Various types of semantics games for deductive fuzzy logics, most prominently for Lukasiewicz logic, have been proposed in the literature. These games deviate from Hintikka’s original game for evaluating classical first-order formulas by either introducing an explicit reference to a truth value from the unit interval at each game state (as in [4]) or by generalizing to multisets of formulas to ...

Sorting is a classic problem and one to which many others reduce easily. In the streaming model, however, we are allowed only one pass over the input and sublinear memory, so in general we cannot sort. In this paper we show that, to determine the sorted order of a multiset s of size n containing σ distinct elements using one pass and o(n log σ) bits of memory, it is generally necessary and suff...

A multiset (also referred to as a bag) is a set (collection of elements where the order is of no importance), where the elements do not need to be unique. A vase with n blue and m red marbles is a multiset for example. We propose a new class of distance measures (metrics) designed for multisets, both of which are a recurrent theme in many data mining [2] applications. One particular instance of...

A new method to study families of finite sets, in particular t-designs, by studying families of multisets (also called lists) and their relationships with families of sets, is developed. Notion of the tag for a subset defined earlier by one of the authors is extended to a submultiset. A new concept t-(v, k, λ) list design is defined and studied. Basic existence theory for designs is extended to...

Some applications of techniques borrowed from multiset theory to elaborate graphematical systems as ‘data’ structures with the operations of union, sum, difference and polycontextural dissemination of mixed data structures, like set, multiset, list, trito-, deuteroand protograms. The metaphor of ‘team’ observation for the study of multisets gets a polycontextural explication and application to ...

We propose extending constraint solvers with multiset variables. That is, variables whose values are multisets. Such an extension can help prevent introducing unnecessary symmetry into a model. We identify a number of different representations for multiset variables, and suggest primitive and global constraints on multiset variables. Surprisingly, unlike finite domain variables, decomposition o...

The problem of enumeration of m-antichains of k-bounded multisets on an n-set is considered. A formula for calculating the cardinality of the corresponding family in terms of the graph theory was obtained. A more general case of multiantichains is also considered. As an illustration the corresponding explicit formulas are given for the case when 1 ≤ m ≤ 4, k ≥ 1 and n ≥ 0.

There are presently many and seemingly different optimization algorithms, based on unrelated paradigms. Herein we propose a framework to encompass those heuristics, providing a common working structure and a basis for their comparison. A formal de nition, based on the multiset formalism is presented. We also show how to express some common operators in our framework and we present some (partial...

Karp et al. (1988) described Deferred Data Structures for Multisets as “lazy” data structures which partially sort data to support online rank and select queries, with the minimum amount of work in the worst case over instances of size n and number of queries q fixed. Barbay et al. (2016) refined this approach to take advantage of the gaps between the positions hit by the queries (i.e., the str...