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Conversely, a strict partial order < on may be converted to a non-strict partial order by adjoining all relationships of that form; that is, := < is a non-strict partial order. Thus, if ≤ {\displaystyle \leq } is a non-strict partial order, then the corresponding strict partial order < is the irreflexive kernel given by a < b if a ≤ b and a ...
A partial-order planner is an algorithm or program which will construct a partial-order plan and search for a solution. The input is the problem description, consisting of descriptions of the initial state, the goal and possible actions. The problem can be interpreted as a search problem where the set of possible partial-order plans is the ...
This "finer-than" relation on the set of partitions of X is a partial order (so the notation "≤" is appropriate). Each set of elements has a least upper bound (their "join") and a greatest lower bound (their "meet"), so that it forms a lattice , and more specifically (for partitions of a finite set) it is a geometric and supersolvable lattice.
Preorders, a generalization of partial orders allowing ties (represented as equivalences and distinct from incomparabilities) Semiorders, partial orders determined by comparison of numerical values, in which values that are too close to each other are incomparable; a subfamily of partial orders with certain restrictions
In linguistics, the partitive is a word, phrase, or case that indicates partialness. Nominal partitives are syntactic constructions, such as "some of the children", and may be classified semantically as either set partitives or entity partitives based on the quantifier and the type of embedded noun used.
A total order is a total preorder which is antisymmetric, in other words, which is also a partial order. Total preorders are sometimes also called preference relations . The complement of a strict weak order is a total preorder, and vice versa, but it seems more natural to relate strict weak orders and total preorders in a way that preserves ...
This involves ordering events based on the potential causal relationship of pairs of events in a concurrent system, especially asynchronous distributed systems. It was formulated by Leslie Lamport. [1] The happened-before relation is formally defined as the least strict partial order on events such that:
In mathematics and computer science, an event structure describes sequences of events that can be triggered by combinations of other events, with certain forbidden combinations of events. Different sources provide more or less flexible mathematical formalizations of the way events can be triggered and which combinations are forbidden.