25 citations · 637 across the 113 of their papers we have counts for
116 papers
Expressing entropy and cross-entropy in expansions of common meadows
Jan A Bergstra, John V Tucker
A common meadow is an enrichment of a field with a partial division operation that is made total by assuming that division by zero takes the a default value, a special element $\bo…
Fracterm Calculus for Partial Meadows
Jan A. Bergstra, Alban Ponse
Partial algebras and datatypes are discussed with the use of signatures that allow partial functions, and a three-valued short-circuit (sequential) first order logic with a Tarski…
Space-time process algebra with asynchronous communication
J. A. Bergstra, C. A. Middelburg
We introduce a process algebra that concerns the timed behaviour of distributed systems with a known spatial distribution. This process algebra provides a communication mechanism t…
Rings with common division, common meadows and their conditional equational theories
Jan A Bergstra, John V Tucker
We examine the consequences of having a total division operation on commutative rings. We consider two forms of binary division, one derived from a unary inverse, the…
A Complete Finite Axiomatisation of the Equational Theory of Common Meadows
Jan A Bergstra, John V Tucker
We analyse abstract data types that model numerical structures with a concept of error. Specifically, we focus on arithmetic data types that contain an error value whose mai…
Conditional logic as a short-circuit logic
Jan A. Bergstra, Alban Ponse
Three-valued conditional logic (CL) is defined by Guzmán and Squier (1990), and based on McCarthy's noncommutative connectives, axiomatises a short-circuit logic (SCL) that defines…