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 science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

who made major contributions to

algebraic logic In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables. What is now usually called classical algebraic logic focuses on the identification and algebraic description of models appropriate for ...

universal algebra Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures. For instance, rather than take particular groups as the object of study, ...

, and

modal logic Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other ...

. 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 or ...

s at the

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

. 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 that presents information in an organized format for a specific audience and purpose. Although summaries of reports may be delivered orally, complete reports are almost always in the form of written documents. Usage In ...

'', 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 *County Donegal, Ireland, Chapman code DON * 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 vi ...

, 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, 20 ...

. 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