construction of arguments is based on propositions and their relations."
"Yes, propositions in propositional logic can be true or false."
"Yes, compound propositions are formed by connecting propositions by logical connectives."
"No, atomic propositions are those that contain no logical connectives."
"Propositional logic does not deal with non-logical objects, predicates about them, or quantifiers."
"Yes, all the machinery of propositional logic is included in first-order logic."
"Propositional logic is included in first-order logic and higher-order logics."
"Propositional logic is sometimes referred to as zeroth-order logic."
"Sentential logic is another term used to refer to propositional logic."
"No, propositional calculus does not involve quantifiers."
"Compound propositions involve the connection of propositions using logical connectives."