We continue our work [5] on the logic of multisets (or on the multiset semantics of linear logic), by interpreting further the additive disjunction t. To this purpose we employ a more general class of processes, called free, the axiomatization of which requires a new rule (not compatible with the full LL), the cancellation rule. Disjunctive multisets are modeled as finite sets of multisets. The...

The aim of this paper is to develop a theory of linear codes over finite chain rings from a geometric viewpoint. Generalizing a well-known result for linear codes over fields, we prove that there exists a one-to-one correspondence between so-called fat linear codes over chain rings and multisets of points in projective Hjelmslev geometries, in the sense that semilinearly isomorphic codes corres...

The article is devoted to two classical combinatorial problems on multisets, which in the existing literature are given unjustifiably little space. Namely, calculation of number all submultisets power $m$ for an arbitrary multiset and $m$-permutations such multisets. first problem closely related width a partially ordered set with inclusion $\subseteq$. contains some important classes Combinato...

A multiset consists of elements, but the notion of a multiset is distinguished from that of a set by carrying information of how many times each element occurs in a given multiset. In this work we will investigate the notion of iterative multisets, where multisets are iteratively built up from other multisets, in the context Martin-Löf Type Theory, in the presence of Voevodsky’s Univalence Axio...

This note corrects two errors that occurred during the typesetting of our paper “Axiomatisations of functional dependencies in the presence of records, lists, sets and multisets”, which appeared in Hartmann et al. [Axiomatisations of functional dependencies in the presence of records, lists, sets and multisets, Theoret. Comput. Sci. 353(2) (2006) 167–196]. © 2006 Elsevier B.V. All rights reserved.

Multisets and multirelations arise naturally in modeling. In this paper, we present a sound and practical mathematical framework, which encodes multisets and multirelations using only ordinary sets and total functions. We implement the encoding as a mutliconcepts library in Alloy, which is declarative, compatible with ordinary sets and relations, and can be incorporated into existing models sea...

Given a ∨ -complete (semi)lattice L, we consider L-labeled transition systems as coalgebras of a functor L(−), associating with a set X the set LX of all L-fuzzy subsets. We describe simulations and bisimulations of L-coalgebras to show that L(−) weakly preserves nonempty kernel pairs iff it weakly preserves nonempty pullbacks iff L is join infinitely distributive (JID). Exchanging L for a comm...

A permutation π of a multiset is said to be quasi-Stirling if there do not exist four indices i<j<k<ℓ such that πi=πk, πj=πℓ and πi≠πj. For M, denote by Q‾M the set permutations M. The polynomial on M defined Q‾M(t)=∑π∈Q‾Mtdes(π), where des(π) denotes number descents π. By employing generating function arguments, Elizalde derived an elegant identity involving polynomials {12,22,…,n2}, in analog...

Gödel logic and its algebraic semantics, namely, the variety of Gödel algebras, play a major rôle in mathematical fuzzy logic. The category of finite Gödel algebras and their homomorphisms is dually equivalent to the category FF of finite forests and order-preserving open maps. The combinatorial nature of FF allows to reduce the usually difficult problem of computing coproducts of algebras and ...