Description Logics (DLs) are a family of knowledge representation languages that have gained considerable attention the last 20 years. It is wellknown that the interpretation domain of classical DLs is a classical set. However, in Science and in the ordinary life the situation is not at all like this. In order to handle these types of knowledge in DLs, in this paper we present a DL framework ba...

This paper completely characterizes the standard Young tableaux that can be reconstructed from their sets or multisets of $1$-minors. In particular, any tableau with at least $5$ entries its set

A reconstruction problem is formulated for multisets over commutative groupoids. The cards of a multiset are obtained by replacing a pair of its elements by their sum. Necessary and sufficient conditions for the reconstructibility of multisets are determined. These results find an application in a different kind of reconstruction problem for functions of several arguments and identification min...

This system description provides an overview of the MUNCH reasoner for sets and multisets. MUNCH takes as the input a formula in a logic that supports expressions about sets, multisets, and integers. Constraints over collections and integers are connected using the cardinality operator. Our logic is a fragment of logics of popular interactive theorem provers, and MUNCH is the first fully automa...

We consider a cumulative hierarchy of multisets over some set of urelements, equipped with additive union ] and a transform relation ¤, and investigate the Horn fragments of Intuitionistic Linear Logic (ILL) that are interpretable in it. The operator ! is defined in an asymptotic way which causes some deviations from the linear-theoretic behavior. Soundness, completeness and partial completenes...

Given a multiset M = V1 ∪ V2 ∪ · · · ∪ VC of n elements and a capacity function ∆ : [1, C] → [2, n− 1], we consider the problem of enumerating all unrooted trees T on M such that the degree of each vertex v ∈ Vi is bounded from above by ∆(i). The problem has a direct application of enumerating isomers of tree-like chemical graphs. We give an algorithm that generates all such trees without dupli...