Frege's Begriffsschrift ( 1879 ) introduced both a complete propositional calculus and what is essentially modern predicate logic.

More ambitious was the Logic Theory Machine, a deduction system for the propositional logic of the Principia Mathematica, developed by Allen Newell, Herbert A. Simon and J. C. Shaw.

For the frequent case of propositional logic, the problem is decidable but Co-NP-complete, and hence only exponential-time algorithms are believed to exist for general proof tasks.

In propositional logic, biconditional introduction is a valid rule of inference.

or as the statement of a truth-functional tautology or theorem of propositional logic:

Category: Theorems in propositional logic

Biconditional elimination is the name of two valid rules of inference of propositional logic.

or as the statement of a truth-functional tautology or theorem of propositional logic:

Category: Theorems in propositional logic

A formula of propositional logic is said to be satisfiable if logical values can be assigned to its variables in a way that makes the formula true.

Conjunction introduction ( often abbreviated simply as conjunction ) is a valid rule of inference of propositional logic.

In propositional logic, disjunctive syllogism ( also known as disjunction elimination and or elimination, or abbreviated ∨ E ), is a valid rule of inference.

and expressed as a truth-functional tautology or theorem of propositional logic:

Disjunction introduction or addition is a simple valid argument form, an immediate inference and a rule of inference of propositional logic.

and expressed as a truth-functional tautology or theorem of propositional logic:

Category: Theorems in propositional logic

: For the theorem of propositional logic which expresses Disjunction elimination, see Case analysis.

In propositional logic, disjunction elimination ( sometimes named proof by cases or case analysis ), is the valid argument form and rule of inference that allows one to eliminate a disjunctive statement from a logical proof.

and expressed as a truth-functional tautology or theorem of propositional logic:

He includes here syllogistic classic logic, propositional logic and that of predicates.

This software showed a radical innovation: it used propositional logic (" Zeroth order logic ") to execute expert systems, reasoning on a knowledge base written with everyday language rules, producing explanations and detecting logic contradictions between the facts.

To emphasize the binary nature of this problem, it is frequently referred to as Boolean or propositional satisfiability.

The propositional satisfiability problem ( PSAT ), which decides whether a given propositional formula is satisfiable, is of central importance in various areas of computer science, including theoretical computer science, algorithmics, artificial intelligence, hardware design, electronic design automation, and verification.

In this article, and in epistemology in general, the kind of knowledge usually discussed is propositional knowledge, also known as " knowledge that.

For Avicenna ( Ibn Sina ), for example, the a tabula rasa is a pure potentiality that is actualized through education, and knowledge is attained through " empirical familiarity with objects in this world from which one abstracts universal concepts " developed through a " syllogistic method of reasoning in which observations lead to propositional statements which when compounded lead to further abstract concepts.

First-order logic is distinguished from propositional logic by its use of quantified variables.

The reason for that is the completeness of propositional logic, with the existential quantifiers playing no role.

In logic, a many-or multi-valued logic is a propositional calculus in which there are more than two values.

Aristotle's assertion that "... it will not be possible to be and not to be the same thing ", which would be written in propositional logic as ¬ ( P ∧ ¬ P ), is a statement modern logicians could call the law of excluded middle ( P ∨ ¬ P ), as distribution of the negation of Aristotle's assertion makes them equivalent, regardless that the former claims that no statement is both true and false, while the latter requires that any statement is either true or false.

In propositional logic, modus ponendo ponens ( Latin for " the way that affirms by affirming "; often abbreviated to MP or modus ponens ) or implication elimination is a valid, simple argument form and rule of inference.

In propositional logic, modus tollens ( or modus tollendo tollens and also denying the consequent ) ( Latin for " the way that denies by denying ") is a valid argument form and rule of inference.

In propositional logic, double negative elimination ( also called double negation elimination, double negative introduction, double negation introduction, or simply double negation ) are two valid rules of replacement.

T is valid in any reflexive frame: if, then since w R w. On the other hand, a frame which validates T has to be reflexive: fix w ∈ W, and define satisfaction of a propositional variable p as follows: if and only if w R u.

In propositional logic and boolean algebra, De Morgan's laws are a pair of transformation rules that are both valid rules of inference.

In propositional logic, distribution refers to two valid rules of replacement.

In standard truth-functional propositional logic, distribution are two valid rule of replacement.

In propositional logic, hypothetical syllogism is the name of a valid rule of inference ( often abbreviated HS and sometimes also called the chain argument, chain rule, or the principle of transitivity of implication ).

In propositional logic, material implication is a valid rule of replacement that allows for a conditional statement to be replaced by a disjunction if and only if the antecedent is negated.

In standard truth-functional propositional logic, commutation, or commutivity are two valid rules of replacement.

Modus ponendo tollens ( Latin: " mode that by affirming, denies ") is a valid rule of inference for propositional logic, sometimes abbreviated MPT.

In propositional logic, simplification ( equivalent to conjunction elimination ) is a valid immediate inference, argument form and rule of inference which makes the inference that, if the conjunction A and B is true, then A is true, and B is true.

Logical systems such as propositional logic are decidable if membership in their set of logically valid formulas ( or theorems ) can be effectively determined.

For example, propositional logic is decidable, because the truth-table method can be used to determine whether an arbitrary propositional formula is logically valid.

Constructive dilemma is a name of a valid rule of inference of propositional logic.

Destructive dilemma is the name of a valid rule of inference of propositional logic.

Other philosophers maintain that norms are ultimately neither true or false, but only successful or unsuccessful ( valid or invalid ), as their propositional content obtains or not ( see also John Searle and speech act ).