Jan Łukasiewicz

Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1.

The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by mathematician Lotfi Zadeh. Basic fuzzy logic had, however, been studied since the 1920s, as infinite-valued logic—notably by Łukasiewicz and Tarski. The works of Zadeh and Joseph Goguen in the 1960's and 1970's went further by considering issues such as linguistic variables and lattices.

Polish notation (PN), also known as normal Polish notation (NPN), Łukasiewicz notation, Warsaw notation, Polish prefix notation, Eastern Notation or simply prefix notation, is a mathematical notation in which operators precede their operands, in contrast to the more common infix notation, in which operators are placed between operands, as well as reverse Polish notation (RPN), in which operators follow their operands. It does not need any parentheses as long as each operator has a fixed number of operands. The description "Polish" refers to the nationality of logician Jan Łukasiewicz, who invented Polish notation in 1924.

The term Polish notation is sometimes taken (as the opposite of infix notation) to also include reverse Polish notation.

Reverse Polish notation (RPN), also known as reverse Łukasiewicz notation, Polish postfix notation or simply postfix notation, is a mathematical notation in which operators follow their operands, in contrast to prefix or Polish notation (PN), in which operators precede their operands. The notation does not need any parentheses for as long as each operator has a fixed number of operands.

The term postfix notation describes the general scheme in mathematics and computer sciences, whereas the term reverse Polish notation typically refers specifically to the method used to enter calculations into hardware or software calculators, which often have additional side effects and implications depending on the actual implementation involving a stack. The description "Polish" refers to the nationality of logician Jan Łukasiewicz, who invented Polish notation in 1924.

Many-valued logic (also multi- or multiple-valued logic) is a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values (i.e., true and false) for any proposition. Classical two-valued logic may be extended to n-valued logic for n greater than 2. Those most popular in the literature are three-valued (e.g., Łukasiewicz's and Kleene's, which accept the values true, false, and unknown), four-valued, nine-valued, the finite-valued (finitely-many valued) with more than three values, and the infinite-valued (infinitely-many-valued), such as fuzzy logic and probability logic.

In mathematics and philosophy, Łukasiewicz logic (/ˌwʊkəˈʃɛvɪtʃ/ WUUK-ə-SHEV-itch, Polish: [wukaˈɕɛvitʂ]) is a non-classical, many-valued logic. It was originally defined in the early 20th century by Jan Łukasiewicz as a three-valued modal logic; it was later generalized to n-valued (for all finite n) as well as infinitely-many-valued (ℵ₀-valued) variants, both propositional and first order. The ℵ₀-valued version was published in 1930 by Łukasiewicz and Alfred Tarski; consequently it is sometimes called the Łukasiewicz–Tarski logic. It belongs to the classes of t-norm fuzzy logics and substructural logics.

Łukasiewicz logic was motivated by Aristotle's suggestion that bivalent logic was not applicable to future contingents, e.g. the statement "There will be a sea battle tomorrow". In other words, statements about the future were neither true nor false, but an intermediate value could be assigned to them, to represent their possibility of becoming true in the future.

Reverse Polish notation (RPN), also known as reverse Łukasiewicz notation, Polish postfix notation or simply postfix notation, is a mathematical notation in which operators follow their operands, in contrast to prefix or Polish notation (PN), in which operators precede their operands. The notation does not need any parentheses as long as each operator has a fixed number of operands.

The term postfix notation describes the general scheme in mathematics and computer sciences, whereas the term reverse Polish notation typically refers specifically to the method used to enter calculations into hardware or software calculators, which often have additional side effects and implications depending on the actual implementation involving a stack. The description "Polish" refers to the nationality of logician Jan Łukasiewicz, who invented Polish notation in 1924.

The Lwów–Warsaw School (Polish: Szkoła Lwowsko-Warszawska) was an interdisciplinary school (mainly philosophy, logic and psychology) founded by Kazimierz Twardowski in 1895 in Lwów, Austro-Hungary (now Lviv, Ukraine).

Though its members represented a variety of disciplines, from mathematics through logic to psychology, the Lwów–Warsaw School is widely considered to have been a philosophical movement. It has produced some of the leading logicians of the twentieth century such as Jan Łukasiewicz, Stanisław Leśniewski, and Alfred Tarski, among others. Its members did not only contribute to the techniques of logic but also to various domains that belong to the philosophy of language.