Willem Johannes "Wim" Blok (1947–2003) was a Dutch

logician Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arg ...

who made major contributions to

algebraic logic In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with Free variables and bound variables, free variables. What is now usually called classical algebraic logic focuses on the identification and algebraic de ...

universal algebra Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures in general, not specific types of algebraic structures. For instance, rather than considering groups or rings as the object of stud ...

, and

modal logic Modal logic is a kind of logic used to represent statements about Modality (natural language), necessity and possibility. In philosophy and related fields it is used as a tool for understanding concepts such as knowledge, obligation, and causality ...

. His important achievements over the course of his career include "a brilliant demonstration of the fact that various techniques and results that originated in universal algebra can be used to prove significant and deep theorems in modal logic." Blok began his career in 1973 as an algebraist investigating the varieties of

interior algebra In abstract algebra, an interior algebra is a certain type of algebraic structure that encodes the idea of the topological interior of a set. Interior algebras are to topology and the modal logic S4 what Boolean algebras are to set theory and ord ...

s at the

University of Illinois at Chicago The University of Illinois Chicago (UIC) is a public research university in Chicago, Illinois, United States. Its campus is in the Near West Side community area, adjacent to the Chicago Loop. The second campus established under the Universi ...

. Following the 1976 completion of his Ph.D. on that topic, he continued on to study more general varieties of

modal algebra In algebra and logic, a modal algebra is a structure \langle A,\land,\lor,-,0,1,\Box\rangle such that *\langle A,\land,\lor,-,0,1\rangle is a Boolean algebra, *\Box is a unary operation on ''A'' satisfying \Box1=1 and \Box(x\land y)=\Box x\land\Box ...

s. As an algebraist, Blok "was recognised by the modal logic community as one of the most influential modal logicians" by the end of the 1970s. He published many papers in the ''

Reports on Mathematical Logic A report is a document or a statement that presents information in an organized format for a specific audience and purpose. Although summaries of reports may be delivered orally, complete reports are usually given in the form of written documen ...

'', served as a member on their editorial board, and was one of their guest editors. Along with

Don Pigozzi Don, don or DON and variants may refer to: Places *Don (river), a river in European Russia * Don River (disambiguation), several other rivers with the name * Don, Benin, a town in Benin * Don, Dang, a village and hill station in Dang district, G ...

, Wim Blok co-authored the monograph '' Algebraizable Logics'', which began the field now known as

abstract algebraic logic In mathematical logic, abstract algebraic logic is the study of the algebraization of deductive systems arising as an abstraction of the well-known Lindenbaum–Tarski algebra, and how the resulting algebras are related to logical systems.Font, 200 ...

. He died in a car accident on November 30, 2003.

References

1947 births 2003 deaths Dutch logicians Modal logicians {{europe-mathematician-stub

See also

References