Related papers: Boolean and ortho fuzzy subset logics
It has previously been an open problem whether all Boolean submodular functions can be decomposed into a sum of binary submodular functions over a possibly larger set of variables. This problem has been considered within several different…
The theory of fuzzy semigroups is a branch of mathematics that arose in early 90's as an effort to characterize properties of semigroups by the properties of their fuzzy subsystems which include, fuzzy subsemigroups and their alike, fuzzy…
We investigate the possibility of extending the non-functionally complete logic of a collection of Boolean connectives by the addition of further Boolean connectives that make the resulting set of connectives functionally complete. More…
By a Ruspini partition we mean a finite family of fuzzy sets $\{f_1, \ldots, f_n\}$, $f_i : [0,1] \to [0,1]$, such that $\sum_{i=1}^n f_i(x)=1$ for all $x \in [0,1]$, where $[0,1]$ denotes the real unit interval. We analyze such partitions…
We consider a combinatorial problem occurring naturally in a group theoretical setting and provide a constructive solution in a special case. More precisely, in 1999 the author established a logarithmic bound for the derived length of the…
Simulations and bisimulations are well-established notions in crisp/fuzzy automata theory and are widely used to compare the behaviors of automata. Their main drawback is that they compare the behaviors of fuzzy automata in a crisp manner.…
The context of this work is that of partial frames; these are meet-semilattices where not all subsets need have joins. A selection function, S, specifies, for all meet-semilattices, certain subsets under consideration, which we call the…
Boolean locales are "almost discrete", in the sense that a spatial Boolean locale is just a discrete locale (that is, it corresponds to the frame of open subsets of a discrete space, namely the powerset of a set). This basic fact, however,…
We describe a feasible logic Bell-state analysis protocol by employing the logic entanglement to be the robust concatenated Greenberger-Horne-Zeilinger (C-GHZ) state. This protocol only uses polarization beam splitters and half-wave plates,…
The notions of infimum and maximal lower bounds of a set $\mathfrak M$ of bounded self-adjoint operators were mainly studied for a set $\mathfrak M$ of two elements. The present paper deals with more general sets $\mathfrak M$, where it is…
We establish completeness for intuitionistic first-order logic, iFOL, showing that a formula is provable if and only if its embedding into minimal logic, mFOL, is uniformly valid under the Brouwer Heyting Kolmogorov (BHK) semantics, the…
Backdoors and backbones of Boolean formulas are hidden structural properties. A natural goal, already in part realized, is that solver algorithms seek to obtain substantially better performance by exploiting these structures. However, the…
Timed temporal logics exhibit a bewildering diversity of operators and the resulting decidability and expressiveness properties also vary considerably. We study the expressive power of timed logics TPTL[U,S] and MTL[U,S] as well as of their…
There are two known general results on the finite model property (fmp) of commutators [L,L'] (bimodal logics with commuting and confluent modalities). If L is finitely axiomatisable by modal formulas having universal Horn first-order…
Combining symbolic and neural approaches has gained considerable attention in the AI community, as it is often argued that the strengths and weaknesses of these approaches are complementary. One such trend in the literature are weakly…
A notorious open question in circuit complexity is whether Boolean operations of arbitrary arity can efficiently be expressed using modular counting gates only. H{\aa}stad's celebrated switching lemma yields exponential lower bounds for the…
We show that an Artinian quotient of K[x, y, z] by an ideal I generated by powers of linear forms has the Weak Lefschetz property. If the syzygy bundle of I is semistable this follows from results of Brenner-Kaid; our proof works without…
Let $\mathfrak{g}$ be a $2n$-dimensional unimodular Lie algebra equipped with a Hermitian structure $(J,F)$ such that the complex structure $J$ is abelian and the fundamental form $F$ is balanced. We prove that the holonomy group of the…
We characterize in terms of the Goldman Lie algebra which conjugacy classes in the fundamental group of a surface with non empty boundary are represented by simple closed curves. We prove the following: A non power conjugacy class X…
For some fixed alphabet A, a language L of A* is in the class L(1/2) of the Straubing-Therien hierarchy if and only if it can be expressed as a finite union of languages A*aA*bA*...A*cA*, where a,b,...,c are letters. The class L(1) is…