Search results for "Transitive relation"
showing 10 items of 74 documents
Theresa May’s Representation of Reality in her Brexit Speeches
2020
This study analyses Theresa May’s three seminal Brexit speeches. These describe the kind of desirable post-Brexit EU-UK relationship that she envisioned, and together constitute a corpus of 18,532 words. The speeches can be considered as landmarks on a timeline that was initially meant to lead to the delivery of Brexit. It is hypothesized that there may be meaningful differences between the speeches, and that these affect the representation of reality. These in turn would have a bearing on May’s discursive self-representation as either an individualized or a collectivized social actor. To account for such representational values, the study draws on Halliday’s Transitivity System (1994), sta…
Periodic Groups Covered by Transitive Subgroups of Finitary Permutations or by Irreducible Subgroups of Finitary Transformations
1999
Let X be either the class of all transitive groups of finitary permutations, or the class of all periodic irreducible finitary linear groups. We show that almost primitive X-groups are countably recognizable, while totally imprimitive X-groups are in general not countably recognizable. In addition we derive a structure theorem for groups all of whose countable subsets are contained in totally imprimitive X-subgroups. It turns out that totally imprimitive p-groups in the class X are countably recognizable.
Querying the Guarded Fragment with Transitivity
2016
We study the problem of answering a union of Boolean conjunctive queries q against a database Δ, and a logical theory φ which falls in the guarded fragment with transitive guards (GF + TG). We trace the frontier between decidability and undecidability of the problem under consideration. Surprisingly, we show that query answering under GF2 + TG, i.e., the two-variable fragment of GF + TG, is already undecidable (even without equality), whereas its monadic fragment is decidable; in fact, it is 2exptime-complete in combined complexity and coNP-complete in data complexity. We also show that for a restricted class of queries, query answering under GF+TG is decidable. © 2013 Springer-Verlag.
ON THE STAR HEIGHT OF RATIONAL LANGUAGES
1994
Two problems concerning the star height of a rational language are investigated: the star height one problem and the relationships between the unambiguity of an expression and its star height. For this purpose we consider the class of factorial, transitive and rational (FTR) languages. From the algebraic point of view a FTR language is the set of factors of a rational submonoid M. Two subclasses of FTR languages are introduced: renewal languages, corresponding to the case of M finitely generated, and unambiguous renewal languages, corresponding to the case of M finitely generated and free. We prove that a FTR language has star height one if and only if it is renewal. This gives a simple de…
M-valued Measure of Roughness for Approximation of L-fuzzy Sets and Its Topological Interpretation
2015
We develop a scheme allowing to measure the “quality” of rough approximation of fuzzy sets. This scheme is based on what we call “an approximation quadruple” \((L,M,\varphi ,\psi )\) where L and M are cl-monoids (in particular, \(L=M=[0,1]\)) and \(\psi : L \rightarrow M\) and \(\varphi : M \rightarrow L\) are satisfying certain conditions mappings (in particular, they can be the identity mappings). In the result of realization of this scheme we get measures of upper and lower rough approximation for L-fuzzy subsets of a set equipped with a reflexive transitive M-fuzzy relation R. In case the relation R is also symmetric, these measures coincide and we call their value by the measure of rou…
Some dissenting views on the transitivity of individual preference
1990
(1) The transitivity property is not a necessary condition for the rationality of all individual preference relations. (2) A weakened definition of the transitivity is not necessarily relevant. (3) The non-transitivity of fuzzy preference relations is not inconsistent with a fuzzy total preorder structure on the set of alternatives.
Some local properties defining $\mathcal T_0$-groups and related classes of groups
2016
We call $G$ a $\operatorname{Hall}_{\mathcal X}$-group if there exists a normal nilpotent subgroup $N$ of $G$ for which $G/N'$ is an ${\mathcal X}$-group. We call $G$ a ${\mathcal T}_0$-group provided $G/\Phi(G)$ is a ${\mathcal T}$-group, that is, one in which normality is a transitive relation. We present several new local classes of groups which locally define $\operatorname{Hall}_{\mathcal X}$-groups and ${\mathcal T}_0$-groups where ${\mathcal X}\in\{ {\mathcal T},\mathcal {PT},\mathcal {PST}\}$; the classes $\mathcal {PT}$ and $\mathcal {PST}$ denote, respectively, the classes of groups in which permutability and S-permutability are transitive relations.
On Finite Satisfiability of the Guarded Fragment with Equivalence or Transitive Guards
2007
The guarded fragment of first-order logic, GF, enjoys the finite model property, so the satisfiability and the finite satisfiability problems coincide. We are concerned with two extensions of the two-variable guarded fragment that do not possess the finite model property, namely, GF2 with equivalence and GF2 with transitive guards. We prove that in both cases every finitely satisfiable formula has a model of at most double exponential size w.r.t. its length. To obtain the result we invent a strategy of building finite models that are formed from a number of multidimensional grids placed over a cylindrical surface. The construction yields a 2NEXPTIME-upper bound on the complexity of the fini…
Counting in the Two Variable Guarded Logic with Transitivity
2005
We show that the extension of the two-variable guarded fragment with transitive guards (GF+TG) by functionality statements is undecidable. This gives immediately undecidability of the extension of GF+TG by counting quantifiers. The result is optimal, since both the three-variable fragment of the guarded fragment with counting quantifiers and the two-variable guarded fragment with transitivity are undecidable. We also show that the extension of GF+TG with functionality, where functional predicate letters appear in guards only, is decidable and of the same complexity as GF+TG. This fragment captures many expressive modal and description logics.
Ranking fuzzy interval numbers in the setting of random sets – further results
1999
Abstract We present some new properties of several fuzzy order relations, defined on the set of fuzzy numbers, from among those introduced in [S. Chanas, M. Delgado, J.L. Verdegay, M.A. Vila, Information Sciences 69 (1993) 201–217]. The main result is proving that four from among the relations considered in [S. Chanas, M. Delgado, J.L. Verdegay, M.A. Vila, Information Sciences 69 (1993) 201–217] are strongly transitive (s-transitive).