ukasiewicz

Jan Łukasiewicz was a Polish logician and philosopher who played a pivotal role in the development of modern many-valued logic. Born in Lwów (then part of Austria-Hungary, now in Ukraine) in 1878, he pursued mathematics and philosophy and became a leading figure in 20th-century logic.

Łukasiewicz introduced the systematic study of logics with more than two truth values. In 1920 he proposed a three-valued logic (often called L3) with truth values 0, 1/2, and 1, and defined the logical connectives by truth-functional rules. This work established the field of many-valued logic and influenced subsequent researchers across logic and philosophy. He later developed an infinite-valued logic in which truth values range over the entire interval [0,1]. In this system, negation, conjunction, disjunction, and implication are given by real-valued functions, such as negation 1 − x, conjunction min(x,y), disjunction max(x,y), and implication min(1, 1 − x + y). This framework provided a rigorous semantic basis for gradual or fuzzy reasoning and influenced later developments in fuzzy logic.

Beyond technical logic, Łukasiewicz contributed to the philosophy of logic and the theory of quantifiers, helping to articulate formal approaches to logic within the Polish school of philosophy. His work laid foundational ideas for later formal and philosophical analyses of truth, consequence, and scientific theories.

Łukasiewicz’s pioneering experiments with multiple-valued logic continue to be studied as foundational chapters in the history and philosophy of logic. He died in 1957 in Warsaw.